
LIBRARY OF CONGRESS 


?i\i i • 


mmi 


\ •; i, >; ■ ’ * ■ 1 ; > i 1 . ■ 

v • . 1 1 l ‘ l i 

: • ■ : : 1 , 

, •, : t t • 

i 

; i i' •. 


i j i * * , i , v * • ; 1 i ' t ' 

• i ’ t V, > ! .s 

; I \\ , i 

» • , 

i : «, ; i 

' i; i: \ : 



; i. * i ;: 

: 1 i 


) i ■ i ; 

: :! l}!' 

' i i > : t 

i ' n *. | *< t, 1 

1 *, '• ‘ > 

’ t ‘ i * i ; 

i *■ i *.: ;>, ) • 

1 ', v: «j« 

. s . \ : i ■ , 

hilt 





V* 

PP'H H 

p 

••» \ » % (; v. i 

■ 

.! i :\;\ i 



n 

f, p 

; i * ■ *’ 4 J 

* ?.'n m 

ip.- 

■:;«. 

• i ;• { ‘ J * i* 

















































































,$ v v 


_cv .•*'*« f o 


‘• 3 *’ ,d* 


i * » « ^C) 

V •» V 


n 1 ’ .«• "♦ G> Ay 'Vf> 

Ad*° /^K’- • _ . 

o5°^ *pyi>° »°-^ vdilSr* •Sl^"* 0 » ^ * 

/ v** / \ *"v ^ ^ ■ ■ 

■ ,*•’<■» y, .0 **•«. > v !*wj_-! -> a-. » a a . , 





* o>^ 

. K »-? ^ ** * 

. *®. . • A <\ 

4 V c *-» ^ 

O ^ -r. 




* A - ** 

* ^ ^ 


r * *\ y * c v v 

, ■*, *;fs;< ^ ^ c y ^ •;*/»;« ^ 

■' * . v -.. **o °' ‘ ,4> ,.>., <(. * ‘ * ‘ •>•'*♦ •*© a* V . °" * * 

C° .w^’. ° .-l 4 .\f5S$XhV. . <-° * - 

* 


^d* 



4 °C 



• * 


°In V* * 




-* o 

* A" * <5. 

0 £> ^ 

, r A.0' V‘‘'<**\^ .. ^ 

<A ,0‘ *« 4 *- <> v <%*> av 

.^d^. -fv A A A .VSgV. V . 

: ^ 'Hf; a % % wW.* 4 * v % ‘era* ^'-v 

. '«.*’* A <, **tvV* A s v 5, '«.»* A <A .G v 

<v c o»«, qV ^ * * * v *b c <>***^ <s>^ r (y 

i .k^ jAi. ^ V— * * 


A . 





^o ^ r 




C U ** 

& * 

v' * * VI/* c> *0 * 

\ % *♦ ''^V- % / ‘ 

> o if/ 051 \Yr * qV ^ * 



* 


% 'V « v - 

* **-CT 

^ * ^4A>~s Of C> * _ 



•* rf v A* * 


0^ »* I, / A*J» ^ 


• »- A 




* A y "> 

* ^ ^ 



• C.^ °X * 

* ip a 

_ % 47 *i* ■ * ^, „ - . 

<* <> ""-t:* 4 aG^ A 

A a 0 h 9 * rv ^ 4 • ‘ 1 * 4 ^b <G c ° ** a ♦ 

l*» • ^ C° *-r*^ 4 





■ ^o/ :■ 

A°* i. 0 -^ -. , __ 

A °o '' 7 ^- 0 ° “* ‘^T** ^ ° 0 d) % *; . 

^ **V*% <T- . 9 ' ^ V s <!>■'* C> . 9 V *' * °- "> 

o v vr/ $ ^ ^ 

, w o*i* A + ^T* A ^ s 




^ ^ * r ^ # * ^ # ^ ^ ^ °^> # *'*Vo° 

..\ / b v ° v ^ v * °- 

' >v 

; ^ V -V V ‘ • f * -' v ^ 

* v <* * 



. A <• A 







*■ 



7 ^ ^ 






o. '<T. 7« A 



. * „ ' ^ . * J 'W«r ♦ „<L r « 

c> 

<> * 4 ^ *Xy Jf i i i *rL 

^■ 4 ? X c° *Jpjjj%^ ° 
O *.’ VM i'^‘.‘ 0 * ''X. X" *%» ’'^^f|P/° f 

* Xis *0 V * « * •<* ^ V v «L*nL% Cv .<)' 

• ■> o* A v^. 


*♦ A <A V7vT* aCT 'o..‘ A <A 

<V «• * • * <$•* (Nv , t 1 * * **Q A % c • • • * <£ 

* < O a * 

J -o' ^ “ 

. »* X <rv # 

^ • ' ' * . ^ 0 ^A * * * 0 

^ v Cv. .0 » 

* rv tMSSh- ff 

7%^sSSS> * aV*\, 

^M\k * aV 'V'j. 

v> ______ _ 

« • * * A <N *-T7T* <G V o 

.-^ # ojV ^ ^ 0^ **‘J ? 1* ^ c 



° c^ ^J\. ° ^ 

„ * -V 3 <>*■) -» n 

A^* V • 

*> 6 ..... ^ 

0° ,v^4 . c ^ A . 

4>t_ 3 0 




r o K 



* »y» 


^ 0 < 


«- ».;••* a0 0 "\, ‘*.,,-‘* 0 ,^ 

C* aO v > V »' * * 

A ■» * -•*. A * 

TS a v«4 







*• aV*\. 

* ^ ^ * 


sv* f .> <y - Xffty' <l v <-> * « (S * . ^ v • 

• • A <A ‘'TV** ,0 V ^ '»•** A <. 

•<b V o “■ “ - o^ , • ‘‘ ♦ o, a 4 .<.“■“ *, •% 






o jO v^ ^ •z^ymzr' 

.. c v i?r: V 0 ..^V‘‘'''V 

?a*- ^ v -‘ja^*- '■•%../' ^ -♦ • 

° V^ v J ' l 5 

■ $ % 







4 

A A. IS 

C? ^vfv ° 

iy ^ o 


.0^ '»•»* A "••* a° "V 

. V » * . A> . O - o „ <S» . •> ' * 4 *c 

■? &mk* ° A .*«^iflt' \. « 0 


r ^ . 


A o> 

r' *<• 




'Cr* c>* 


v <> > . 

° ° 

: , 4 .^ '.wf- aV-** - 

r 'o, i * A v. 

. -. v ^ 

X^rs / "v^P' o^ \;-^'\, 

Oa ^ v % * »aV 1^ C\ > v^ 


















Frontispiece Harvard Stadium 






A TREATISE 


ON 

CONCRETE 

PLAIN AND REINFORCED 


MATERIALS, CONSTRUCTION, AND DESIGN OF 
CONCRETE AND REINFORCED CONCRETE 


WITH CHAPTERS BY 

R. FERET, WILLIAM B. FULLER, FRANK P. McKIBBEN AND 

SPENCER B. NEWBERRY 


BY 

FREDERICK W. TAYLOR, M.E., Sc.D. 

<1 

AND 

SANFORD E. THOMPSON, S.B. 

M.Am.Soc.C.E. 

Consulting Engineer 


SECOND EDITION 

TOTAL ISSUE, FOURTEEN THOUSAND 


> * ^ 

> « 

0 4 

NEW YORK 

JOHN WILEY & SONS 
London: CHAPMAN & HALL, Limited 


1911 



Copyright, 1905, 1909, bt 
FREDERICK W. TAYLOR 


All rights reserved 


om 

Mishas? 

■Alt 31 IS11 



IFaver iy Press , % alii more, Md. 







PREFACE TO FIRST EDITION 


This treatise is designed for practicing engineers and contractors, and 
also for a text and reference book on concrete for engineering students. 

To broaden the scope of the work and avoid personal inaccuracies, each 
chapter has been submitted for critcism to at least one, and, in some cases, 
to three or four specialists in the particular line treated. We have aimed 
to refer by name to all authorities quoted, and where the data is taken from 
books or periodicals, to give the original publication, so that each subject 
may be investigated further. Proof clippings have also been submitted for 
approval to those whose names are mentioned. Numerous cross refer¬ 
ences will be found as well as many repetitions, inserted for the purpose of 
emphasizing important facts. 

The chapters are arranged for convenience in reference, and therefore 
are not always in logical order. 

The Concrete Data in Chapter I presents a list of definitions of words 
and terms relating distinctively to cement and concrete; a summary of the 
most important facts and conclusions, with references to the pages discuss¬ 
ing them; data on concrete labor, and conversion ratios. 

The Elementary Outline of the Process of Concreting, Chapter II, is de¬ 
signed, not for the civil engineer, but for those seeking simple directions as 
to the exact procedure in laying a small quantity of concrete. Most of the 
subjects there treated are discussed at length in subsequent chapters. 

The Specifications for Cement in Chapter III include the latest recom¬ 
mendations of committees of our national societies, with incidental changes 
to adapt them for direct use in purchase specifications. The Concrete 
Specifications have been prepared by the authors to represent standard 
practice. Specifications for First-class or High Steel, drawn up by Mr. 
Taylor, are, we believe, the first recommendations which have been made 
to safely adapt this important material to reinforced concrete construction. 

In Chapter IV the Choice of Cement is considered in an elementary 
fashion, which will serve as a guide to the constructor. Classification oi 
Cements, Chapter V, distinguishes the various cements and limes manu¬ 
factured in the United States and Europe. 

ni 



IV 


PREFACE 


Mr. Spencer B. Newberry, an international authority on the subject 
treated, has very kindly written for us Chapter VI on the Chemistry of 
Hydraulic Cement, discussing this complex subject in such a clear and prac¬ 
tical manner that it will be of interest not only to the scientist, but also to 
the general reader and to the cement manufacturer. Mr. Newberry has 
also criticised Chapter V. 

Chapters VII and VIII give the latest information on the testing of ce¬ 
ment. Chapter IX presents practical rules for selecting sand for mortar, 
and the effect of different sands and of foreign ingredients upon its quality. 
Characteristics of the Aggregate are further treated, and practical data in 
regard to it are given in Chapter X. 

The subject of Proportioning Concrete has been treated, at our request, 
by Mr. William B. Fuller, the concrete expert, and his practical use of 
mechanical analysis is fully discussed. 

The tables of Quantities of Materials for Concrete and Mortar, in Chapter 
XII, and the diagram of curves, will be found useful in estimating materials. 

The Strength of Concrete, Chapter XX, is taken up from a practical 
standpoint so that the data may be directly employed in design. 

The theory and design of reinforced concrete are as yet in an elementary 
stage, but the rules and tables in Chapter XXI represent the most ad¬ 
vanced knowledge on the subject. 

Practical methods of Mixing and Laying Concrete are treated in Chap¬ 
ters XIII, XIV and XV. 

Mr. Rene Feret, of Boulogne-sur-Mer, France, whose extended researches 
enable him to speak with authority, has kindly written for us Chapter 
XVI, entitled The Effect of Sea Water. 

Chapters XVII, XVIII and XIX, on Freezing, Fire and Rust Protection, 
and Water-Tightness are of practical interest to the contracting engineer. 

Plain and Reinforced Concrete Structures are treated in as much detail 
as space permits in Chapters XXIII to XXVIII inclusive. The designs 
are taken mostly from original drawings redrawn by the authors. They 
have been selected, not as extraordinary productions, but because the data 
in regard to them may be of use in designing similar structures. 

Methods of Cement Manufacture in its modern types are described in 
detail in Chapter XXX. 

The References in Chapter XXXI will be found especially valuable to 
one pursuing more extended investigations than can be presented in a 
volume of this size. 

They have been selected from the large number contained in the authors’ 
index, as those which it may be to the advantage of the reader to consult. 

Note: The chapter numbers have been changed to agree with the Second Edition. 


PREFACE 


\ 


The articles are usually described by their subject-matter rather than by 
their titles verbatim. 

Appendix I gives the method of chemically analyzing cement and cement 
materials according to the recommendations of the American Chemical 
Society. 

Additional formulas for reinforced concrete beams, too complicated for 
insertion in the body of the book, are given in Appendix II, these having 
been kindly compiled by Prof. Frank P. McKibben for this treatise. 

The authors desire to express their sincere appreciation of the various 
kindnesses extended to them while compiling the work. It has been neces¬ 
sary, because of the lack of authoritative information on many fundamental 
questions, not only to conduct numerous original investigations, but also to 
correspond with the most prominient engineers in this country, and with 
experts in England, France, and Austria. 

Mr. Feret, besides writing the chapter on The Effect of Sea Water, has 
kindly criticised Chapter IX, and made numerous suggestions which have 
been incorporated. 

Mr. Fuller has examined and criticised all the chapters on practical con¬ 
struction, and Prof. McKibben has rendered material assistance in the line 
of investigations and criticisms relating to the theories of reinforced con¬ 
crete. 

The authors are indebted to many gentlemen for careful criticism of 
chapters or portions of chapters, for drawings, or for replies to questions, 
and take this opportunity to express their sincere appreciation of all such 
assistance. Among those to whom especial acknowledgment is due are 
the following: 

Messrs. Earle C. Bacon, David B. Butler (England), Harry T. Buttolph, 
Howard A. Carson, Edwin C. Eckel, William E. Foss, George B. Francis, 
fohn R. Freeman, Charles S. Gowen, Allen Hazen, Rudolph Hering, 
James E. Howard, Richard L. Humphrey, A. L. Johnson, George A. Kim¬ 
ball, Robert W. Lesley, Alfred Noble, William Barclay Parsons, Henry 
H. Quimby, George W. Rafter, Ernest L. Ransome, Clifford Richard¬ 
son, Thomas F. Richardson, A. E. Schutte, W. Purves Taylor, Edwin 
Thacher, Leonard C. Wason, George S. Webster, Robert Spurr Weston, 
Joseph R. Worcester; and Professors Ira O. Baker, Lewis J. Johnson, 
Edgar B. Kay, Gaetano Lanza, Charles L. Norton, Charles M. Spofford, 
George F. Swain, Arthur N. Talbot. 

Cuts have kindly been furnished by Allis-Chalmers Co., Austin Manu¬ 
facturing Co., Automatic Weighing Machine Co., Bonnot Co., Bradley 
Pulverizer Co., Clyde Iron Works, Contractors Plant Co., Drake Standard 


VI 


PREFACE 


Machine Works, Fairbanks Co., Falkenau-Sinclair Machine Co., Farre] 
Foundry and Machine Co., Iroquois Iron Works, Kent Mill Co., Link-Belt 
Engineering Co., McKelvey Concrete Machinery Co., W. F. Mosher & Son, 
Tinius Olsen and Co., Philadelphia Pneumatic Tool Co , Thos. Prosser and 
Son, Ransome Concrete Machinery Co., Riehle Bros. Testing Machine 
Co., Robins Conveying Belt Co., Sherburne and Co., T. L. Smith, Henry 
Troemner, Tucker and Vinton. 

FREDERICK W. TAYLOR. 
SANFORD E. THOMPSON. 

February, 1905. 

The writer wishes to state that the investigation and study necessary for 
the writing of this book were done bv his colleague, Mr. Thompson, and 
desires that full credit for this should be given to him. 

Frederick W. Taylor. 


PREFACE TO SECOND EDITION 


The second edition aims to cover the developments in the design and con¬ 
struction of reinforced concrete since the issue of the first edition. To 
accomplish this, more than 200 pages of entirely new and original text and 
tables have been added, giving to the constructing engineer, the architect, 
and the contractor data for design and for building, and to the student a 
comprehensive and practical text and reference book. 

One of the principal objects also in writing and in revising the book has 
been to make it useful to those men who are practically engaged in this class 
of work and yet who are unable to devote enough of their time to make 
either a profound or an original study of it. Attention is directed to the 
new Chapter I, in which many of the essentials of concrete construction are 
pointed out and the reader is warned against the serious errors that have 
frequently been made in this field. 

The chapter on Reinforced Concrete Design, which is increased from 51 
to 131 pages, includes a comprehensive statement of the details of design. 
Features of special interest in this chapter are the treatment of column design; 
the discussion of shear and diagonal tension; the design of the supports of 
beams and girders; the treatment of bending moments; the design of flat 
plates; the most recent tests on hooked bars; the analysis of shrinkage and 
temperature reinforcement; and careful notes relating to many smaller 
though not less important details. Tables and diagrams for design cover¬ 
ing over 20 pages are prepared for office use. A complete example of 
floor design gives the mathematical computations in detail for all the parts 
of the several members. 

In subsequent chapters are treated the designs of retaining walls, footings, 
culverts, and chimneys. 

Prof. Frank P. McKibben has kindly prepared the chapter on Arches, 
which presents the design of the arch by the elastic theory and gives a com¬ 
plete example with all the steps to be followed. 

In Chapter XXIX brief reference is made to a variety of structures in 
which concrete is employed as the building material. 

Prominent among the changes in the first part of the book, which is 
devoted to plain concrete, are the revised Specifications for Cement and Con- 

vii 


Vlll 


PREFACE 


crete in Chapter III; Chapter IX on Proportioning; the enlargement of 
Chapters XIV and XV on Mixing and Depositing; the addition on pages 
236 and 237 of tables for quantities of materials for rubble concrete; and 
the insertion of the most recent tests and conclusions on the strength and 
permeability of concrete. The list of references in Chapter XXXI has been 
increased over fifty per cent, new references having been carefully selected 
from the immense quantity of current literature published since the first 
issue of our book. 

The large increase in the quantity of material has necessitated a rearrange¬ 
ment of the matter and beyond page 235 the pages have been renumbered. 
To simplify the formulas, the demonstrations have been placed as far as 
possible in footnotes or appendices. By the use of a thinner but higher 
quality of paper the book is increased but slightly in size. 

The authors desire to express their appreciation of assistance rendered in 
the work of revision. Special acknowledgment is due to Messrs. E. D. 
Boyer, R. D. Bradbury, William B. Fuller, Frank P. McKibben, Spencer 
B. Newberry, George F. Swain, Arthur N. Talbot, and Joseph R. Worces¬ 
ter; also to Mr. Edward Smulski for his original studies for the matter 
on Reinforced Concrete Design. 


September , 1909 


FREDERICK W. TAYLOR. 
SANFORD E. THOMPSON. 


CONTENTS 


CHAPTER I 

PAGE 

Essential Elements in Concrete Construction i 

CHAPTER la 
Concrete Data 

Definitions. 2C 

Weights and Volumes. .. 2C j 

Cement Testing for the Small Purchaser. .. ^ 

Summary of Important Facts and Conclusions.. 5 

Data on Handling Concrete. 9 

Conversion of Foreign to American Measures. 9 

CHAPTER II 

Elementary Outline of the Process of Concreting 

Where Concrete may be Used. xx 

Selection of Materials. I2 

Proportions.... x ^ 

Quantities of Material. I4 

Tools and Apparatus required for Concrete Work... 17 

Construction of Forms.. . X g 

Directions for Mixing and Placing Concrete. 20 

Approximate Cost of Concrete Materials and Labor.. 24 

The Strength of Concrete. 26 

CHAPTER III 
Specifications 

Brief Specifications for Purchase of Cement. 29 

Full Specifications for Purchase of Portland Cement. 29 

Full Specifications for Purchase of Natural Cement. 31 

Contract and Specifications for Portland Cement Concrete. 32 

, Specifications for First-Class Steel for Reinforced Concrete. 38 

CHAPTER IV 

The Choice of Cement 

The Class of Cement.. 41 

The Selection of the Brand. 45 

ix 

























X 


CONTENTS 


CHAPTER V 

Classification of Cements 

PAGE 

Portland Cement. 48 

Natural Cement; Le Chatelier’s Classification of Natural Cements. .... 49 

Puzzolan Cement. .. 50 

Hydraulic Lime; Common Lime. 52 

Sub-Classification of Portland Cements.. 53 

CHAPTER VI 

Chemistry of Hydraulic Cements.—By Spencer B. Newberry 

Introduction. .. 54 

Materials.. 55 

Proportion of Ingredients. 57 

Effect of Composition on Quality. 62 

CHAPTER VII 
Standard Cement Tests 

Standard Methods of Cement Testing.. 6 3 

Elementary Directions for Testing Soundness. 79 

Apparatus for a Cement Testing Laboratory. 80 

Specific Gravity of Different Cements. 81 

Advantages of Fine Grinding. 82 

American vs. European Sieves. 84 

Separating Material passing No. 200 Mesh Sieve.. 8^ 

Quantity of Water for Neat Paste and Mortar. 8^ 

Arbitrary Periods of Setting. 88 

European Methods for Determining Set... 89 

Rate of Setting. 90 

American and European .Standard Sands Compared. 90 

Form of Briquette for Tensile Tests. 92 

Conversion of Metric Units of Strength to English Units. 9^ 

Machines for Testing Tensile Strength. 9 3 

Effect of Eccentricity in placing Briquettes. 93 

Rate of Applying Strain. 94 

Tensile Tests of Neat Cement and Mortar. 97 

Soundness or Constancy of Volume. 101 

CHAPTER VIII 

Special Tests of Cement and Mortar 
C olor of Cement.. in 

O 

Weight of Cement. 114 

Microscopical Examination of Portland Cement Clinker. nc; 

Compressive Tests of Cement.. 116 

Transverse Tests of Cement.. .. I2 o 

Adhesion Tests of Cement. 12I 




































CONTENTS xi 

PAGE 

Shearing Tests of Cement and Mortar.. 125 

Abrasion and Porosity Tests. 125 

Permeability or Percolation Tests.. 128 

Yield Tests of Paste and Mortar. ... 129 

Tests of Rise in Temperature while Setting. 130 

Tests of Sand for Mortar. 131 

CHAPTER IX 

Strength and Composition of Cement Mortars 

Laws of Strength .. 133 

Strength of Similar Mortars Subjected to Different Tests.. 134 

Relation of Density to Strength. . . 134 

Granulometric Composition of Sand—Feret’s Three-Screen Method of 

Analysis..... 142 

Effect of Size of Sand upon the Strength of Mortar.. 147 

Tests of Density and Strength of Mortars of Coarse vs. Fine Sand.149 

Practical Applications of the Laws of Density. 149 

Conversion of Mechanical Analysis to Granulometric Composition. ..... 151 

Effect of Quantity of Water upon Strength of Mortars.. 152 

Sand vs. Broken Stone Screenings. 153 

Sharpness of Sand.. ; .154a 

Effect of Natural Impurities in Sand upon Strength of Mortar.154a 

Effect of Mica in Sand upon Strength of Mortar.154c 

Effect of Lime upon Strength of Mortar.i54d 

Ground Terra-Cotta or Brick as a Substitute for Sand. .. 156 

Effect of Regaging Mortar and Concrete. .. 157 

Tests of Sand for Mortar and Concrete./ 159 

Effect of Gaging with Sea Water.159b 

CHAPTER X 

Voids and Other Characteristics of Concrete Aggregates 

Laws of Volumes and Voids.. 160 

Classification of Broken Stone. .. 161 

Average Specific Gravity of Sand and Stone. 163 

Method of Determining Specific Gravity. 164 

Method of Determining Voids.. 165 

Voids and Density of Mixtures of Different Sized Materials. 168 

Photographs of Sand.. 175 

Effect of Moisture on Sand and Screenings. .. 176 

Compacting of Broken Stone, Gravel, and Sand. 179 

Defining Coarseness of Sand by its Uniformity Coefficient. .. 181 

CHAPTER XI 

Proportioning Concrete,—By William B. Fuller 

Importance of Proper Proportioning. 183 

Methods of Proportioning.. 184 






































Xll 


CONTENTS 


PAGE 

Principles of Proper Proportioning... . 185 

Determination of the Proportion of Cement. 186 

Proportioning by Arbitrary Selection of Volumes. 187 

Screened vs. Unscreened Gravel or Broken Stone. 188 

Proportioning by Void Determination. ... . 189 

Rafter’s Method of Proportioning. 192 

French Method of Proportioning. 192 

Mechanical Analysis. 193 

Studies of the Density of Concrete. 200 

Relation of Density to Strength. 204 

Laws of Proportioning. 204 

Application of Mechanical Analysis Diagrams to Proportioning. 206 

Curve of Mix to Best Fit the Maximum Density Curve. 208 

Volumetric Synthesis or Proportioning by Trial Mixtures. 210 

Proportions of Concrete in Practice. 213 

CHAPTER XII 

Tables of Quantities of Materials for Concrete and Mortar 

Expressing the Proportions. 217 

Theory of a Concrete Mixture. ... 220 

Formulas for Quantities of Materials and Volumes. ./. 221 

Tables and Curves of Quantities of Materials and Volumes. .. 225 

Tables of Rubble Concrete... 238 

CHAPTER XIII 

Preparations of Materials for Concrete 

Storing Cement.. 239 

Screening Sand and Gravel. Methods and Costs. 239 

Stone Crushing. Methods and Costs. 241 

Washing Sand and Stone. 250 

CHAPTER XIV 
Mixing Concrete 

Mixing Concrete by Hand... 2si 

Mixing by Machinery. 255 

Concrete Plants. 266 

CHAPTER XV 
Depositing Concrete 

Handling and Transporting Concrete. .. 276 

Depositing Concrete on Land.. 277 

Consistency of Concrete. 279 

Ramming or Puddling.. 281 

Bonding Old and New Concrete. 284 

Contraction Joints. 28s 



































CONTENTS 


PAGE 

Facing Concrete Walls. 288 

Forms for Mass Concrete. 293 

Rubble Concrete. 296 

Depositing Concrete under Water. 301 

CHAPTER XVI 

Effect of Sea Water upon Concrete and Mortar.—By R. Feret 

External Phenomena. 309 

Action of Sulphate Waters.. 310 

Chemical Processes of Decomposition. 311 

Search for Binding Materials Capable of Resisting the Action of Sea Water 312 
Methods of Determining the Ability to Resist Action of Sulphate Waters 314 

Mechanical Processes of Disintegration. 315 

Proportions for Mortars and Concretes. 316 

Mixtures of Puzzolan and Slag with Cements. 317 

Various Plasters and Coatings... 318 

CHAPTER XVII 

Laying Concrete and Mortar in Freezing Weather 

Effect of Freezing. 319 

Methods of Construction in Freezing Weather.. 323 

CHAPTER XVIII 
Fire and Rust Protection 

Protection of Steel by Concrete. 327 

Chemical Union of Steel and Cement. 330 

Fire Protection. 331 

Concrete vs. Terra-Cotta; Cinder vs. Stone Concrete. 333 

Thickness of Concrete required to Protect Metal from Fire... 333 

Theory of Fire Protection. 334 

Tests of Fire Resistance; Conductivity of Concrete and Imbedded Steel. 335 
Influence of Cracks in Reinforced Concrete upon the Corrosion of Steel. . . 336 
Protecting Structural Steel.. 337 

CHAPTER XIX 
Water-Tightness 

Laying Concrete for Water-Tight Work. 338 

Proportioning Water-Tight Concrete. 339 

Thickness of Concrete for Water-Tight Work. .. 340 

Special Treatment of Surface.. 341 

Introduction of Foreign Ingredients. 342 

Layers of Waterproof Material. 344 

Construction without Waterproofing. 347 

Methods of Testing Permeability.. 347 

Results of Tests of Permeability.■ . 35 1 































XIV 


CONTENTS 


CHAPTER XX 
Strength of Plain Concrete 

PAGE 

Compressive Strength of Concrete.. 355 

Table of Compressive Strength.. 359 

Weight of Concrete of Different Proportions. 362 

Compressive Tests of Plain Concrete... 362 

Effect of Concentrated Loading.. 367 

Strength of Short Prisms. 369 

Plain Concrete Columns. 371 

Strength of Machine vs. Hand Mixed Concrete.. 372 

Eccentric Loading.. 372 

Concrete vs. Brick Columns. /..... 373 

Safe Strength of Concrete.. 373 

Growth in Strength of Concrete. 374 

Transverse Strength of Concrete. .. 378 

Formula for Transverse or Bending Stress in Plain Concrete. 379 

The Fatigue of Cement. 381 

Strength of Concrete in Shear. 382 

Effect of Consistency upon the Strength. .. 383 

Gravel vs. Broken Stone Concrete. 385 

Effect of Size and Quality of Stone or Gravel upon Strength of Concrete . . 389 

Effect of Percentage of Cement upon the Strength of Concrete.. 392 

Destructive Agencies. 392 

Strength and Elasticity of Cinder Concrete. 394 

Making Concrete Specimens for Testing. 395 

CHAPTER XXI 
Reinforced Concrete Design 

General Principles of Reinforced Beams. 400 

Modulus of Elasticity of Steel. 402 

Modulus of Elasticity of Concrete. .. 403 

Value to Use for the Ratio of Elasticity in Compression. 408 

Elongation or Stretch in Concrete.. 408 

Quality of Reinforcing Steel.. 413 

Straight Line Theory. 41^ 

Location of Neutral Axis. 416 

Design of a Rectangular Beam. 416 

Depths and Loads for Different Bending Moments.. 419 

Formulas to Review a Beam already Designed. 419 

Design of Slabs. 421 

Square and Oblong Slabs.. 422 

Design of T-Beam. 423 

Beams with Steel in Top and Bottom. >. . 427 

Design of a Continuous Beam at the Supports... 428 

Effect of Varying Moment of Inertia upon the Bending Moment. 430 

Span of a Continuous Beam or Slab.., >.; ^ r 

Distribution of Slab Load to the Supporting Beams... 4^1 












































CONTENTS 


xv 


PAGE 

Distribution of Beam and Slab Loads to Girders. 432 

Bending Moments and Shears.. 4^0 

Shear and Bending Moment Diagrams ... 43- 

Bending Moments to Use in Design of Reinforced Beams. 439 

Shearing Forces in a Beam or Slab. 44 x 

Diagonal Tension. 443 

Reinforcement to Prevent Diagonal Cracks in Beams.. 445 

Computation of Shear and Diagonal Tension. 446 

Vertical and Inclined Reinforcement. 448 

Graphical Method for Spacing Stirrups.. 452 

Diameter of Stirrups. 433 

Ratio of Span to Depth which Renders Stirrups Unnecessary. 435 

Bond of Steel to Concrete in a Beam. 436 

Points to Bend Horizontal Reinforcement.. 438 

Spacing of Tension Bars in a Beam. 439 

Depth of Concrete below Rods. 460 

Bond of Concrete to Steel to Resist Direct Pull. .. 461 

Length of Bar to Prevent Slipping.. 464 

Value of Hooked Bars in Bond. 466 

Example of Beam and Slab Design. 468 

Example of Bent Bars as Reinforcement for Diagonal Tension. 474 

Miscellaneous Examples of Beam and Slab Design. 476 

Experiments upon Reinforced Beams. 477 

Flat Slabs. 483 

Example of Flat Slab Design. 487 

Concrete Columns. 488 

Vertical Steel Bar Reinforcement. 489 

Hooped or Banded Columns. 492 

Structural Steel Reinforcement. 497 

Column Examples. 498 

Reinforcement for Temperature and Shrinkage Stresses.. 499 

Systems of Reinforcement. 504 

Table 1. Areas, Weights'and Circumferences of Bars. 507 

Tables 2 to 7. For Designing Beams and Slabs. 508 

Table 8. For Beams with Steel in Top and Bottom. 516 

Table 9. Flat Slabs. 518 

Tables 10 and 11. Tables for Constant C.. 519 

Table 12. Ratio of Depth of Neutral Axis to Depth of Steel. .. 521 

Diagrams 1, 2 and 3. Bending Moments for Different Spans and Loads. 522 

Diagram 4. Curves for Design of T-Beams... 525 

Working Stress in Reinforced Concrete.. 527 

Standard Notation.. 5 2 9 

Common Formulas. 53 ° 

CHAPTER XXII 
Arches.—By Frank P. McKibrkn 

Concrete versus Steel Bridges. 534 

Lise of Steel Reinforcement. 535 














































XVI 


CONTENTS 


History of Concrete Arch Bridges... 

Classification of Arches. 

Arrangement of Spandrels and Rings.. 

Hinges. 

Shape of the Arch Ring. 

Thickness of Ring at Crown.. 

Live Loads for Highway Bridges.. 

Live Loads for Railroad Bridges.. 

Dead Loads and Earth Pressure. 

Outline of Discussion on Arch Design.. 

Relation between Outer Loads and Reactions at Supports. 

Notation.. 

Three-Hinged Arch. 

Two-Hinged Arch. 

“Fixed” or “Continuous” Arches. 

Relation between Outer Forces and the Thrust, Shear and Bending 

Moment for the Fixed Arch. 

Thrust, Shear and Moment at the Crown. 

Graphical Method for Finding Constant j .. 

Line of Pressure. 

Effect of Temperature and Thrust. 

Effect of Rib Shortening Due to Thrust. 

Distribution of Stress over Cross Section. 

Distribution of Stresses in Plain Concrete or Masonry Arch. Sections. . . 

Distribution of Stresses in Reinforced Concrete Sections. 

Method of Procedure for the Design of an Arch. 

Loadings to Use in Computations... 

Allowable Unit Stresses. 

Design of Abutment. 

Erection.. 

Examples of Arch Bridges. 


PAfiK 

53 6 

53 6 

538 

539 

540 

540 

54 1 

543 

544 

544 

545 

545 

546 

547 

548 


549 

55 i 

554 

555 
555 
558 
558 
560 

5 6 3 

574 

580 

583 

583 

586 

590 


CHAPTER XXIII 


Sidewalks, Basement Floors and Pavements 


Materials for Concrete Sidewalks. . 593 

Tools .• *;.. • • 597 

Method of Laying Sidewalks. 598 

Cost and Time of Sidewalk Construction. .. 604 

Driveways. 606 

Concrete Street Pavements. 606 


CHAPTER XXIV 
Concrete Building Construction 


Concrete Floors. 608 

Safe Floor Loads.. ..•. 610 

Weight of Concrete in Floors and Girders. . ... .. 611 








































CONTENTS 


xvn 


PAGE 

Floors in Ingalls Building. 611 

Laying Floors...... 615 

Concrete Stairs. 617 

Concrete Roofs. 618 

Concrete Walls. 619 

Wall Forms.•. 621 

Concrete Columns. 623 

Cost of Concrete Building Construction. .. 624 

Domes. 626 

Walls of Mortar Plastered upon Metal Lath. 627 

Ornamental Construction. .. 628 

Concrete Building Blocks ; Concrete Tile.. 629 

Reinforced Concrete Chimneys. 630 

Design of Reinforced Concrete Chimneys. 632 

Summary of Essentials in Design and Construction. 634 

Example of Chimney Design. .. 636 


CHAPTER XXV 
Foundations and Piers 


Bearing Power of Soils and Rock. 639 

Concrete Capping for Piles. 641 

Design of Concrete Foundations and Footings. 641 

Reinforced Concrete Footings. 644 

Combined Footings. 647 

Spread Footings. . .. 649 

Foundation Bolts. 650 

Concrete Piles. 650 

Sheet Piling. 653 

Bridge Piers. 654 

Foundations Under Water .. 656 


CHAPTER XXVI 
Dams and Retaining Walls 


Retaining Walls. 659 

Foundations. 660 

Design of Retaining Walls of Gravity Section... 661 

Angle of Internal Friction. 662 

Weight of Earth ; Backing.. 662 

Earth Pressure. .. 663 

Design of Reinforced Retaining Walls .. 666 

Example of Retaining Wall of T-Type.. 668 

Example of Retaining Wall with Counterforts.... 671 

Copings.*... 674 

Dams. 674 

Core Walls... ^7 6 










































xviii CONTENTS 

CHAPTER XXVII 
Conduits and Tunnels 

Conduits. Design and Construction. 

Tunnels. Design and Construction. 

Subway Design. 

Design of Conduits. 


PAGE 

670 

689 

692 

6 9 3 


CHAPTER XXVIII 
Reservoirs and Tanks 


Open and Covered Reservoirs. 695 

Tanks. Method of Construction. 698 

Storage Reservoirs. 701 


CHAPTER XXIX 
Cement Manufacture 


Historical. 705 

Production of Cement. 706 

Portland Cement Manufacture. 707 

Natural Cement Manufacture. 722 

Puzzolan Cement Manufacture. 723 


CHAPTER XXX 
Miscellaneous Structures 

CHAPTER XXXI 

References to Concrete Literature 
APPENDIX I 

Method for Analysis of Limestone, Raw Materials and Portland Cements 
of the American Chemical Society, with the advice of W. F. Hillebrand. 

APPENDIX II 

Deduction of Formulas for Rectangular Beams; T-Beams ; Beams with 
Steel in Top and Bottom; Rectangular Beams, Concrete Bearing Tension; 
and Rectangular Beams, Compression Stress as a Parabola. 

APPENDIX III 

Deduction of Formulas for Chimney and Hollow Circular Beam Design. 

APPENDIX IV 


Method of Combining Mechanical Analysis Curves. 














A Treatise on Concrete 

CHAPTER I. . 

ESSENTIAL ELEMENTS IN CONCRETE 
CONSTRUCTION 

The forming of concrete structures is essentially a manufacturing opera¬ 
tion, and requires more close attention to detail both in the design and 
the building than most other classes of construction. For the benefit of 
those who are not thoroughly experienced, a number of the most essential 
elements are recorded below with references to pages upon which more 
detailed information may be obtained. 

General properties of materials and of concrete are outlined in Chapter 
la on Concrete Data, and Chapter II, page n, gives in elementary form 
an outl ne of the process of concreting. 

CEMENT 

PAGE 


Except for unimportant structures, the cement should be sampled and 

tested in a laboratory... 63 

Even if not tested, cement should be purchased with the requirement 
that it must pass the specifications of the American Society for 

Testing Materials. 29 

Portland cement is the only cement that can be used for all kinds of 

concrete work. 12 


SAND 

Tests of the sand, unless it comes from a bank which has been pre¬ 
viously tested, are as necessary as tests of the cement. 159 

Even a small amount of vegetable matter in sand prohibits its use 154b 
Fine sand, even if free from vegetable matter, makes a much weaker 
concrete than coarse sand. If it is necessary to use fine sand, 
therefore, the proportion of cement should be increased.... 136, 159a 
If the grains are mostly less than 3^ inch diameter, nearly double 
the amount of cement should be used than with an equally clean 
sand having mixed grains running up to \ inch, in order to 

obtain equal strength. 159a 

For unimportant work, fine sand, if clean, may sometimes be used, 
but it is usually cheaper to import a coarse sand and use leaner 
proportions..— 149, 159a 









2 


A TREATISE ON CONCRETE 

COARSE AGGREGATE pARF 

The maximum size of the stones should be such that the concrete is 

» 

readily placed around the steel reinforcement and into the cor¬ 
ners of the forms. For reinforced concrete a maximum size of 

one inch is frequently specified.. 34 

If the stone contains dust, it must be uniformly distributed through- . 
out the stone, and the proportion smaller than J inch should be 
determined by test and considered as sand when proportioning.. 34 

Soft stone should be avoided in important structures. 390 

Gravel, if used, must be clean; that is, the particles must be free 
from coating of vegetable matter or clay which will retard the 
setting or prevent the cement from sticking to the pebbles— 34,386 

Gravel can be washed satisfactorily only with special apparatus.... 250 

REINFORCEMENT 

All steel should be subject to the bending test. 415 

Steel must be placed in exact position called for on plans. 37 

Steel must be fixed in place so that it cannot be moved during the 

process of concreting. 37 

Round steel can be safely used in reinforced concrete since with 
proper imbedment the concrete adheres to it with sufficient bond 

to develop the full strength of the steel at its elastic limit. 461 

Square and flat bars do not bond as well as round. 463 

Deformed bars, that is, bars with irregular surfaces, are especially 

useful where the stress falls off rapidly, as in footings.463, 645, 670 

Deformed bars are also advantageous for temperature reinforcement 500 
Structural steel, like T-bars and I-beams, are not so good for rein¬ 
forcement as plain round or deformed steel bars. 465 

Structural steel may be used in columns either to take the entire load 
with concrete around it for protection, or else to act with the 
concrete. Although generally less economical than plain bars, 

it may permit smaller sized columns. 497 

High carbon steel, if of satisfactory quality and thoroughly tested, 

may be used with a higher working stress than mild steel.38, 414 

High carbon steel, unless of special quality, is apt to be brittle, and 

should not receive higher working stress than mild steel. 413 

Steel will not rust if completely surrounded with concrete of a wet 

consistency. 327 

Changes in temperature will not cause separation of steel from the 

concrete. 287 
















ESSENTIAL ELEMENTS 


20 - 


PAGE 


PROPORTIONING, MIXING AND PLACING 

Proportions must be accurately measured. 251 

Mixing must be thorough; concrete is improved by long mixing.... 251 

Machine mixing is better than hand mixing. 255, 372 

Enough water must be used in reinforced concrete so that the mass 

will just flow sluggishly around the steel to thoroughly imbed it. 36, 280 
For foundations of mass concrete, a jelly-like mass which will shake 

when being rammed is best... 36, 280 

If concrete stiffens in barrows or in mixer it indicates that the cement 
has a “flash” set and it should not be used. 

If cement with a flash set has been used inadvertently the concrete 
must be soaked with water until it hardens. 

Old and new concrete must be bonded for tight work.37, 284, 338 

Joints in floor construction should be made in center of span.37a, 284 

Surface treatment must be skillful, roughening is usually best. 288 

Plastering on external surfaces should be avoided. 288 


FORMS 

% 

Forms must be braced securely to avoid being thrown out of line by 

the concrete or by the workmen. 19, 37, 294 

Struts and braces supporting the forms must be strong enough to 
withstand the weight of the concrete above it and also a construc¬ 
tion load of 50 to 75 pounds per square foot.294, 617 

Boards and planks need but few nails unless the forms are built so 

that the pressure tends to separate them from the cleats. 620 

Forms should be tight enough to prevent mortar flowing away and 

leaving unsightly stone pockets.37, 623 

Forms should be thoroughly cleaned of all dirt and chips before 

laying concrete. A steam hose is effective for this purpose_ 36 

Column forms should be made with cleanout opening in lower end. 

Forms cannot be straightened or lined up after concrete is placed 295 

Wall forms usually may be removed in 24 to 48 hours. 296/ 

Forms supporting reinforced members should be left in place until the 
concrete rings sound and is not readily chipped by a blow 
from a pick. In mild weather 1 to 4 w r eeks is usually sufficient, 

according to the character of the member. 296 

Great caution must be used in cold weather, as the concrete sets 

slowly; sometimes the forms must remain until warm weather.. 296 
If dead load, that is, weight of the concrete itself, is large, the forms 

must be left longer for concrete to attain sufficient strength. 296 
















A TREATISE ON CONCRETE 


2 b 

-PAGE 

Earth must not be backfilled against a wall until it is 3 to 4 weeks 

old unless forms are left in place and braced. 620 

DESIGN 

Reinforced concrete should be designed by experienced engineers.. . 702 
Bending moments must be selected for individual conditions....433, 439 
Neither steel nor concrete must be overstressed in any part.... 418,420 


A T-beam must be deep enough to prevent overstressing concrete in 

the flange.. 424 

Width of flange of T-beam is limited by span and thickness of slab.. 423 

Steel must be placed across the top of a girder. 422, 443 

A continuous beam or slab must be designed at its support to resist 
negative bending moment. This requires as much steel at the 

top over the support as at center of member in the bottom_ 428 

Provision must be made for compression in the bottom of a continu¬ 
ous beam or slab at the support.. 428 

Shear in a T-beam must be studied to see that the stem is large enough 424 
Vertical or inclined steel is usually necessary to resist diagonal tension. 445 

Bars must be small enough to resist the bond stress.. 457 

Ends of bars must be imbedded far enough to provide bond sufficient 

to prevent danger of pulling out.. 464 

Columns may be reduced in size by using rich proportions, vertical 

reinforcement, hooping, or a combination of these. 489 

Hooping serves to increase the toughness of the column. 492 

The working strength of a hooped column, however, must not be based 

on its ultimate crushing strength. 495 


ESTIMATING. 

Cost of materials is readily estimated from the quantity used..--24, 231 
Cos: of labor of mixing, and placing concrete can be estimated with 

close approximation.. 24 

The cost of forms and incidental expense are the most difficult items 
to correctly estimate and vary largely with surrounding condi¬ 
tions. For this reason, estimates for reinforced concrete must be 
based upon very accurate data and large experience 


26 













CONCRETE DATA 


2C 


CHAPTER la 

CONCRETE DATA 
DEFINITIONS 

SEE PAGE 

Aggregate is the inert material, such as sand, broken stone, etc., with 
which the cement or other adhesive material is mixed to form con¬ 
crete or mortar. The term is sometimes erroneously applied to 
the coarse material, such as broken stone, only. 

Akron Cement is a Natural cement from the vicinity of Akron, N. Y. 49 
Beton is the French word for concrete. 

Beton-Coignet is a mixture of hydraulic lime, cement, and sand_ 42 

Concrete* is an artificial stone made by mixing cement, or some simi¬ 
lar material — which after mixing with water will set or harden 
so as to adhere to inert material, — and an aggregate com¬ 
posed of hard, inert particles of varying size, such as a combina¬ 
tion of sand or broken stone screenings, with gravel, broken stone, 
cinders, broken brick, or other coarse material. 

Concrete Rubble is masonry of large stones, usually of derrick size, 

with joints of concrete instead of mortar. 296 

Density represents the ratio of the sum of the volumes or mass of the 
particles, or absolutely solid substance, of a material contained 
in a measured unit volume to the total measured unit volume. . 138a 
Granolithic is concrete consisting of Portland cement and fine broken 


stone or sand troweled to form a wearing surface. 600 

Grappiers Cement (Ciment de grappiers ) is made in France from 
particles which have escaped disintegration in the manufacture 

of hydraulic lime. 50 

Hydrated Lime is specially prepared powdered slaked lime. 53 

Hydraulic Lime contains lime and clay in such proportions that it 

hardens under water. 52 

James River Cement is a Natural cement from the James River Valley 49 
Laitance is decomposed cement formed in the presence of an excess 

of water . 302 

Laitier Cement (Ciment de laitier ) is the French name for Puzzolan 

or slag cement. 5° 


♦Also applied to mixtures of an aggregate with a material such as asphalt - which liquefies 
on application of heat. 










2(1 


A TREATISE ON CONCRETE 


SEE PAGE 

Lime of Teil (Chaux du Teil ) is a celebrated hydraulic lime of France 52 
Louisville Cement is a Natural cement from the vicinity of Louisville, 

Ky... 49 

Mortar is a mixture of cement or lime and sand or other fine aggregate 
having water added so as to make it like a paste. 

Natural Cement is made from natural rock containing the required 


constituents in approximately uniform proportions. 49 

Parker’s Cement is a term sometimes used in England for Natural or 

Roman cement... 49 

Paste is a mixture of neat, i.e., pure, cement or lime with water. 

Portland Cement is made from an artificial mixture of materials con- 

taming lime and clay. 48 

Puzzolan Cement is a mechanical mixture of slaked lime with 
blast furnace slag, or with natural puzzolanic matter, such as vol¬ 
canic ash. 50 

Reinforced Concrete is concrete in which steel is imbedded to 
increase its strength. 

Roman Cement is the English name for Natural cement. 49 

Rosendale Cement is a Natural cement from the Rosendale District in 

eastern New York State. 49 

Rubble Concrete is concrete in which large stones are placed. 296 

Sand Cement or Silica Cement is a mechanical mixture of Portland 

cement and fine sand... 42 

Slag Cement is the name sometimes given to Puzzolan cement.... 50 
Vassy Cement (Ciment de Vassy) is a common French Natural cement 49 
Voids are the spaces throughout a mass of concrete, mortar, or paste 

that are filled with air or water..... 135 


WEIGHTS AND VOLUMES 


Portland Cement weighs per barrel, net. 

/“ “ bag “ . 

Natural Cement weighs per barrel, net. 

“ “ “ “ bag, net. 

Cement Barrel weighs from 15 to 30 lb., averaging about 
Portland Cement is assumed in standard proportioning to 

weigh per cubic foot. 

Packed Portland Cement, as in barrels, averages per cubic 

foot about. 

Packed Portland Cement based on 3.5 cubic feet barrel 
contents weighs per cubic foot ..... 


3 76 

lb. 

29 

94 

• • 

29 

282 

a 

31 

94 

u 

31 

20 

u 


100 

u 

217 

TI 5 

11 

219 

io8£ 

«( 




















CONCRETE DATA 


3 


Loose Portland Cement averages per cubic foot about ... 
Volume of Cement Barrel, if cement is assumed to weigh 
ioo lbs. per cubic foot . 

American Portland Cement Barrel averages between heads 
about . 

Foreign Portland Cement Barrel averages between heads 

about . 

Natural Cement Barrel averages between heads about .... 
Weight of Paste of neat Portland cement averages per cubic 
foot about . 

Volume of Paste made from ioo lb. of neat Portland ce¬ 
ment averages about. 

Volume of Paste made from one barrel of neat Portland 
cement averages about. 

Weight of Portland Cement Mortar in proportions i :2\ 

averages per cubic foot. 

Weight of Concrete and Mortar varies with the proportions 
as well as with the materials of which it is composed 
Weight of Portland Cement Concrete per cubic foot.... 

Cinder Concrete averages. 

Conglomerate Concrete averages. 

Gravel Concrete averages. 

Limestone Concrete averages. 

Sandstone Concrete averages . 

Trap Concrete averages . 

Loose Unrammed Concrete is 5% to 25% lighter than con¬ 
crete in place, varying with the consistency. 


SEE PAGE 

9 2 lb. £19 
3.8 cu.ft. 217 
3.5 “ “ 218 

3.25 “ “ 219 
3*75 “ “ 

137 lb. 376 


0.86 cu.ft. 229 


3.2 “ “ 229 

i35 lb. 


112 


(< 


150 “ 

150 “ 

148 “ 
«< 


*43 

155 


u 


362 
611 



277 


CEMENT TESTING FOR SMALL PURCHASERS 


Soundness. A sound cement will not go to pieces on the work. The 
test is therefore of greatest importance, and is often the only one necessary. 
Take about \ pound, or one cupful, of Portland cement and mix by knead¬ 
ing ij minutes with sufficient water to form a paste of a consistency like 
putty. Press portions of the paste on to 3 pieces of window glass 4 inches 
square, so as to make 3 pats each about 3 inches in diameter and J inch 
thick at center tapering to a thin edge, and place in moist air for 24 hours. 
Then keep one pat in air at moderate temperature (about 6o° or 70° Fahr.) 
for 28 days, keep second pat in water for 28 days, and place third pat in 
loosely closed vessel over boiling water and keep there for five hours. 
Reject cement if any pats show radial cracks or curl or crumble. The air 
















4 


A TREATISE ON CONCRETE 


pat should not change color. Portland cements may be accepted on the 
steam test alone if time is limited. Natural cements should be subjected 
to water and air but not to steam. (See p. 79.) 

Fineness. The finer the cement of a certain class the higher is its 
value. Sift 5 ounces of dry cement containing no lumps through a sieve 
about 6 to 8 inches diameter with 100 meshes per linear inch. Not 
more than \ ounce of either Portland or Natural cement should remain 
on sieve. To compare quality of two brands otherwise similar, sift 
through a 200-mesh sieve and choose the finer cement. (See p. 67.) 

Setting. A quick-setting cement is difficult to handle on the work and 
a too slow setting cement delays removal of forms. If a Vicat needle cannot 
be obtained for testing, use the Gillmore needles, — two steel rods, one, 
one-twelfth inch diameter at its end, loaded to weigh £ pound, the other, 
one-twenty-fourth inch diameter loaded to weigh 1 pound. A pat of pure 
Portland cement paste made like the soundness pat must not be able to 
support the weight of the lighter needle until 30 minutes after mixing, and 
must support the heavier needle in less than 10 hours. A paste or mortar 
or concrete has reached its final set when it will support a pressure of the 
thumb without indenting. (See p. 70.) 

Purity. “Provide a glass-stoppered bottle of muriatic acid, two shallow 
white bowls or two J-inch by 6-inch test tubes, a glass rod, and a pair of 
rubber gloves. Put in a bowl or a tube as much cement as can be taken on 
a nickel 5-cent piece; moisten it with half a teaspoonful of water; cover with 
clear muriatic acid poured slowly upon the cement while stirring it with the 
glass rod. Pure Portland cement will effervesce slightly, and will give off 
some pungent gas and will gradually form a bright yellow jelly without 
any sediment. Powdered limestone or powdered cement-rock mixed with 
the pure cement will cause a violent effervescence, the acid boiling and 
giving off strong fumes until all the carbonate of lime has been consumed, 
when the bright yellow jelly will form. Powdered sand or quartz or-silica 
mixed with cement will produce no other effect than to remain undissolved 
as a sediment at the bottom of the yellow jelly. Reject cement which has 
either of these adulterants.”* (See p. 65.) 

Tensile Strength. The tensile test is frequently unnecessary with a 
standard brand of cement employed in ordinary construction. Neat 
Portland cement should test at least 500 pounds in 7 days and 600 
pounds in 28 days. Mixed with three parts standard sand by weight, it 
should test at least 150 pounds in 7 days and 200 pounds in 28 days. 
(See p. 30.) 


*Judson’s City Roads and Pavements, 1902. 


CONCRETE DATA 


5 


Specific Gravity. The test requires delicate apparatus and is seldom nec¬ 
essary. Specific gravity of Portland cement should exceed 3.1. (See p. 30.) 
Magnesia must not exceed 4%. (See p. 30.) 

Sulphuric Anhydride must not exceed 1.75%. (See p. 30.) 

Color is no indication of quality. (See p. 113.) 

Weight is no indication of quality. (See p. 114.) 

PROPERTIES OF SAND AND SCREENINGS 

SEE PAGE 


Sharpness of grain is not necessary. 154a 

Quality of sand is chiefly dependent upon the coarseness and relative 

coarseness of its grains. 147 

Clay or Loam in sand is sometimes injurious to mortars because 
introducing too much fine material, while in other cases it may 

be beneficial because the fine material is needed. 154# 

Specific Gravity of dry sand may be taken at 2.65. 163 


Voids in sand cannot be accurately determined by pouring water into 


it, but can be found by weighing the sand and finding its moisture 165 
Comparison of Sands cannot be made by a study of voids because of 

the effect of varying degrees of moisture. 177 

Moist Sand measured loose is lighter in weight than loose dry sand .. 176 
Coarse Sand requires less water than fine sand, and when mixed with 

cement makes a denser mortar. 216 


Fine Sand with grains of uniform size weighs nearly the same when 
dry and has nearly the same percentage of voids as screened coarse 
sand. Fine sand with ordinary moisture is, on the other hand, 

lighter and more porous than coarse sand. 170 

Mixed Sand usually weighs more and contains a smaller volume of 

voids than coarse or fine sand ..................» 171 


PROPERTIES OF COARSE OR MIXED AGGREGATE 

Equal Spheres if symmetrically piled in the theoretically most compact 
manner would have 26% voids, but by experiment it is found that 
in practice it is impossible to pile them so as to get below 44% 

voids..... o»— .. 169 

Voids are approximately equal in the different portions of a dry ma¬ 
terial which has been screened to uniform sizes ... 170 

Smallest Percentage of Voids occurs in a mixture of sizes so graded 
that the voids of each size are filled with the largest particles which 
will enter them „.... - - ° ° . -. l l 1 













6 


A TREATISE ON CONCRETE 


SEE PAGE 

Density of a mixture of coarse stones and sand is greater than that 

of the sand alone. I 7 2 

Fuller and Thompson’s Experiments show that the perfect gradation 
of sizes of aggregate appears to occur when the percentages of 
the mixed aggregate passing different sizes of sieves are defined by 
a curve which is a combination of an ellipse and a straight line.. 202 
Gravel, because of its rounded grains, contains fewer voids than 
broken stone even when the particles in each have passed 
through and been caught by the same screens. 174 

STRENGTH OF CONCRETE AND MORTAR 

With the same Aggregate the strength and water-tightness of a con¬ 
crete or mortar increases as the percentage of cement in a unit 


volume of mortar or concrete is increased. 133 

With the same Percentage of Cement the strength and the water¬ 
tightness of a concrete or mortar usually increases with the den¬ 
sity .- - 133 

Concrete may often be increased in strength and made more water¬ 
tight by substituting more stone for a portion of the sand. 173 

Strongest Mortar for any given proportions of cement to dry sand by 
weight is obtained from sand which produces the smallest volume 

of plastic mortar.. 151 

Sharp Sand produces but slightly stronger mortar than rounded sand 154# 
Coarse Sand produces stronger and usually more impervious mortar 

than fine sand. T47 

Mixed Sand, i. e., sand containing fine and coarse grains, in mortars 
leaner than 1:2, usually produces stronger and more impervious 

mortars than coarse sand. T52 

Fine Sand always produces mortars of lower strength than coarse 

sand... . .147 

Screenings from broken stone usually produce stronger mortar than 

sand.,.. 153 


Mixtures of fine and coarse sand or of sand and screenings (or crusher 

dust) often produce better mortar than either material alone_150 

Variation of Sand in different portions of the same bank may be util¬ 
ized by requiring the contractor to mix two sizes without exact 
measurement, so that the material as delivered shall contain not 
less than a definite percentage of sand coarse enough to be re¬ 
tained on a certain sieve.....149 













CONCRETE DATA 


7 

SEE PAGE 

Form of Sand Grains and mineralogical nature of sand have but little 

effect upon the strength of the mortar.154a 

Clay or Loam in the sand is apt to weaken rich mortars and 

strengthen lean mortars... 154a 

Gravel vs. Broken Stone Concrete. The difference in quality is so 
slight that usually the cheaper material may be selected. Gravel 
concrete, because of the smooth, rounded surfaces, appears from 
tests to be weaker than broken stone concrete if the sizes of par¬ 
ticles in the two cases are alike, but a gravel mixture may require 

less cement because of better gradation of sizes of particles.387 

Wet vs. Dry Concrete. A medium wet quaking mixture gives the 
most uniformly strong concrete. A very wet or mushy mixture 
is best for concrete rubble or rubble concrete, for thin walls and 
columns and for reinforced work. Dry mixed concrete may be 


strongest at very short periods. 280 

Excess of Water decomposes the cement.384 

REINFORCED CONCRETE 

Steel is placed near the tension surface. 400 

Beams may be designed from tables...509 to5n 

Slabs may be designed from tables ......512 to 515 

Area of Steel varies from \°/ 0 to 1% of area of section of beam.. 4° x 
Tensile Strength of Concrete must not be considered in the design 

of reinforced beams. 412 


Yield Point in Mild Steel may be taken as 30,000 lb. per sq. in.. 414 
Modulus of Elasticity of Steel averages 30,000,000 lb. per sq. in... 402 
Modulus of Elasticity of Stone Concrete varies from 1,500,000 to 
5,000,000 lb. per sq. in. An average value may be taken as 

2,000,000. . 408 

The Higher the Modulus of the Concrete the lower should be the 
percentage of steel and the greater the depth of the beam. 
Compression in Concrete and Pull in Steel cannot, with a given per¬ 
centage of steel, be selected independently since they bear a 


constant ratio to each other. 4 X & 

High Working Strength in Concrete requires a high percentage of 

steel . 5 I 9 

High Working Strength in Steel permits low percentage of steel.. 519 
High Carbon Steel, if of a first-class quality, is better than mild 

steel for reinforced concrete... 4 X 4 














8 .4 TREATISE ON CONCRETE 

SEE PAGE 

Cinder Concrete requires a low percentage of steel.515 

Rods should be Imbedded a proper length in each direction, and 

also, if possible, anchored.465 

WATER-TIGHTNESS OF CONCRETE AND MORTAR 

Excess of Cement increases water-tightness. 339 

Aggregates should be carefully proportioned and graded. 339 

Clean Gravel is better than broken stone for water-tight concrete.. 339 

Quaking or Wet Consistency produces best results. 338 

Lay Concrete in one continuous operation. 338 

Layers of Waterproof Material are sometimes necessary.343 

EFFECT OF SEA WATER 

No Cement or other hydraulic product has yet been found which pre¬ 
sents absolute security against the decomposing action of sea 

water. 309 

Fine Sand must never be used in sea water construction. 316 

Density and imperviousness are essential qualities for concrete or 

mortar designed to resist sea water. 316 

Sulphates are the most injurious compounds in sea water. 310 

Aluminum should be low in Portland cement used in sea water .... 312 

Lime should be as low as possible in cements used in sea water.313 

Puzzolanic material is a valuable addition to cement for sea water 

construction. 313 

Gypsum, for regulating the time of setting, may be added only in 

smallest possible quantity to cements which are used in sea water 310 

1 

EFFECT OF FREEZING 

Natural Cements may be completely ruined by freezing. 320 

Setting and Hardening of Portland cement in concrete or mortar is 

retarded by freezing. 321 

Ultimate Strength of Portland cement concrete and mortar appears 

to be but slightly, if at all, affected by freezing. 321 

Thin Scale is apt to crack from the surface of walks or walls which 

have been frozen. 320 

Heating the Materials hastens setting and retards the action of frost. 323 
Salt Lowers the freezing point. 323 





















9 


CONCRETE DATA 

FIRE AND RUST PROTECTION 

Mix Concrete Wet to render it impervious.. 

Protection of Steel requires ^ inch to 2 inches of concrete 
Cinders do not corrode metal. 


SEE PAOE 
.. 329 

•• 333 
•• 3 2 9 


it n 


DATA ON HANDLING CONCRETE 

Average load of broken stone or gravel for wood wheelbarrow . 2.4 cu. ft 

“ sand for wood wheelbarrow. 2.5 

Large load of broken stone or gravel for iron wheelbarrow on 

short haul in concrete work . 3.0 

Large load of sand for iron wheelbarrow on short haul in con¬ 
crete work . 3.5 

Average load of ordinary concrete* for iron wheelbarrow_ 1.9 

T C»rfTA 11 11 11 il “ it tt _ _ 

j-«arge .... 2.2 

Number of shovelfuls of concrete per barrow in average load .. 13 
“ “ “ “ “ “ “ “large “ ..15 

Average net time of one man filling wheelbarrow with concrete, 1^ min. 


a 


a 


n 


it 


it 


it 


tt 


tt 


a tt 


tt tt 


n 


Quick . ” ** ** 1 

Average quantity concrete* mixed, wheeled 50 ft., and rammed, 

per man, per day of 10 hoursf. 2.2 cu. yd. 

Large quantity concrete* mixed, wheeled 50 ft. and rammed, 

per man, per day of 10 hoursf. 3 

Average quantity concrete* laid as above with a gang of 15 

men per day of 10 hoursf . 33 “ 

Large quantity concrete* laid as above with a gang of 15 men 

per day of 10 hoursf .. 47 “ 

Approximate average quantity of concrete* leveled and rammed 

in 6-inch layers, per man, per day of 10 hours. 11 

Approximate large quantity of concrete* leveled and rammed 

in 6-inch layers, per man, per day of 10 hours. 16 

Approximate average surface of rough braced plank form built 

and removed by one carpenter per day of 10 houm. 25 sq. 


tt 


tt 


n 


tt 


a 


u 


u 


u 


CHANGING FOREIGN TO AMERICAN MEASURES 

To convert values of kilograms per square centimeter to pounds per 
square inch, multiply the former by 14.2 (more exactly 14.2234). 

To convert values of pounds per square inch to kilograms per square 
centimeter, multiply the former by 0.07 (more exactly, 0.07031). 

♦All measurements of concrete are reduced to terms of quantity in place after ramming. 
fNote that the leveling and ramming, but not the labor on form, are included in this item. 















IO 


A TREATISE ON CONCRETE 


To convert values of pounds per square inch to tons (2,000 lb.; per 
square foot, divide the former by 14 (more exactly 13.89) 

To convert Centigrade to Fahrenheit temperatures, multiply the former 
by 1.8 and add 32 0 to the product. 

To convert Fahrenheit to Centigrade temperature, deduct 32 0 from the 
former and divide by 1.8. 

One millimeter = 0.0394 inch 
One centimeter = 0.3937 “ 

One meter = 39.37 inches or 3.281 feet 
One square centimeter = 0.155 square inch 
One “ meter = 10.764 square feet or 1.196 square yards 
One cubic centimeter = 0.061 cubic inch 
One “ meter = 35.31 cubic feet, or 1.308 cubic yards 
One liter = 61.02 cubic inches or 0.0353 cubic foot, or 1.057 U. S. liquid 
quarts or 0.2642 U. S. liquid gallon 
One gram = 0.0353 avoirdupois ounce 
500 grams = 1.1 pounds avoirdupois 
One kilogram = 2.2046 pounds avoirdupois 

One tonne or metric ton = 2204.62 pounds or 1.1023 tons (of 2,000 lb.) 

One English penny = $0.0203 

One “ shilling = $0.2433 

One “ pound = $4.8665 

One French franc = $0,193 

One German ma.rk= $0,238 


ELEMENTARY OUTLINE OF CONCRETING 


IT 


CHAPTER II 

ELEMENTARY OUTLINE OF THE PROCESS OF 

CONCRETING 

This chapter is not written for experienced civil engineers and contrac¬ 
tors, nor for those who desire to make a scientific study of methods and 
principles. On the contrary, it is merely an elementary outline, indicating 
to the inexperienced the various steps which must be taken with this class 
of masonry. In subsequent chapters the various divisions of the subject 
are treated in detail. 

The question as to whether concrete is preferable to some other form of 
masonry may often resolve itself into a question of cost. The cost, in 
turn, is dependent upon the character of the structure, the rate of labor 
and the price of the various materials entering into the work. Portland 
cement concrete has been laid in large masses at as low a price as $3 per 
cubic yard, while for thin walls built under disadvantageous conditions the 
cost of constructing molds may cause it to run as high as $30 per cubic 
yard, and in the case of ornamental work even above this. Before esti¬ 
mating the cost in any case, the materials must be chosen and the relative 
proportions of the ingredients determined from a consideration of the 
design of the structure. 

WHERE CONCRETE MAY BE USED 

By far the largest proportion of Portland cement concrete is laid in 
heavy foundation work and in other structures, such as tunnels and sub¬ 
ways, below the surface of the ground. It is peculiarly adapted for foun¬ 
dations of engines or machinery, heavy walls, piers, etc. In the former 
the concrete is often carried all the way up to the base of the engine or 
machine, instead of being topped with brick or stone. It is widely used 
for sidewalks or floors upon the ground level, and for suspended floors. 
When suitably reinforced with steel, it furnishes probably the most econom¬ 
ical and effective material for fire-proof construction. Its use for walls of 
buildings is largely increasing, but on account of the very indefinite time 
required in the building and moving of forms the cost may largely exceed 
the original estimate unless the builder is experienced in this class of work. 
Under favorable conditions, however, a 6-inch wall of concrete will cost no 
more, and usually less, than a 12-inch wall of brick work, and will be 


12 


A TREATISE ON CONCRETE 


stronger, more durable, and fire-proof. The strength of concrete columns 
and beams is readily calculated by means of formulas. 

Concrete is destined to be used to a large extent in the construction of 
tanks and vats for holding various liquids which attack wood and iron. 
Their construction is comparatively simple, but the work must be care¬ 
fully performed if the result is to be permanent and satisfactory. Concrete 
is especially suitable for all kinds of arches, because the stresses therein 
are chiefly compressive. Other classes of work for which concrete is largely 
employed are dams, retaining walls, penstocks, bridges, abutments, sewer 
and water conduits, and reservoirs. For ornamental work developments 
are constantly being made, and it is noteworthy that concrete or mortar 
can be cast in molds in a somewhat similar manner to that in which piaster 
of Paris is run for interior decoration. 


SELECTION OF MATERIALS 

Concrete is ordinarily composed of cement, sand, gravel or crushed 
stone, or both, and water. The selection of each of these materials is 

7 7 ^ ( ' C ' . • 

largely dependent upon local conditions, and no unalterable rule can be 
laid down in regard to it, but certain general conditions may serve as a 
guide to the inexperienced. 

Cement. It is a wise rule to use Portland cement for nearly ail classes 
of concrete, and the remarks in this chapter are based entirely upon this 
material. Portland cement is more uniform and therefore more reliable, 
while its strength is so much higher than Natural cement that by mixing it 
with larger proportions of sand and stone, properly graded, it will usually 
yield better results at less cost than Natural cement. 

If the job is small and unimportant, it is generally safe to select in the 
market a brand of Portland cement of American manufacture which has 
a first-class reputation, and to use it without testing. As a precaution, 
however, it is usually advisable that samples from a few of the packages of 
every shipment be tested for soundness. This can be done after a little 
practice with scarcely any apparatus. (See p. 79.) For very important 
concrete construction complete specifications should be prepared before 
purchasing the cement, and a small laboratory established for conducting 
tests to determine whether it is fulfilling the requirements. (See p. 28.) 

Aggregate. The sand and broken stone or gravel are termed the 
aggregate. The sand should be clean. One may obtain some idea of its 
cleanliness by placing it in the palm of one hand and rubbing it with the 
fingers of the other. If the sand is dirty, it will badly discolor the palm, 


ELEMENTARY OUTLINE OF CONCRETING 


1 3 


If the use of dirty sand is unavoidable, its effect upon the strength of the 
mortar should be investigated. Preference should be given to sand con¬ 
taining a mixture of coarse and fine grains. Extremely fine sand can be 
used alone, but it makes a weaker mortar than either coarse sand alone or 
a mixture of coarse and fine sand. 

Either crushed stone or clean gravel, or both, is suitable for the coarse 
material of the aggregate. It is chiefly a question of which can be delivered 
upon the work at the least cost. If the gravel is chosen greater uniformity 
is attained by screening it over, say a f-inch mesh screen, and then re¬ 
mixing the sand which falls through the screen with the coarser gravel in 
definite proportions, than by taking the run of the bank. If the gravel is 
dirty or clayey it should be washed with a hose, a little at a time, before it 
is shoveled on to the mixing platform. 

Broken stone, if selected, may be used unscreened as it comes from the 
crusher, although it is preferable to screen out the dust and to use the 
latter as a portion of the sand. The maximum size is usually limited 
to 2\ inches. A smaller size than this, say one inch, will give, with less 
care, a finer surface. In a thick wall large sound stones may be placed 
by hand or derrick without detriment to the work, providing the con¬ 
sistency of the concrete is thin enough to properly imbed them. 


PROPORTIONS 



Accurate methods of proportioning the cement and aggregate in concrete 
are discussed in chapter XI, page 183, and if a large or very important mass 
is under consideration, or if the work must be water-tight, the correct pro¬ 
portioning requires more careful consideration than can be given it in 
this chapter. The method often adopted of pouring water into the coarser 
material to determine the percentage of voids, and thus finding the quan¬ 
tity of sand to use for filling them, is apt to be misleading, because so much 
depends upon the compactness of the stone, due to the method of handling 
it — that is, whether placed quietly, dropped, thrown, or shaken down — 
and because in the majority of cases the sand contains many grains so 
large that they will not enter the smaller voids of the coarser material. 
In a small job it is sufficiently accurate to select the proportion of cement 
to sand which will give the required strength to the concrete, and then use 
twice as much gravel or broken stone as sand. In figuring the capacities 
of the measures for the sand and stone it must be remembered that a barrel 
of Portland cement weighs 376 pounds, not including the barrel, and a 
bag of Portland cement 94 pounds, and we may assume for convenience 



14 


A TREATISE ON CONCRETE 


that a cement barrel holds 3.8 cubic feet. This is a fair average measure¬ 
ment of a heaped barrel, or a barrel with both heads removed—a con¬ 
venient measure for sand. 

As a rough guide to the selection of materials for various classes of work, 
we may take four proportions which differ from each other simply in the 
relative quantity of cement: 

(a) A Rich Mixture for columns and other structural parts subjected to 

high stresses or requiring exceptional water-tightness: Proportions 
1 : 1^ : 3; that is, one barrel (4 bags) packed Portland cement to 
1^ barrels (5.7 cubic feet) loose sand to 3 barrels (11.4 cubic feet) 
loose gravel or broken stone. 

(b ) A Standard Mixture for reinforced floors, beams and columns, for 

arches, for reinforced engine or machine foundations subject to 
vibrations, for tanks, sewers, conduits, and other water-tight work: 
Proportions 1 : 2 : 4; that is, one barrel (4 bags) packed Portland 
cement to 2 bbl. (7.6 cu. ft.) loose sand to 4 barrels (15.2 cu. ft.) 
loose gravel or broken stone. 

(c) A Medium Mixture for ordinary machine foundations, retaining walls, 

abutments, piers, thin foundation walls, building walls, ordinary 
floors, sidewalks, and sewers with heavy walls: Proportions 1 : 2b : 5; 
that is, one barrel (4 bags) packed Portland cement to 2\ barrels 
(9.5 cu. ft.) loose sand to 5 barrels (19 cu. ft.) loose gravel or broken 
stone. 

(d) A Lean Mixture for unimportant work in masses, for heavy walls, for 

large foundations supporting a stationary load, and for backing for 
stone masonry: Proportions 1 : 3 : 6; that is, one barrel (4 bags) 
packed Portland cement to 3 barrels (11.4 cu. ft.) loose sand to 6 
barrels (22.8 cu. ft.) loose gravel or broken stone. 

The above specifications are based upon fair average practice. If the 
aggregate is carefully graded and the proportions are scientifically fixed, 
smaller proportions of cement may be used for each class of work. 


QUANTITIES OF MATERIAL 

Inexperienced contractors have often lost money by assuming that the 
quantity of gravel plus the quantity of sand required will be equivalent to 
the volume of the finished concrete — that is, that 7^ cubic yards of con¬ 
crete in the proportions of 1: 2\: 5 will require 2^ cubic yards of sand and 
5 cubic yards of gravel. This is absolutely wrong, since the grains of sand 
fill, to a certain extent, the spaces between the larger pebbles. It is incor¬ 
rect. on the other hand, to figure a quantity of gravel equal to the total 


ELEMENTARY OUTLINE OF CONCRETING 




!5 


volume of the concrete, because the introduction of the mortar, which is 
always in excess of the actual voids, swells the bulk. 

If gravel or stone having particles of uniform size is used it must be 
recognized that the work will cost from 5 to 10 per cent, more, on account 
of the additional quantity of material required to make a given volume of 
concrete. In measuring the gravel or stone before mixing there will be 
less solid matter in a measure, and consequently more sand and cement 
will be necessary to fill the spaces between the stones. This fact, 
which is often overlooked even by experienced men, is illustrated in a 
somewhat exaggerated fashion in Figs. 1 and 2. Here Fig. 1 illustrates 





Fig. 1.—Diagram illustrating measurement of Dry Materials and the Mixture 
when Broken Stone is of uniform size. (See p. 15.) 




Fig. 2.—Dry Materials and Mixture when the Stone is of varying sizes. (See p. 15.) 


the measurement of the dry materials and the mixture produced therefrom 
when the stone has been screened to one uniform size, while Fig. 2 shows 
the drv materials and the mixture when the stone is what is termed “ crusher 
run” — that is, of varying sizes as it comes from the crusher. 

It is obvious at a glance that the uniform stone measured in Fig. 1 con¬ 
tains less solid stone than the graded stone measured in Fig. 2. The spaces 
between the stones in the first case are very nearly equal to the volume of 

































































r6 


A TREATISE ON CONCRETE 




the solid particles, and as the measure of the sand is one-half that of the 
stone, and the particles of cement fill the voids in the sand, this sand and 
cement mixes in between the stones, filling the spaces or voids, and re¬ 
sulting in a mixture but very slightly greater in volume than the stone 
alone. In the second case, Fig. 2, the spaces between the large stones in 
the stone measure are filled with graded smaller stones, so that there is a 
much smaller volume of spaces or voids. Hence, when the sand and 
cement, which are identical with that in Fig. 1, are mixed with it the 
volume of mixture becomes considerably larger than the original bulk of 
the stone. Consequently, if we start with definite proportions of materials, 
more concrete will be made with graded stone — such as “crusher run” 
broken stone, or gravel containing various sizes, ranging, say, from J inch 
up to 2 inches — than if the stone has been screened to uniform size. If, 
on the other hand, the proportions of the materials are changed on account 
of the fewer voids in the mixed stone, and less sand and cement are used, 
a saving in these materials results. 

Fuller’s Rule For Quantities —The simplest rule for determining the 
quantities of materials for a cubic yard of concrete is one devised by 
William B. Fuller. Expressed in words, it is as follows: 

Divide n by the sum of the parts of all the ingredients, and the quotient 
will be the number of barrels of Portland cement required for 1 cubic yard 
of concrete. The number of barrels of cement thus found, multiplied 
respectively by the “parts” of sand and stone, will give the number of 
barrels of each required for 1 cubic yard of concrete, and multiplying 
these values by 3.8 (the number of cubic feet in a barrel), and dividing by 
27 (the number of cubic feet in a cubic yard), will give the quantities of 
sand and stone, in fractions of a cubic yard, needed for 1 cubic yard of 
concrete. 

To express this rule in the shape of formulas: 


Let 

c = number of.parts cement; 
s = number of parts sand; 
g = number of parts gravel or broken stone. 
Then 
11 


c+s+g 


— P — number of barrels Portland 
cubic yard of concrete. 


cement required for one 


3.8 

PXsX — 
2 7 


= number of cubic yards of sand required for one cubic yard of 
concrete. 




ELEMENTARY OUTLINE OF CONCRETING 


i7 


3.8 

PXgX —-= number of cubic yards of stone or gravel required for 

one cubic yard of concrete. 

The following table is made up from Fuller’s rule and represents fair 
averages of all classes of material. The first figure in each proportion 
represents the unit, or one barrel (4 bags), of packed Portland cement (weigh¬ 
ing 376 pounds), the second figure,the number of barrels loose sand (3.8 
cubic feet each) per barrel of cement, and the third figure, the number of 
barrels loose gravel or stone (of 3.8 cubic feet each) per barrel of cement: 


Materials for One Cubic Yard of Concrete. 



Cement, 

Sand, 

Gravel or stone. 

Proportions. 

Barrels. 

Cubic yards. 

Cubic yards. 

1:2:4 

i -57 

O.44 

0.88 

1: 2 i : 5 

1.29 

o -45 

0.91 

1:3:6 

1.10 

0.46 

o -93 

1:4:8 

0.85 

0.48 

0.96 


If the coarse material is broken stone screened to uniform size it will, as 
is stated above, contain less solid matter in a given volume than an average 
stone, and about 5 per cent, must be added to the quantities of all the 
materials. If the coarse material contains a large variety of sizes 
so as to be quite dense, about 5 per cent, may be deducted from all of 
the quantities. 

Example .— What materials will be required for six machine founda¬ 
tions, each 5 feet square at the ottom, 4 feet square at the top, and 8 feet 
high ? 

Answer. — Each pier contains 163 cubic feet, and the six piers therefore 
6 X 163 

contain - = 36.2 cubic vards. If we select proportions 1: 2\: 5, 

2 7 

we find, multiplying the total volume by the quantities given in the table, 
that there will be reqm *ed, in round numbers, 47 barrels packed cement, 
16 J cubic yards loose sa id, 33 cubic yards loose gravel. 

TOOLS AND APPARATUS REQUIRED FOR CONCRETE WORK 

The quantity of tools will, of course, vary with the size of the gang. 
The following schedule is based upon a small gang of eight or ten men, 
making concrete by hand: 

Eight square pointed shovels, size No. 3, and such as illustrated in 
Fig. 3, page 18. (If a very wet mixture is used substitute small 
coal scoops.) 

Three iron wheelbarrows, Fig. 4, page 18. 

Two rammers, Figs. 99, 100, or 101, pages 281 and 282. 




i8 


A TREATISE ON CONCRETE 


One mixing platform, about 15 feet square, built so substantially that it 
can be moved without coming to pieces, and having a 2 by 3-inch 
strip around the edge to prevent waste of materials and water. 
On a small job this may be of i-inch stuff, resting on joists about 
3 feet apart, provided it is stiffened by being tongued and grooved. 



Fig. 3.—Square Pointed Shovel. {See p. 17.) 



Fig. 4.—Concrete Wheelbarrow. {See p. 17.) 



Fig. 5.—Measuring Box for Gravel. {See p. 18.) 


One measuring box or barrel for sand, of a capacity for one batch of con¬ 
crete. A convenient measure is a cement barrel, either whole or 
sawed in two, with both heads removed. It is filled and then lifted in 
such a manner as to spread the sand. 

One measuring box for gravel (see Fig. 5) of a capacity for one batch of 
concrete. 





ELEMENTARY OUTLINE OF CONCRETING 


19 

Lumber for making and bracing forms. 

Nails and, for some kinds of work, bolts, for forms. 

CONSTRUCTION OF FORMS 

Green spruce or fir lumber is suitable for forms. If a smooth face is 
required the surface of the boards or plank next to the concrete must be 
dressed and the edges tongued and grooved or beveled. The forms must 
be nearly water-tight. The sheeting, which is usually laid horizontal, may 
be 1 inch, 1^ inch or 2 inches thick, the distance apart of the studding being 
governed by the thickness selected. The studs must be placed not more 
than 2 feet apart for i-inch sheeting nor more than 5 feet apart for 2-inch 
sheeting. They must be securely braced so as to withstand the pressure 
©f the soft concrete and of the puddling or ramming. 

The lower portion of a foundation wall in a trench excavated in earth so 
stiff as to stand nearly vertical may sometimes be laid with no form at all, 
and then narrowed in at the top to the required thickness, but if the 
sides of the trench are sloping it is generally cheaper to save concrete 
material by carrying the forms to the bottom. A thin wall may be 



Fig. 6. — Construction of Form when Base of Wall is Spread. (See p. 19.) 












20 


A TREATISE ON CONCRETE 


greatly strengthened by spreading the base, which is readily accomplished 
by starting the boards or plank 6 or 8 inches above the bottom of the exca¬ 
vation and allowing the soft concrete to flow out under them on both sides 
of the wall so as to make footings, as shown in Fig. 6. The studs may 
run to the bottom, as indicated by the dotted lines, but should be tapered 
and greased so that they may be withdrawn without injury to the 
concrete. 

For all walls under 9 or 10 inches in thickness, small steel rods \ or 
| inch in diameter, spaced about 18 inches apart, will greatly increase the 
stiffness and add to the safety of the structure, especially while the con¬ 
crete is hardening. 

Forms must be left in place for three or four weeks if there is earth or 
water pressure against the wall. If, on the other hand, there is no strain 
upon it, 24 hours setting, or until the concrete will stand the pressure of 
the thumb without indentation, is sufficient. 

Further descriptions of form construction and methods of facing are 
given in Chapter XV. Forms for special structures are described and 
illustrated in subsequent chapters treating of concrete design. 

MIXING AND LAYING CONCRETE 

The advisability of employing machinery for mixing the concrete depends 
chiefly upon the quantity to be laid. On a small job the first cost cf 
mixing machinery and the running expenses, such as the labor of the engine- 
man, which continue when the machine is idle, may bring the cost of ma¬ 
chine-mixed concrete higher than hand-mixed. The decision may be 
based entirely upon the cost per cubic yard of concrete laid, provided a 
first-class machine is employed, since good concrete can be made either by 
machine or by hand. The various types of concrete mixers and the methods 
of employing them are discussed in Chapter XIV. 

The foreman for a gang of concrete mixers need not be of great intelli¬ 
gence, but must be one who will obey orders strictly, and know how to 
keep all of his men constantly busy. The amount of work turned out will 
depend to quite an extent on the arrangement of the gang, whether each 
man has certain definite operations to perform over and over again, and 
whether these operations fit into the work of the rest of the gang so that 
none of the men have idle moments. 

A gang of at least 6 men besides the foreman is required even on small 
work, while as many as 23 men may be effectively employed. In addition 
to these, an inspector is generally necessary to watch the placing of the 


ELEMENTARY OUTLINE OE CONCRETING 


21 


concrete and see that the mixture is uniform and of proper consistency. 
Cheap laborers, as for instance Italians, make good men for mixing and 
transporting the concrete. 

The materials for the concrete ought, of course, to be deposited as near 
the work as possible. The cement, whether it comes in bags or barrels, 
must be sheltered from the rain. Covering with plank is insufficient. 
Bags should be protected from moist atmosphere; a cellar is likely to be 
too damp. To keep the sand and stone as near the mixing platform as 
possible, it may be advantageous to haul the materials as they are required 
from day to day. If the sand or stone pile is at any time farther from the 
measuring boxes than a man can profitably throw with shovels without 
walking, say more than 8 or io feet, do not hesitate to have it loaded into 
wheelbarrows and dumped into the measuring boxes. Materials can be 
wheeled in barrows to a distance of io to 25 feet from the platform at 
about the same cost that they can be shoveled direct with a long throw. 

There are many methods of mixing concrete by hand, as discussed in 
Chapter XIV, all of which with care produce good work. For the con¬ 
venience of the inexperienced the following directions for the work of a 
small gang of six men with foremen may be useful. They are given merely 
for illustration, and must be more or less varied to suit local circumstances. 

Directions for Mixing Concrete. Assume a gang of four men to 
wheel and mix the concrete, with two other men to look after the placing 
and ramming. 

When starting a batch, two mixers shovel or wheel sand into the measur¬ 
ing box or barrel — which should have no bottom or top — level 
it and lift off the measure, leveling the sand still further if necessary. 
They then empty the cement on top of the sand, level it to a 
layer of even thickness, and turn the dry sand and cement with shovels 
three times, as described below, after which the mixture should be of 
uniform color. 

While these two men are mixing sand and cement, the other two fill the 
gravel measure about half full, then the two sand men take hold with them, 
and complete filling it. The gravel measure is lifted, the gravel hollowed 
out slightly in the center, and the mixture of sand and cement shoveled on 
top in a layer of nearly even thickness.* A definite number of pails are 
filled with water, and poured directly on the top of these layers, greater 
uniformity being thus attained than by adding the water directly from 
a hose. After soaking in slightly the mass is ready for turning. 

* Some engineers prefer.to spread the stone on top of the sand and cement, while others 
prefer to mix the water with the sand and cement before adding them to the stone. 


A TREATISE ON CONCRETE 


The method illustrated in Fig. 7 of turning with shovels materials 
which have already been spread in layers is as follows: 

Two men, a and b, with square pointed shovels, stand facing each other 
at one end of the pile to be turned, one working right-handed and the other 
left-handed. Each man pushes his shovel along the platform under the 
pile, lifts the shovelful, turns with it, and then, turning the shovel com¬ 
pletely over, and with a spreading motion drawing the shovel toward him¬ 
self, deposits the material about 2 feet from its original position. Repeti¬ 
tions of this operation will form a flat ridge of the material, on a line with 
the pile as it originally lay, and flat enough so that the stones will not roll. 
As soon as, but not before, a single ridge is complete, two other men, 
c and d, should start upon this ridge, turning the materials for the 
second time, as shown in the illustration, and forming as before a flat ridge 
and finally a level pile which gradually replaces the last. A third mixing 
is accomplished in a similar way. 

Fig. 7 gives the position of the piles as the concrete is being turned. 



MAN 

X 


b 


NEXT BATCH 
TO BE 

STARTED HERE 


1 ST. 

/ TURN 


\_ 

2 J ' 

MAN d 



X 

no 

2 NO. 

Pfl 

TURN 


tiG. 7. Position of Men and Concrete on Platform while Turning. (See p. 22.) 
























ELEMENTARY OUTLINE OF CONCRETING 


2 3 


A portion of the original layers is shown at p, the ridge formed by men a 
and b shoveling from pile p is shown at q , and the beginning of the 
ridge formed by men c and d is shown at rr. The third turning is not 
shown. 

The quantity of water used must be varied according to the moisture in 
the materials and the consistency required in the concrete. While the 
opinions of engineers regarding the proper consistency vary widely, it is 
advisable, the authors believe, for an inexperienced gang to use an excess 
of water. The rule may be made in hand mixing to use as much water as 
can be thoroughly incorporated with the materials. Concrete thus made 
will be so soft or “mushy” that it will fall off the shovel unless handled 
quickly. 

After the material has been turned twice, as described, and as soon as 
the third turning has been commenced, two of the mixers who have 
finished turning may load the concrete into barrows and wheel to place. 
They should fill their own barrows, and after the mass has been com¬ 
pletely turned for the third time by the other two men the latter should 
start filling the gravel measure for the next batch. 

If the concrete is not wheeled over 50 feet, four experienced men ought 
to mix and wheel on the average about 10^ batches in ten hours. This 
figure is based on proportions 1: 2J: 5, and assumes that a batch consists 
of one barrel (four bags) Portland cement with 9.5 cubic feet of sand and 
19 cubic feet of gravel or stone. 

Assuming, as given on page 17, that 1.29 barrels of cement are re¬ 
quired for 1 cubic yard of concrete, one barrel of cement — that is, one 
batch — will make 0.78 cubic yard of concrete; hence io| batches mixed 
and wheeled by four men in ten hours are equivalent to 8^ cubic yards of 
concrete. This is for the very simplest kind of concreting and makes no 
allowance for the labor of supplying materials to the mixing platform or 
for building forms. 

Placing Concrete. The concrete may be transported and handled by 
any means which will not cause the materials to separate. If mixed 
wet it may be dropped directly from shovels or barrows to place, or it 
may be run down an inclined pipe or chute. The layers should be about 
6 inches thick. For a dry or a jelly-like mixture common square ended 
rammers are employed and the mass must be rammed until the mortar 
flushes to the surface. Wet concrete must be merely puddled or 
“ joggled ” to expel the air and surplus water. Before placing a fresh layer 
upon work which has set, the surface must be cleaned of dirt and scum, 
and thoroughly wet. 


24 


A TREATISE ON CONCRETE 


The placing of concrete and the kinds of rammers for different classes of 
work are discussed more at length in Chapter XV. 


APPROXIMATE COST OF CONCRETE 

The cost of concrete depends more upon the character of the con¬ 
struction and the conditions which govern it than upon the first cost 
of the materials. In a very general way, we may say that when laid in large 
masses or in a very heavy wall, so that the construction of the forms is 
relatively a small item, the cost per cubic yard in place is likely to range 
from $4 to $7. The lower figure represents contract work under favorable 
conditions with low prices for materials, and the higher figure small jobs 
and inexperienced men. Similarly, we may say that for sewers and 
arches, where centering is required, the price may range from $7 to $14 
per cubic yard. Thin building walls under eight inches thick may cosl 
from $10 to $20 per cubic yard, according to the character of construction 
and the finish which is given to the surface. 

These ranges in price seem enormous for a material which is ordinarily 
supposed to be handled by unskilled labor, but it must be borne in mind 
that skilled workmen are required for constructing forms and centers, and 
often the labor upon these may be several times that of mixing and placing 
the concrete. As a rule, unless the job is a very small one or under the 
personal supervision of a competent engineer, it is cheaper and more satis¬ 
factory to employ an experienced contractor than day labor. Green men 

i 

under an inexperienced foreman may not be counted upon to mix and lay 
over one-half the amount of concrete that will be handled by a skilled 
gang under expert superintendence. 

A close estimate of cost may be reached, in cases where the conditions 
are known in advance, by taking up in detail and then combining the 
various units of the material and labor as outlined below. 

Cost of Cement. As the price of Portland cement varies largely with 
the demand, it is necessary to obtain quotations from dealers for ever) 
purchase. It is such heavy stuff that the freight usually enters largely 
into the cost, and quotations should therefore be made f.o.b. the nearest 
point of delivery to the work. The cost of hauling by wagon may be 
readily estimated by assuming that a barrel of cement weighs 400 pounds 
(gross), and that a pair of horses will hatd over an average country road 
a load of, say, 5 000 pounds, traveling in all a distance of 20 to 25 miles in 
a day, that is, 10 to T2^ miles with load. This assumes, of course, 
that the teams are good and properly handled. 


ELEMENTARY OUTLINE OF CONCRETING 


2 5 


Having found the cost of the cement per barrel, delivered, the approxi¬ 
mate cost per cubic yard is at once obtained from the table on page 17. 
If, for example, the cost is $2 per barrel and proportions 1:2^: 5 are 
selected, the cost of the cement per cubic yard of concrete will be 1.29 X $2.00 
= $2.58. 

Cost of Sand. The cost of sand depends chiefly upon the distance 
hauled. With labor at 15 cents per hour, the cost of loading (including 
the cost of the cart waiting at pit) may be estimated, if handled in large 
quantities, at 18 cents per cubic yard, or on a small job at 27 cents per 
cubic yard. For hauling add one cent for each 100 feet of distance from 
the pit. The additional cost of screening, if required, will vary with the 
coarseness of the material, but 15 cents per cubic yard may be called an 
average price for this, unless the sand is obtained by screening the gravel, 
when no allowance need be made. After finding the cost of one cubic 
yard of sand, the cost of the sand per cubic yard of concrete is readily 
figured from the table referred to. If, for example, the cost of sand 
screened, loaded and hauled 1 oco feet is 52 cents per cubic yard, the cost 
per cubic yard of concrete for proportions 1: 2J: 5 will be 0.45 X $0.52 = 
$0.23^. 

Cost of Gravel or Broken Stone. If broken stone is used upon a small 
job for the coarse aggregate, it is usually purchased by the ton or cubic 
yard. A 2coo-lb. ton of broken stone may be considered as averaging 
approximately 0.9 cubic yards, although differences in specific gravity 
cause considerable variation. A two-horse load is generally considered 
i| to 2 yards, the latter quantity requiring very high sideboards. The cost 
of screening gravel, if this is necessary, while a very variable item, may be 
estimated at 35 cents per cubic yard. The cost of loading gravel into 
double carts, with labor at 15 cents per hour, may be estimated on a 
small job at 38 cents per cubic yard. If handled in large quantities, 25 
cents is an average cost. The cost of loading includes loosening and 
also the cost of the cart waiting at the pit. Hauling costs about one cent 
per cubic yard additional for each 100 feet of distance hauled under load. 
If, to illustrate, the cost of gravel picked, screened, loaded and hauled 
1 000 feet is 83 cents per cubic yard, the cost of the gravel per cubic yard 
of concrete for proportions 1: 2\\ 5 will be 0.91 X $o.83 = $o.75T 

For distances up to 300 feet both sand and gravel can be hauled more 
economically by wheelbarrows than by teams. The cost of loading wheel¬ 
barrows is about half the cost of loading carts, while the cost of hauling 
with barrows per 100 feet is about four times greater. 

Cost of Labor. With an experienced gang working at the rate of 15 


26 


A TREATISE ON CONCRETE 


cents per hour, the cost of mixing and laying concrete, if shoveled directly 
to place from the mixing platform, will average about 80 cents per cubic 
yard, in addition to the work on forms. If, as is usually the case, the con¬ 
crete is wheeled in barrows, 9 cents per cubic yard must be added to the 
above price for the first 25 feet that the barrows are wheeled under load, 
and 1 1 cents for each additional 25 feet wheeled. With other rates of 
wages, the cost may be considered as proportional. With a green gang, 
the cost will be nearly double the above figures, but as the men become 
worked in and the organization perfected, the cost should approximate 
more nearly the prices given. 

In building construction where the material is mixed by machinery and 
hoisted to place, there are numerous incidental expenses and delays, so that 
it is not safe to figure the cost of labor for simply mixing and laying the 
concrete under ordinarily good conditions at less than $1.50 to $2.00 per 
cubic yard. The cost of materials must be added to this, so that the cost 
of the concrete itself laid in place but not including forms nor reinforcement 
is apt to be about $7.50 per cubic yard. Approximate costs per cubic foot 
of finished concrete are given in Chapter XXIV. 

Cost of Forms. The labor on forms is not included in the above. This 
is an extremely variable item. The cost of rough plank forms, includ¬ 
ing labor and lumber for both sides of a 3-foot wall, may be as low as 50 
cents per cubic yard of concrete, with other thicknesses of wall in inverse 
proportion. On elaborate work the price, which is really dependent upon 
the face area, will reach several dollars per cubic yard of concrete, the cost 
of the form work, in fact, usually exceeding the cost of the concrete. In 
building construction, such as a factory six stories in height of symmetrical 
design, the cost of materials and labor on forms may be estimated at from 
9 to 12 cents per square foot of surface of forms. If forms am to be used 
only once, or if conditions are disadvantageous, these values may be doubled. 
The costs vary with the price of lumber, the design of the structure, the 
design of the forms, the character of the supervision, and the skill of the 
workmen. 

Cost of Steel. The cost of bending and placing steel for reinforced 
concrete is apt to vary from i to per pound. If, therefore, the cost 
of the steel is about $40.00 per ton or 2$ per pound, the cost in place may be 
estimated at 3^ per pound. 

THE STRENGTH OF CONCRETE 

The strength of concrete varies (1) with the quality of the materials; (2) 
with the quantity of cement contained in a cubic yard of the concrete; and 
(3) with the density of the mixture. 


ELEMENTARY OUTLINE OF CONCRETING 


27 


We may say that the strongest and most economical mixture consists of 
an aggregate comprising a large variety of sizes of particles, so graded 
that they fit into each other with the smallest possible volume of spaces or 
voids, and enough cement to slightly more than fill all of these spaces or 
voids between the solids of the aggregate. It is obvious that with the 
same aggregate the strongest cement will make the strongest concrete. 

On important construction the various materials to be used should Us 
carefully tested, and specimens of the mixture selected made up in advance 
and subjected to test. As a guide to the loads which concrete will stand 
in compression, that is, under vertical loading where the height of the 
column or mass is not over, say, 12 times the least horizontal dimension, 
we may give the following approximate figures as safe strengths, after 
the concrete has set at least one month, for the proportions which have 
previously been selected in this article as typical mixtures. 

The figures, compared with the results of recent experiments on long 
columns, allow with first-class construction a factor of safety of at least four 
at the age of one month, or about five and one-half at the age of six months, 
and are based on conservative practice. The relative strengths of the 
different mixtures are calculated from original investigations of the authors 
discussed in Chapter XX. 


Safe Strength of 


Proportions. 

I : li : 3 
1:2:4 
1 : 2b : 5 
1:3:6 

1:4:8 


Portland Cement Concrete in Direct Compression. 


Pounds per 
square inch. 
300 

45° 

400 

36° 

290 


Tons per 
square foot. 


3 6 

3 2 

29 

26 
21 


With a large mass foundation, take values one-third greater. 

With a vibrating or pounding load, take one-half these values. 

The tensile strength of concrete, is very much less than the compressive 
strength. Experiments made by the authors, with mixtures of average 
proportions, give the ultimate fiber stress in beams not reinforced as about 
one-eighth the breaking strength in compression. For this reason it is 
not safe to use concrete for beams unless reinforced with steel. 


28 


A TREATISE ON CONCRETE 


CHAPTER III 

SPECIFICATIONS 

In the following pages are given specifications for 

Cement, in brief, for the small purchaser. (See p. 29.) 

Portland cement, in full, for the large purchaser. (See p. 29.) 

Natural cement, in full, for the large purchaser. (See p. 31.) 

Concrete and Reinforced Concrete. (See p. 32.). 

First class steel for reinforced concrete. (See p. 38.) 

These specifications cover all ordinary concrete construction, and are 
adapted as far as possible for direct use in placing contracts for material 
and construction, although concrete specifications for structures of intricate 
design will require the insertion of additional paragraphs referring speci¬ 
fically to the particular work. 

If sand, screenings, gravel, stone, or steel are purchased on separate 
contracts, paragraphs 3, 4, 5, or 7 (pp. 33 and 34) may be extracted from 
the concrete specifications. 

The full specifications for cement are advised for important work, whether 
large or small, although the brief specifications which precede them may 
be sometimes useful. 

Even when purchasing by the full specifications it may often be unneces¬ 
sary actually to test the cement, except for set soundness and fineness, but 
the strict detail specifications are necessary so that if the cement is found 
to work unsatisfactorily samples may be subjected to complete tests on the 
ground, or sent to testing laboratories, and the remainder of the shipment 
or subsequent shipments rejected. 

Printed specifications are frequently preceded by a “Notice to Con¬ 
tractors” stating the place and time of receiving bids, the amount of the 
check to be deposited with each bid and the bond required, and specifying 
that the contractor shall give references and shall state what work of a 
similar character he has performed. A “Form of Bid” is also sometimes 
inserted. 

The specifications and contract are based upon the authors’ practice 
supplemented by a careful study of the reports of the Joint Committee on 
Concrete and Reinforced Concrete, the Reinforced Concrete Committee of 
the National Cement Users Association and the specifications of the Amei- 
ican Society for Testing Materials, of the American Railway Engineering 
& Maintenance-of-Way Association, of the City of Philadelphia, of the 


SPECIFICATIONS 


29 


United States Army, of the United States Navy, of the Massachusetts 
Metropolitan Commissions, of the New York Rapid Transit Commission, 
and others. 

BRIEF SPECIFICATIONS FOR PURCHASE OF CEMENT 

The cement shall be a first-class Portlandf cement of a standard brand 
bearing a good reputation. It shall conform to the standard specifications 
of the American Society for Testing Materials. It shall be free from lumps 
and shall be packed in sound barrels. J 

FULL SPECIFICATIONS FOR PURCHASE OF PORTLAND CEMENT 

1. Packages. Cement shall be packed in strong cloth or canvas sacks. § 
Each package shall have printed upon it the brand and name of the manu¬ 
facturer. Packages received in broken or damaged condition may be rejected 
or accepted as fractional packages. 

2. Weight. Four bags shall constitute a barrel, and the average net 
weight of the cement contained in one bag shall be not less than 94 lb. 
or 376 lb. net per barrel. A cement bag may be assumed to weigh one 
pound. The weights of the separate packages shall be uniform. 

3. Requirements.* Cement failing to meet the seven-day requirements 
may be held awaiting the results of the twenty-eight-day tests before rejec¬ 
tion. 

4. Tests.* All tests shall be made in accordance with the methods pro¬ 
posed by the Committee on Uniform Tests of Cement of the American 
Society of Civil Engineers, presented to the Society January 21, 1903, and 
amended January 20, 1904, with all subsequent amendments thereto. (See 
Chapter VII, page 63.) 

5. Sampling. Samples shall be taken at random from sound packages, 
one from every 10 barrels or 40 bags, and mixed. The total sample should 
weigh about 10 lb. 

6. * The acceptance or rejection shall be based on the following require 
ments: 

7. Definition of Portland Cement.* This term is applied to the finely 
pulverized product resulting from the calcination to incipient fusion of an 
intimate mixture of properly proportioned argillaceous || and calcareous^ 
materials, and to which no addition greater than 3 % has been made subse¬ 
quent to calcination. 

*Paragraphs designated by an asterisk are quoted from the Standard Specifications of the Amer¬ 
ican Society for Testing Materials. 

-j-Or Natural. 

Jlf stored in a dry place to be used immediately, it may be packed in stout cloth or canvas bags 
which are of course cheaper than barrels. 

§If the cement is to be stored in a damp place or near the sea, it must be packed in well- 
made wooden barrels lined with paper. 

IlClayey. ^Consisting chiefly of lime or calcium. 


30 


A TREATISE ON CONCRETE . 


8. Specific Gravity.* The specific gravity of cement shall not be 
lees than 3.10. Should the test of cement as received fall below this • 
requirement, a second test may be made upon a sample ignited at a 
low red heat. The loss in weight of the ignited cement shall not 
exceed 4%. 

9. Fineness.* It shall leave by weight a residue of not more than 8% on 
the No. 100, and not more than 25% on the No. 200 sieve. 

10. Time of Setting.* It shall not develop initial set in less than thirty 
minutes; and must develop hard set in not less than one hour nor more 
than ten hours. 

11. Tensile Strength.* The minimum requirements for tensile 
streng h for briquettes one square inch in cross section shall be as fol¬ 
lows, and the cement shall show no retrogression in strength within 
the periods specified: 


Neat Cement. 

Age 

24 hours in moist air. 

7 days (x day in air, 6 days in water) 
28 days (1 “ “ 27 “ “ ) 


Strength 

175 lb. 
coo “ 
600 “ 


One Part Cement, Three Parts Standard Ottawa Sand 
Age Strength 

7 days (1 day in moist air, 6 days in water). 200 lb. 

28 days (1 “ “ “ 27 “ “ ). 275 “ 

12. Soundness or Constancy of Volume.* Pats of neat cement about 
three inches in diameter, one-half inch thick at the center, and tapering 
to a thin edge, shall be kept in moist air for a period of twenty-four hours. 

(a) A pat is then kept in air at normal temperature, and observed at 

intervals for at least 28 days. 

(b) Another pat is kept in water maintained as near 70° Fahr. as 

practicable, and observed at intervals for at least 28 days. 

( c ) A third pat is exposed in any convenient way in an atmosphere of 

steam, above boiling water, in a loosely closed vessel for five 

hours. 

These pats to satisfactorily pass the requirements, shall remain firm and 
hard and show no signs of distortion, checking, cracking, or disintegration. 

I 3 - Sulphuric Acid and Magnesia. The cement shall not contain more 
than 1.75% of anhydrous sulphuric acid (S 0 3 ), nor more than 4% of 
Magnesia (MgO). 

♦Paragraphs designated by an asterisk are quoted from the Standard Specifications of the 
American Society for Testing Materials. 







SPECIFIC A TIONS 


FULL SPECIFICATIONS FOR THE PURCHASE OF NATURAL 

CEMENT 

1. Packages. Cement shall be packed in strong cloth or canvas sacks.*)* 
Each package shall have printed upon it the brand or the name of the 
manufacturer. Packages received in broken or damaged condition may 
be rejected or accepted as fractional packages. 

2. Weight. Three bags shall constitute a barrel, and the average net 
weight of the cement contained in one bag shall be not less than 94 lb., or 
282 lb. net per barrel. A cement bag may be assumed to weigh one pound. 
The weights of the separate packages shall be uniform. 

3. Requirements.* Cement failing to meet the seven-day requirements 
may be held awaiting the results of the twenty-eight day tests before re¬ 
jection. 

4. Tests.* All tests shall be made in accordance with the methods pro¬ 
posed by the Committee on Uniform Tests of Cement of the American 
Society of Civil Engineers, presented to the Society January 21, 1903, and 
amended January 20, 1904, with all subsequent amendments thereto. 
(See Chapter VII, p. 63.) 

5. Sampling. Samples shall be taken at random from sound packages, 
and the cement from each package shall be tested separately. 

6. * The acceptance or rejection shall be based on the following require¬ 
ments: 

7. Definition of Natural Cement.* This term shall be applied to the 
finely pulverized product resulting from the calcination of an argillaceous 
limestone at a temperature only sufficient to drive off the carbonic acid 
gas. 

8. Fineness.* It shall leave by weight a residue of not more than 10% 
on the No. 100, and 30% on the No. 200 sieve. 

9. Time of Setting.* It shall not develop initial set in less than ten 
minutes, and shall not develop hard set in less than thirty minutes, or in 
more than three hours. 

10. Tensile Strength.* The minimum requirements for tensile 
strength for briquettes one square inch in cross section shall be as fol¬ 
lows, and the cement shall show no retrogression in strength within 
the periods specified: 

*Paragraphs designated by an asterisk are quoted from the Standard Specifications of the 
American Society for Testing Materials. 

tlf the cement is to be stored in a damp place or near the sea, it must be packed in well-made 
wooden barrels lined with paper. 


3 2 


A TREATISE ON CONCRETE 


Neat Cement. 

Age Strength 

24 hours in moist air... 75 lb. 

7 days (1 day in air, 6 days in water) .150 “ 

28 days (1 “ “ 27 “ “ ) . 250 “ 

One Part Cement, Three Parts Standard Ottawa Sand. 

Age Strength 

7 days (1 day in air, 6 days in water). 50 lb. 

28 days (1 “ “ 27 “ “ ) 125 “ 

ii. Constancy of Volume.* Pats of neat cement about 3 inches in 
diameter, one-half inch thick at the center, and tapering to a thin edge, 
shall be kept in moist air for a period of 24 hours. 

(a) A pat is then kept in air at normal temperature. 

(b) Another pat is kept in water maintained as near 70° Fahr. as 

practicable. 

These pats are observed at intervals for at least 28 days, and, to satisfac¬ 
torily pass the tests, shall remain firm and hard and show no signs of 
distortion, checking, cracking, or disintegrating. 


CONTRACT AND SPECIFICATIONS FOR PORTLAND CEMENT 

CONCRETE^ 

(These specifications essentially embody the recommendations of the Joint Committee on 
Concrete and Reinforced Concrete (1900) and the Report of the Reinforced Concrete Com¬ 
mittee (1909) of the National Association of Cement Users.) 

This agreement made this day of.in the year 19. 

by o,nd between (Name of party letting the contract.) 

party of the first part, a n d ... ■ N ame of . ae b epted . c . on . tra .^ or ;A... .of. t 

party of the second part. 


Witnesseth: That the parties to these presents, each in consideration of 
the covenants and agreements on the part of the other, herein contained, 
have covenanted and agreed, and do hereby covenant and agree, for them¬ 
selves and their heirs, executors, administrators, and assigns, and under the 

^Paragraphs designated by an asterisk are quoted from the Standard Specifications of the 
American Society for Testing Materials. 

jFor Natural cement concrete paragraphs 1, 11 and 14 must be slightly altered, and paragraphs 
7 and 13c omitted. 














SPECIFIC A TIONS 


33 


penalty expressed in a bond bearing even date with these presents, and 
hereto annexed, as follows: 

The contractor shall begin work within..days of the date 

of this contract, and shall, at his own proper cost and expense, provide and 
deliver all of the materials and perform all of the work called for by these 
specifications, and supply all implements, apparatus, and appliances needed 
in performing the work. 

1 he entire work shall be completed on or before. 

19.* 

1. Gcmsnt.f The cement shall be first-class Portland cement of repu¬ 
table brand which shall conform in all respects to the cement specifications 
herewith annexed. The cement shall be stored in a building which will 
protect it from the weather. The floor upon which the cement is placed 
shall be at least 6 inches above the ground. It shall be stored so as to 
permit of easy access for inspection and identification of each shipment. 
A sufficient quantity shall be kept on hand at all times so that the Engineer 
may have opportunity and time to make tests sufficient to determine 
its quality. At least 12 days shall be allowed for inspection and necessary 
tests. 

2. Fine Aggregates. The fine aggregate shall consist of sand, crushed 
stone or gravel screenings passing when dry a screen having ^ inch diam¬ 
eter holes or a screen having four meshes to the linear inch. It shall be 
clean, coarse, and free from vegetable loam and other deleterious matter. 
A gradation of the size of grain is preferred. Mortars composed of one 
part Portland cement and three parts fine aggregate by weight when made 
into briquets shall show a tensile strength of at least 70% of the 
strength of 113 mortar of the same consistency made with the same cement 
and standard Ottawa sand. To avoid the removal of any coating on the 
grains which may affect the strength, bank sands shall not be dried before 
being made into mortar but shall contain natural moisture. The percent¬ 
age of moisture may be determined upon a separate sample for correct¬ 
ing weight. From 10 to 40% more water may be required in mixing 
bank or artificial sands than for standard Ottawa sand to produce the same 
consistency. 

*A premium and forfeiture clause may here be inserted, but a forfeiture clause without a pre¬ 
mium in many cases cannot be legally enforced. The word “penalty’’ should never be employed. 

fit is often advisable that the cement be furnished by the party letting the contract or, to pre¬ 
vent waste of cement, that it be sold by them to the contractor at an arbitrary price per barrel,—’ 
say, about one-half the actual cost of the cement,—which price must be definitely stated in the con¬ 
tract. 


* 





34 


A TREA T1SE ON CONCRETE 


3. Coarse Aggregates. The coarse aggregate shall consist of inert 
material such as crushed stone, or gravel, which is retained on a screen 
having f inch diameter holes. The particles shall be clean, hard, durable, 
and free from all deleterious material. Aggregates containing soft, flat, 
or elongated particles, should be excluded from reinforced concrete. A 
gradation of sizes of the particles is advantageous. The maximum size 
of the coarse aggregate shall be such that it will not separate from the 
mortar in laying and will not prevent the concrete fully surrounding the 
reinforcement or filling all parts of the forms. Where concrete is used in 
mass, the size of the coarse aggregate may be such as to pass a 3 inch ring. 
For reinforced concrete a size to pass a 1 inch ring or a smaller size may 
be used. 

4. Gravel.* The gravel shall be composed of clean pebbles free from 
sticks and other foreign matter and containing no clay or other material 
adhering to the pebbles in such quantity that it cannot be lightly brushed 
off with the hand or removed by dipping in water. It shall be screenedf to 
remove the sand, which shall afterwards be remixed with it in the required 
proportions. 

5. Broken Stone.* The broken or crushed stone shall consist of pieces 
of hard and durable rock, such as trap, limestone, granite, or conglomerate. 
The dust shall be removed by a sand screen, to be afterwards, if desired, 
mixed with and used as a part of the sand, except that if the product of the 
crusher is delivered to the mixer so regularly that the amount of dust, as 
determined by frequently screening samples, is uniform, the screening 
may be omitted and the average percentage of dust allowed for in measur¬ 
ing the sand. 

6. Water. The water shall be free from oil, acid, strong alkalies, or 
vegetable matter. 

7. Reinforcing Steel.*J Steel for reinforcement shall have an “ulti¬ 
mate tensile strength of 55,000 to 65,000 pounds per square inch, an elastic 
limit of not less than one-half the ultimate strength (i. e. not less than 27,000 
lb.) and a minimum elongation in 8 inches of 1,400,000 divided by the ulti- 

*Omit paragraphs for materials which are not used. If two or more sizes of any aggregate are 
used, define them. 

fin exceptional cases where the relation of pebbles to sand is very uniform, the mixture of sand 
and pebbles may be used without screening. Frequent tests shall then be made to see that the pro¬ 
portions of the coarse and fine grains are correct. 

JSpecifications for high carbon steel are given in full on page 38. High carbon steel is distrusted 
by many, but may be safely employed if it fulfills the requirements there given, and owing tc its 
greater strength will be more economical than ordinary merchant steel. 


SPECIFIC A TIONS 


35 


mate strength per cent.”* The fracture shall be silky Test specimens 
for bending shall be bent cold to i8o° flat without fracture. 

8. Proportions. The proportions of the raw materials for the concrete 
shall be exactly determined from time to time by the Engineer in accord¬ 
ance with the relative coarseness of the aggregate, so as to attain as dense 
a concrete as is consistent with the terms of the specifications which follow. 
The unit of measure shall be the barrel, which shall be taken as containing 
3.8 cubic feet. Four bags containing 94 pounds of cement each shall be 
considered the equivalent of one barrel. The following paragraphs desig¬ 
nate the average relative volumes of material for each class of work. 

For.f, one barrel (376 lb.) cement to . 

cubic feet sand| to ... .cubic feet broken stone ,X the cement to be measured 
as packed by the manufacturer, and the fine and coarse aggregate to be 
measured separately as loosely thrown into the measuring receptacle. If 
the coarse aggregate contains sand or other fine material, that which passes 
a sieve with \ inch round holes shall be considered as sand in measuring 
proportions. In general, the concrete on the work shall contain enough 
and only enough mortar to cover all particles of stone and fill the voids 
without an appreciable excess of mortar. 

9. Hand Mixing.§ If the concrete is mixed by hand, the cement and 
aggregate shall be mixed and the water added on a tight platform large 
enough to provide space for the partially simultaneous mixing of two batches 
of not more than one cubic yard each. The sand and cement shall be 
spread in thin layers and mixed dry until of uniform color. This mix¬ 
ture may be spread upon the layer of stone or the stone shoveled upon 
it before adding the water, or it may be made into a mortar before spread¬ 
ing it with the stone. In the former method the materials shall be turned 
at least three times,—in addition to the mixing of the sand and cement 
already mentioned, the water being added on the first turning,—and in 
addition to the shoveling from the platform to place or into the vehicle for 
transportation. In the latter method, that is, if the sand and cement are 
first made into a mortar, the mass of mortar and stone shall be turned at 
least twice. Whatever method is employed, the number of turnings shall 
be sufficient to produce a resulting loose concrete of uniform color and 


♦Suggested for structural steel by the Committee on Boston Building Laws of the Boston Society 
of Civil Engineers. 

-j-Insert a description of portion of structure. Repeat paragraph as required. 

Jlf other materials are selected for the aggregate alter the wording accordingly. 

§With an experienced contractor this paragraph may be abbreviated to substantially the form 
of the final sentence. 




3 6 


A TREATISE ON CONCRETE 


appearance, with the cement uniformly distributed through the mass, the 
stones thoroughly incorporated into the mortar and the consistency uniform 
throughout, thus producing a concrete uniform in color and homogeneous. 

10. Machine Mixing.* If the concrete is mixed in a machine mixer 
a machine shall be selected into which the materials, including the water, 
can be precisely and regularly proportioned, and which will produce a 
concrete of uniform consistency-and color with the stones and water thor¬ 
oughly mixed and incorporated with the mortar. 

n. Consistency, (a) A medium or quaking mixture of a tenacious, 
jelly-like consistency, which quakes on ramming, shall be used for ordinary 
mass concrete, such as foundations, heavy walls, large arches, piers, and 
abutments. 

(b) Wet or mushy concrete, so soft that it will flow when agitated, but 
not so wet as to produce a separation of the materials in transferring to 
the work, shall be used for rubble concrete, and for reinforced concrete, 
such as thin building walls, columns, doors, conduits, and tanks. 

12. Placing Concrete. Concrete shall be conveyed to place in such 
a manner that there shall be no distinct separation of the different ingredi¬ 
ents, or, in cases where such separation inadvertently occurs, the concrete 
shall be remixed before placing. It shall be placed in the work immediately 
after mixing and deposited and rammed or agitated by suitable tools in such a 
manner as to produce thoroughly compact concrete of maximum density. No 
concrete shall be placed until the reinforcing steel has been placed and firmly 
secured by wiring or other methods to prevent displacement. Concrete 
shall be frequently wet for several days to prevent too rapid drying out. 
Concrete shall not be placed in water, unless unavoidable. Where con¬ 
crete must be placed under water, unusual care must be taken to prevent 
the cement from being floated away. This usually can be accomplished 
in still water by placing the concrete through a large pipe or tube, or in 
large work by means of a bottom dump concrete bucket. 

Before placing fresh concrete, all shavings and debris of every nature 
must be removed and the old concrete surface thoroughly cleaned from 
all dirt and scum or laitance and drenched with w T ater.f Noticeable voids 
or stone pockets discovered when the forms are removed shall be filled 

♦Mixing by machine is preferred because the most thorough and uniform consistency can be 
thus obtained. 

j-Tanks and other structures having thin walls to resist water pressure should be built prefer¬ 
ably as monoliths, that is, with no interruption in the work, proceeding, if necessary, night and 
day. 


SPECIFICATIONS 


immediately with mortar mixed in the same proportions as the mortar in 
the concrete. The lines and grades of the completed concrete shall accurately 
conform to the plan annexed to and forming a part of these specifications. 

13. Placing Reinforcement. The reinforcement shall accurately con¬ 
form in the finished structure to the plans annexed to and forming a part 
of these specifications. All reinforcement shall be free from rust, scale or 
coating of any character which would tend to reduce or destroy the bond 
Before placing concrete the reinforcement must be placed in the position 
required in the finished structure, and each piece or member so firmly fixed 
as to positively prevent any subsequent displacement. 

14. Freezing Weather.* Concrete for reinforced concrete structures 
shall not be mixed or deposited at a freezing temperature, unless special 
precautions are taken to avoid the use of materials containing frost and to 
provide means for preventing the concrete from freezing after being placed 
in position and until it has thoroughly hardened. 

15. Forms. The lumber for the forms and the design of the forms 
shall be adapted to the structure and to the kind of surface required on th: 
concrete. For exposed faces the surface next to the concrete shall be dressed. 
Forms shall be substantially built and secured to prevent movement or 
deflection during concreting, and tight to prevent leakage of mortar. Before 
the removal of forms, the concrete shall be carefully inspected and its 
strength ascertained. Much care shall be given to this portion of the work, 
which is fraught with danger under incompetent direction. No exact time 
for the removal of forms can be safely prescribed because of the varying 
character of the work, the variations in the setting of different cements 
and the influence of atmospheric conditions. Forms shall be thoroughly 
cleaned before being used again. 

16. Joints. Temperature changes and shrinkage during setting neces¬ 
sitate joints at frequent intervals or else effective reinforcement, depending 
upon the range in temperature and the design of the structure. In massive 
work, such as retaining walls, abutments, etc., built without reinforcement, 
joints shall be provided approximately every 30 feet throughout the length 
of the structure. Girders shall never be constructed over freshly formed 
columns without allowing a period of at least two hours to elapse to permit 
settlement in the columns. Before resuming work the top of the column 
shall be thoroughly cleansed of foreign matter and laitance. To obtain 
tight joints between old and new concrete the old surface shall be roughened, 

♦Natural cement concrete must never he exposed to frost until thoroughly hard and dry. 


37 <* 


A TREATISE ON CONCRETE 


thoroughly cleaned of all foreign material and laitance or scum, drenched, 
and slushed with neat cement or a mortar not leaner than one part 
Portland cement to two parts fine aggregate. Joints in reinforced concrete 
shall be avoided when possible by casting the entire structure at one 
operation. In building construction, joints may be made in the columns 
flush with the lower side of the girders, and joints in members t>f a floor 
system in general shall be made at or near the center of the span. In all 
cases joints shall be at right angles to their surfaces. 

17a.* Ordinary Surface. Surfaces shall have no special treatment 
further than care in placing the concrete to avoid noticeable voids or ston 1 
pockets. Forms shall be wet (except in freezing weather) before placing 
the concrete against them. 

17 b.* Exposed Faces. Faces exposed to view shall be made smooth by 
thrusting a spade or chisel through the concrete close to the form to force 
back the large stones and prevent stone pockets. The forms shall be 
thoroughly wet or greased with crude oil before placing the concrete against 
them. On removal of the forms, surfaces shall be.t 

17c.* Mortar Surface. Moldings, cornices, and other ornaments re¬ 
quiring mortar surface, shall be formed by spreading plastic mortar upon 
the interior of finely constructed molds, just as the concrete is being laid. 

18. Construction Details. (Here may be placed descriptive para¬ 
graphs referring to special parts of the structure.) 

19. General Requirements. Imperfect work or materials, or work or 
materials which may become damaged from any cause before its acceptance, 
shall be properly replaced to the satisfaction of the Engineer. 

Foremen employed by the contractor shall be skilled in concrete mixing, 
and they shall receive and obey orders from the Engineer. 

No claims for extra work shall be allowed unless made in writing previous 
to its performance and signed by both parties or by their authorized repre¬ 
sentatives. 

In case of disagreement as to the meaning of the terms of the contract 
or as to the manner of its execution, one arbitrator shall be appointed by 
each party within one week after notification in writing by either party, 
and in case these cannot agree, a third arbitrator shall be selected by these 
two, and the decision of the majority of the arbitrators shall be final and 
binding on both parties. The cost of this arbitration shall be divided 
equally between the two parties to this contract. 


Select one or more paragraphs from 17a, 17b and 17c. 
•j-State kind of finish desired, see page 288. 



SPECIFICATIONS 


37^ 


20. Prices for Work. The following prices shall be paid to the con¬ 
tractor as full compensation for the furnishing and use of all materials and 
implements required on the work and for all labor. 

(Here shall be inserted all unit prices for all divisions of the work, or the 
lump sum for the entire work, or the lump sums for different divisions of 
the work, or for alternate proposals, followed by a paragraph stating the 
manner and time of payments and the amount withheld each month.) 

In witness whereof the parties to these presents have affixed their hand 

and seals this.day of., 19. 

Signed in the presence of 

.(Seal) 


(Seal; 


Bond to Accompany the Contract.* 
Know all men by these presents, That we 


as sureties, are held and firmly bound unto. 

in the sum of.dollars 

($.), to be paid said., for which 

payment, well and truly to be made, we bind ourselves, our heirs, executors 
and administrators, jointly and severally, firmly by these presents. 

The condition of this obligation is such, that if the above bounden 

heirs, executors, administrators or assigns, shall in all things stand to and 
abide by, and well and truly keep and perform, the covenants, conditions 
and agreements in the foregoing contract on his or their part to be kept and 
performed, at the time and in the manner therein specified, and shall in¬ 
demnify and save harmless the said. 

as therein stipulated, then his obligation shall become and be null and 
void; otherwise it shall be and remain in full force and virtue. 

I11 witness whereof we hereunto set our hands and seals on this. 

.day of.in the year nineteen 

hundred and. .(Seal) 

.(Seal) 

Signed and sealed in presence of . 


♦Form adopted by Metropolitan Commissioners, Mass. 
























38 


A TREA T1SE ON CONCRETE 


SPECIFICATIONS FOR FIRST CLASS STEEL TO BE USED IN 

REINFORCED CONCRETE * 


1. Process of Manufacture. Steel shall be made by the open hearth 

process. 

2. Chemical Properties. Steel shall conform to the following limits 
in chemical composition: 

Phosphorus shall not exceed 0.06. 

Sulphur shall not exceed 0.06. 

Manganese shall not exceed o.So or be below 0.40. 

3. Physical Properties. The steel shall conform to the following 
physical qualities: 

4. Tensile Tests. Tensile strength in pounds per square inch shall 

be not less than.85000 

Yield point in pounds per square inch shall be not less than 52500 

Elongation per cent, in eight inches shall be not less than.10 

5. For material less than live-sixteenths inch ( r V') and more than three- 
fourths inch (}") in thickness the following modifications shall be made 
in the requirements for elongation: 

(a) For each increase of one-eighth inch (|") in thickness above three- 
fourths inch (f") a deduction of one per cent. (1%) shall be made from 
the specified elongation. 

(h) For material from J inch to, but not including, T \ inch thick the 
elongation shall be 8%. 

For material from inch to, but not including, J inch thick the 
elongation shall be 7%. 

For material from -J- inch to, but not including, T 3 g inch thick the 
elongation shall be 6%. 

For material less than inch thick the elongation shall be 5% 

6. Bending Test. Test specimens for bendingf shall be bent cold to 
the following angles without fracture on the outside of the bent portion: 

Around twice their own diameter. Around their own diameter. 


For specimens 1 inch thick 8o°. 
For specimens f inch thick 90°. 
For specimens \ inch thick no°. 


For specimens J inch thick 130°. 
For specimens fV inch thick 140°. 
For specimens J inch thick 180°. 


♦Steel of this hardness should not be used unless enough of it is to be bought to warrant the 
making of complete tests as per specifications. Ordinary mild steel may be purchased in t’ e 
open market without specifications. In using steel bought in open market, it is not safe to count 
on a tensile strength oreater than 55,000 lb.— Frederick W. Taylor. 

fThe most important test of all is the bending test, but any soft steel will stand the bendin^ 
test, so that the tensile test is needed to secure a steel which is strong enough. 




SPECIFIC A TIG NS 


39 


No steel which fails to pass the bending test shall under any circum¬ 
stances be used. 

7. Test Pieces and Methods of Testing. Where practicable the 
standard test specimen of eight-inch (8") gaged length shall be used to 
determine the physical properties specified in paragraphs Nos. 4 and 5. 
The standard shape of the test specimen for sheared plates shall be as 
shown by the following sketch: 



For material from which it is impracticable to obtain test specimens 
like those for sheared plates, the test specimen may be pinned cr turned 

parallel throughout its entire length, and in all cases where possible two 

* 

opposite sides of the test specimen shall be the rolled surfaces. Small 
rolled bars of uniform section shall be tested full size as rolled. 

8. All test specimens shall be cut from the finished material as it 
comes from the rolls, unless such materials are to be annealed, in which 
case the test specimens will be taken after the annealing process. In case 
several shapes are rolled from one heat, two test specimens will be taken 
from two different shapes, representing their class, for tension, and two 
for bending. When only one shape is rolled from a heat, two test speci¬ 
mens for tension and two for bending will be taken from each ten tons 
or fraction thereof. 

9. Where practicable the bending test specimen shall be one and 
one-half inches (1 \") wide, and for material three-quarters inch (§") and 
less in thickness, this specimen shall have the natural rolled surface on 
two opposite sides. For material more than three-quarters inch (f") thick, 
the bending test specimen may be cut to one-half inch (|") thick. 

10. The bending test may be made by pressure or bv blows. 

11. In case a test specimen develops flaws or in case it breaks outside 
of the middle third of its gaged length, it may be discarded and another test 
specimen substituted therefor. 
































40 


A TREA T1SE ON CONCRETE 


12. For the purposes of this specification, the yield point shall be deter¬ 
mined by the careful observation of the drop of the beam, or halt in the 
gage, of the testing machine. 

13. In order to determine if the material conforms to the chemical 
limitations prescribed in paragraph No. 2 herein, analysis shall be made 
of clean drillings taken from a small test ingot. 

14. Variation in Weight. A variation in cross section or weight of 
more than 2\% from that specified will be sufficient cause for rejection. 

15. Finish. Finished material must be free from injurious seams, 
flaws, or cracks, and have a workmanlike finish. 

16. Annealing. All bars which, owing to their shape or size, are 
liable to be under strain after cooling, must be reheated to a temperature 
not less than 1250° (Fahrenheit) nor more than 1375 0 , and this heating 
and subsequent cooling must be done in an approved manner. 


THE CHOICE OF CEMENT 


4 '- 


CHAPTER IV 

THE CHOICE OF CEMENT 

When the construction under consideration is not of a grade to warrant 
the testing of different cements before making a selection, the question 
often arises as to whether, for example, Portland or Natural cement is 
most desirable from the standpoint of economy, or whether common lime 
or a mixture of lime and cement is suitable for the purpose. 

Although the decision must often depend upon local conditions, a few 
general rules may be formulated relating to the classes of construction for 
which different kinds of cement and lime are adapted, followed by illustra¬ 
tions of the methods for making a selection where there is a choice between 
two cements and between different brands of the same cement. 


THE CLASS OF CEMENT 

Portland Cement should be used in concrete and mortar for structures 
subjected to severe or repeated stresses; for structures requiring strength 
at short periods of time; for concrete building construction; for work laid 
under water or with which water will come in contact immediately after 
placing; for thin walls subjected to water pressure; for masonry exposed to 
wear or to the elements; and for all other purposes where its cost will be 
less than that of Natural cement concrete, or mortar of similar quality. 

Natural Cement may be substituted for Portland in concrete, if economy 
demands it, for dry unexposed foundations where the load in compression 
can never exceed, say, 75 lb. per square inch (5 tons per sq. ft.) and will 
not be imposed until three months after placing; for backing or filling in 
massive concrete or stone masonry where weight and mass are the 
essential elements; for sub-pavements of streets, and for sewer founda¬ 
tions. 

In mortar Natural cement is adapted for ordinary brickwork not sub¬ 
jected to high water pressure or to contact with water until, say, one month 
after laying, and for ordinary stone masonry where the chief requisite is 
weight and mass. 

. Natural cement concrete or mortar should never be allowed to freeze, 
should never be laid under water, in exposed situations, in columns, beams, 
floors or building walls, or in marine construction. 


42 


A TREATISE ON CONCRETE 


Mixtures of Portland and Natural Cements, unless mixed at the factory 

and sold as Improved Natural Hydraulic Cements, are not advised under 
any conditions. 

Sand Cement* is recommended by the United States Army Engineers 
for groutingf, and it is sometimes employed as a substitute for Natural 
cement. Its use in place of pure Portland cement is often worth investiga¬ 
tion and testing in combination with the aggregate. 

Puzzolan or Slag Cements are limited to certain proper uses by the 
engineer officers of the U. S. ArmyJ as follows: 

Puzzolan cement never becomes extremely hard like Portland, but 
Puzzolan mortars and concretes are tougher or less brittle than Portland. 

The cement is well adapted for use in sea water,§ and generally in all 
positions where constantly exposed to moisture, such as in foundations of 
buildings, sewers, and drains, and underground works generally, and in the 
interior of heavy masses of masonry or concrete. 

It is unfit for use when subjected to mechanical wear, attrition, or 
blows. It should never be used where it may be exposed for long periods 
to dry air, even after it has well set. It will turn white and disintegrate, 
due to the oxidation of its sulphides at the surface under such exposure. 

Hydraulic Lime, which has the property of setting under water, is extern 
sively employed on the continent of Europe, especially in France, when 
in the United States common lime would be used, and frequently in place 
of hydraulic cement. Beton-Coignet is a mixture of hydraulic lime with 
cement and sand. Candlot|| gives as the proportions most frequently em¬ 
ployed, i cubic meter (35.3 cu. ft.) sand, 125 to 150 kilograms (276 to 331 
lb.) lime, and 50 to 60 kilograms (no to 132 lb.) cement. Hydraulic 
lime is not manufactured in the United States. 

Common Lime is not suitable for a principal ingredient in concrete. 
It will not set in contact with water, sustain heavy loads, or resist wear. 

The use of lime mortar, in the building laws of some cities, is limited to 
chimney construction in frame buildings, while other cities permit its use 
in walls of all except fireproof buildings. The Boston building laws (1896) 
limit the stresses on brick laid in lime mortar to 7 tons per square foot. 

Lime and Natural Cement mortar is suitable for ordinary building 
brickwork, for light rubble foundations and for building walls. 

Lime and Portland Cement mortar is adapted for the same purposes 

*See page 48. 

•^Professional Papers No. 28. 

^Professional Papers No. 28. 

§See Chapter XVI, by R. Feret. 

||Ciments et Chaux Hydrauliques, 1898, p. 289. 


THE CHOICE OF CEMENT 43 

as mortars of lime and Natural cement, but are of superior quality and 
strength. 

Hydrated Lime* is preferable to common lime paste or putty for use 
with Portland cement, because if properly manufactured it is more thor¬ 
oughly slaked and is easily handled and measured. 

Choice Determined by Cost. — When the character of the structure 
admits of either Portland or Natural cement, the choice is based upon the 
relative cost, which, in turn, is dependent upon the proportions that may 
be adopted in either case. The sand in Portland cement mortar is usually 
limited, by practical considerations of handling with the trowel, to propor¬ 
tions 1:3 in some instances and to 1: 4 in others, while the most common 
proportions for Natural cement mortar are 1: 2, that is, one part cement to 
two parts sand, by volume. 

The relative cost, after assuming the proportions of the two substitute 
classes of mortar, is governed primarily by the quantity of cement in a 
cubic yard of mortar. For example, from table on page 229, 3.32 bbl. 
of cement (based on a barrel of 3.8 cu. ft.) are required per cubic yard of 
1:2 mortar, while 2.48 bbl. are required for 1:3 mortar. Hence, if a 
decision lies between 1: 2 Natural mortar and 1: 3 Portland mortar, and 
the smaller item of quantity of sand is disregarded, the mortar produced 
from Natural cement at $1.00 per barrel will cost the same as that produced 

from Portland cement at (fi.ooX = $^34 per barrel. Similarly, 

2.48 

since 1:4 mortar requires 1.98 bbls. of cement per cubic yard, Portland 
cement mortar one part cement to 4 parts sand is equivalent in cost to 1: 2 
Natural cement mortar when Natural cement is $1.00 per barrel and 

3.32 

Portland cement is ($1.00 X-)== $1.68 per barrel; that is, when Port- 

1.98 

land cement delivered on the job costs 68% more than Natural cement. 
Allowance for difference in quantity of sand brings the Portland values still 
lower, as shown in the table on page 45. With Portland and Natural ce¬ 
ment mortars of equal cost, the Natural cement produces brickwork of 
lower cost because, a fact usually overlooked in estimates, a bricklayer can 
lay in a given time about 10% more brick with Natural cement mortar 
of proportions 1: 2 than with Portland cement mortar of proportions, 
say, 1:3. 

From the results of the comparatively few available tests, Portland 
cement concrete at the age of six months appears to be at least three times 

♦See S. Y. Brigham in Engineering News , Aug. 27, 1903, p. 177, and Charles Warner in 
Rock Products, Feb., 1904, p. 26. 




44 


A TREATISE ON CONCRETE 


as strong as Natural cement concrete in the same proportions, while at 
earlier periods the ratio is still larger. Since Portland cement concrete 
mixed i: 2: 4 is only about ij times stronger than a 1:4: 8 Portland mixture, 
it is very evident that the choice between Portland and Natural cement 
for concrete is determined, as in mortars, by practical considerations 
other than relative strength. 

The following elementary example illustrates the method of estimating 
the comparative cost of Portland and Natural cement concrete: 

Example. — What price can be paid per barrel for Portland cement to 
make a concrete 1: 4: 8 of equivalent cost to a 1: 2: 4 Natural cement con¬ 
crete, if Natural cement costs $1.00 per barrel, sand $0.75 per cubic yard, 
and stone havin'g 45% voids $1.50 per cubic yard? 

Solution. — By reference to the table of quantities of materials on page 
17, we find that the 1:2:4 Natural concrete will cost per cubic yard for 
materials only: 


1.57 barrels cement at $1.00.$1.57 

0.44 cubic yards sand “ 0.7c. 0.33 

0.88 “ “ stone “ 1.50. 1.32 

Total materials.$3.22 


The sand and stone for the 1:4:8 Portland mixture will cost, on the other 
hand, per cubic yard of concrete: 


0.48 cubic yards sand at $0.75.$0.36 

0.96 “ “ stone “ 1.50. 1.44 

Cost of sand and stone.$1.80 


Subtracting $1.80 from $3.22 leaves a difference of $1.42 which may be 
paid for the Portland cement in one cubic yard of concrete, and since by 
the quantity table 0.85 barrels of cement are required for a cubic yard of 
1: 4: 8 concrete, the price for the Portland cement may be $1.42 -f- 0.85 = 
$1.67 per barrel. 

If the Natural cement had cost $1.25 per barrel, the price which could 
have been paid for Portland would have been approximately 25% 
higher or $2.09 per barrel. 

This determination may be expressed in a formula: 

am-\-bn-\- cr — (b'nA-c'r) 

x= - 

a' 

in which a , b, and c represent respectively the quantities of cement, sand, 
and stone required for a cubic yard of the Natural cement concrete, and 
m, n, and r their respective unit costs, while a', b', and c' represent similar 










THE CHOICE OF CEMENT 


45 


quantities for the Portland cement concrete, and x the required price per 
barrel of the Portland cement. 

The following table is made out on this basis. 


Prices of Portland Cement to produce Mortar or Concrete of equal cost to that from 
Natural Cement at $1.00 per barrel. (See p. 44.) 


. 1 

Proportions of Natural 
Cement Mortar 

PROPORTIONS OF PORTLAND CEMENT 

MORTAR. 

Proportions of Natural 
Cement Concrete. 

PROPORTIONS OF PORTLAND 

CEMENT CONCRETE. 

I: I 

$ 

i: *4 

i: 2 

$ 

1:2$ 

1 '• 3 

i: 3i 

1:4 

1:2:4 

1 : 2 4: 5 

1:3:6 

1:4:8 

I: 5 :i ° 

$ 

$ 

$ 

$ 

$ 

s 

$ 

$ 

$ 

$ 

1: 1 

I.OO 

1.23 

1.46 

1.69 

1.92 

2.15 

2.38 

1:2:4 

1.00 

I * I 5 

1 - 3 2 

1.67 

2.01 

1 '• 


T.OO 

1.18 

I *37 

I *55 

1.74 

1.92 



1.00 

1.14 

1.44 

1.72 

1: 2 



1.00 

i-i 5 

1.30 

1.46 

1.61 

r: 3: 6 



1.00 

1.26 

1 * 5 I 

i: 2| 




1.00 

1 - 1 3 

1.26 

i -39 







I: 3 





1.00 

1.12 

1.23 








Note. —When the Natural cement is higher or lower than $1.00 per barrel, multiply its cost by the 
figures in the table to obtain approximate corresponding cost of Portland cement with which it is com¬ 
pared. Values make no allowance for difference in strength or labor of laying mortar. 


The equivalent prices for Portland cement in mortars will be still nearer 
the price for Natural if allowance is made for the difference in the labor of 
laying brick, which in some cases may correspond to a difference of 30 
cents per barrel of cement. It is evident from the table that for mortar 
Portland can rarely be substituted for Natural cement without increasing 
the cost of the work. A field still open for investigation is the employment 
as a substitute for Natural cement of Portland cement mixed with slaked 
lime or hydrated lime. The lime is so finely divided that it fills the voids 
and thus permits the use of more sand. 

SELECTION OF THE BRAND 

A precise comparison of costs of different brands of the same class of 
cement is impossible without thorough laboratory tests, described in 
Chapter VII, page 63. If the choice lies between two cements both of 
which have been found to be sound (see p. 77) and to set up properly, the 
degree of fineness, which may be readily ascertained with two sieves as 
described on page 67* is an aid to the decision. The finer cement will 

usually produce the stronger mortar. 

The cheapest cement is not always the most economical. A method of 
the relative economy of cements offered b\ bidders at different 
prices is illustrated in the following table for which the authors are indebted 






































A TREATISE ON CONCRETE 


16 


to Mr. D. M. Andrews. Ten brands of Portland cement were submitted 
to the Government at prices ranging from $2.77 to $3.29.* Experiments 
showed that sample No. 5 was the strongest, with No. 4 a close second. 
The relative strength of the different brands in proportions 1:3, based 
on the strongest as 100.0, is given in the column headed Relative Strength 
of Mortar, and the column following this gives the product of the relative 
strength multiplied by the relative cheapness. In the case under consider¬ 
ation brand No. 5 was selected for purchase, because, although No. 4 
gave higher economy, it appeared slightly unsound. Other data with 
reference to each brand was observed, including the volumes of the barrels, 
their gross net weights, the percentages of water used in mixing the pastes 
and mortar, the time of setting of the mortar, and the strength and relative 
economy of mortars with sand proportioned to price of cement, that is, for 
example, using 19% more sand with cement No. 10 than with No. 1, because 
the former’s price was 19% greater. 

*The price of Portland cement has since been materially lowered. 


Relative Economy oj Different Priced Portland Cements. 
By D. M. Andrews. 


No. of Sample Barrel. 

PRICE 

PER 

BARREL. 

Relative cheapness. 

V 

FINENESS. 

TIME 

OF 

SETTING 

TENSILE STRENGTH. 

§Relative 
Strength of 

1:3 Mortar 

Relative Econo¬ 
my 1:3 Mortar. 
Strength X 
Cheapness- 

REMARK 1 ' 

INITIAL. 

FINAL. 

NEAT. 

1:3 

MORTAR. 

No 50 
sieve. 

No. 100 
sieve. 

Hours. 

Hours. 

7 days. 

30 days. 

60 days. 

7 days. 

30 days. 

60 days. 

60 days. 

60 days. 

I 

$ 2.77 

100.0 

93-3 

87.6 

2 

8 

324 

437 

43 ° 

66 

128 

168 

79-7 

79-7 


2 

2.79 

99-3 

99-3 

8 7-3 

n 

8t 

282 

429 

468 

62 

103 

124 

59 -i 

58.7 


3 

2.82 

98.2 

98.2 

89.7 

2 

3r 

272 

373 

431 

35 

6 5 

87 

41.2 

40.5 

f Air pat 

4 

2.82 

98.2 

100.0 

99.6 

5 

9 1 

369 

460 

564 

144 

184 

209 

99.4 

97-7 

< cracked very 

5 t 

2.89 

95 - 8 

99.0 

86.2 

7 i 

74 

74 

449 

543 

631 

114 

175 

2 IO 

100.0 

95-8 

1 slightly. 

6 

2.9O 

95-5 

94.6 

77.0 

4 

G 

I 5 ° 

227 

264 

25 

57 

9 C 

42.8 

40.9 

ILumpy rnd 
1 grittv on 

7 

2-93 

94-5 

100.0 

90.0 

4 

8 

440 

588 

568 

127 

i5 6 

2 02 

96.2 

90.9 

mixing. 

8 

3-° 2 

91.7 

99-5 

89.4 

2 i 

7 

418 

476 

56x 

89 

i34 

J 74 

82.4 

75 - 6 


9 

3-°5 

90.8 

9 8 -5 

91.2 

3 h 

71 

436 

5i8 

502 

93 

126 

144 

68.2 

62.0 

Jrats crack c 
| slightly. 

iO 

3- 2 9 

84.2 

99.4 

92.7 

2 h 

5 

365 

49 6 

573 

78 

117 

141 

67.1 

56.5 



tAccepted in preference to No. 4 because air pat slightly defective. 
% Cement not yet set. 

§ Based on the highest, No. 5, as 100.0. 




















































CLASSIFICATION OF CEMENTS 


47 


CHAPTER V 

CLASSIFICATION OF CEMENTS. 

From an engineering standpoint, limes and cements may be classified as 
Portland cement. 

Natural cement. 

Puzzolan cement. 

Hydraulic lime. 

Common lime. 

Typical analyses of each of these are presented in the following table 
The composition of Natural cement, even different samples of the same 
brand, is so extremely variable that their analyses cannot be regarded as 
characteristic of locality. 


Typical Analyses of Cements. 



PORTLAND 

CEMENT 



NATURAL CEMENT 


Puzzolan Cement 7 

Hydraulic Lime 
(Le Tiel) 8 

COMMON LIME 

Lehigh Valley 1 
(mixed rock) 

Western 2 
(marl and clay) 

AMERICAN 

engl’h 

FRENCH 

a 

CD 

E 

3 

O 

X 

£ 

c 

.2 

*55 

<L> 

a 

to 

S 

Eastern 

Rosendale 3 

Western 

Louisville 3 

'T' 

a 

a 

£ 

0 

& 

Vassy 5 

Grappiers 6 

Silica Si O2 

21.31 

21.93 

18.38 

20.42 

25.48 

22.60 

26.5 

28.95 

21.70 

1.03 


1.12 

Alumina AI2 O3 

6.89 

5-98 




4.76 

10.30 

8.90 

2-5 

I 1.40 

3 -i 9 



c 68 





15-201 








• 1 . 27 - 



Iron Oxide Fe 2 O3 

2-53 

2-35 

_ 



3-40 

7-44 

5-30 

i-5 

0.54 

0.66 




Calcium Oxide Ca O 

62.89 

62.92 

35-84 

46.64 

44-54 

52.69 

63.0 

50.29 

60.70 

97.02 

58.51 

Magnesian Oxide Mg O 

2.64 

1.10 

14.02 

12.00 

2.92 

X-I5 

I .O 

2.96 

0.85 

0.68 


30.69 

Sulphuric Acid S O3 

i -34 

i -54 

0-93 

2-57 

2.61 

3-25 

o -5 

i -37 

0.60 




Loss on Ignition 

1-39 

2.91 

3-73 

6-75 

3-68 

6.11 

5 -o 

3-39 

12.20 




Other constituents 

0-75 


11.46 

3-74 

1.46 



0.30 

0.10 





! W. F. Hillebrand, Society of Chemical Industry, igo2, Vol. XXI. 

2 W. F. Hillebrand, Journal American Chemical Society, 1903, 25, 1180. 

3 Clifford Richardson. BrickbuilJer. 1897, p. 229. 

4 Stanger& Blount, Mineral Industry, Vol. V, p. 69. 

5 Candlot, Ciments et Chaux Hydrauliques, 1898, p. 174. 

6 Le Chatelier, Annales des Mines, September and October, 1893, p. 36. 

7 Report of the Board of U. S. Army Engineers on Steel Portland Cement, 1900, p. 52. 
8 Candlot, Ciments et Chaux Hydrauliques, 1898, p. 24. 

9 Rockland-Rockport Lime Co. 

10 Western Lime and Cement Co. 














































4 8 


A TREATISE ON CONCRETE 


PORTLAND CEMENTt 

Portland cement is defined by Mr. Edwin C. Eckel of the U. S. 
Geological Survey as follows: “By the term Portland cement is to be 
understood the material obtained by finely pulverizing clinker produced by 
burning to semi-fusion an intimate artificial mixture of finely ground 
calcareous and argillaceous materials, this mixture consisting approxi¬ 
mately of 3 parts of lime carbonate to i part of silica, alumina and iron 
oxide.” 

The definition is often further limited by specifying that the finished 
product must contain at least 1.7 times as much lime, by weight, as of silica, 
alumina, and iron oxide together. 

The only surely distinguishing test of Portland cement is its chemical 
analysis and its specific gravity. (See pp. 64 and 65.) In the field it may 
often be recognized by its cold bluish gray color (see p. 113), although 
the color of Puzzolan and of some Natural cements is so similar that this 
is by no means a positive indication. 

The term Natural Portland Cement arose from the discovery in Bou¬ 
logne-sur-Mer, France, as early as 1846, of a natural rock of suitable com¬ 
position for Portland cement. A similar discovery in Pennsylvania gave 
rise to the same term in America, but the manufacturers soon found it 
necessary to add to the cement rock a small percentage of purer limestone. 
Since the chemical composition of Portland cement, as defined above, is 
substantially uniform regardless of the materials from which it is made, 
in the United States the terms “natural” and “artificial” are meaningless. 

In France, cements intermediate between Roman and Portland are 
called “natural Portlands.”* 

Sand Cement. Sand or silica cement is a mechanical mixture of Port¬ 
land cement with a pure, clean sand very finely ground together in a 
tube mill or similar machine. For the best grades the proportions of 
cement to sand are 1:1, although as lean a mixture as 1:6 has been made 
to compete with Natural cements. The coarser particles in any Portland 
cement have little cementitious value, hence if a portion of the cement is 
replaced by inert matter and the whole ground extremely fine, its advocates 
maintain that the product is scarcely inferior to the unadulterated article. 
As made in the United States, the mixture is ground so fine that 95% of it 
will pass through a sieve having 200 meshes to the linear inch, and all of 
the 5% of residuum is said to be sand. In other words, all of the cement 
passes a No. 200 sieve. . 

4 A sub-classification of Portland cement is presented on page 53. 

* Candlot’s Ciments et Chaux Hydrauliques, 1898, p. 164. 


CLASSIFICATION OF CEMENTS 


49 


NATURAL CEMENT 

Natural cement is “made by calcining natural rock at a heat below 
incipient fusion, and grinding the product to powder.”* Natural cement 
contains a larger proportion of clay than hydraulic lime, and is consequently 
more strongly hydraulic. Its composition is extremely variable on account 
of the difference in the rock used in manufacture. 

Natural cements in the United States in Numerous instances bear the 
names of the localities where first manufactured. For example, Rosendale 
cement, a term heard in New York and New England more frequently 
than Natural cement, was originally manufactured in Rosendale, Ulster 
County, N. Y. Louisville cement first came from Louisville, Ky. 
The James River, Milwaukee, Utica, and Akron are other Natural 
cements named for localities. 

The United States produces a few brands of “Improved Natural Hy¬ 
draulic Cement,” intermediate in quality between Natural and Portland, 
by mixing inferior Portland cement with Natural cement clinker. 

In England the best known Natural cement is called Roman cement. 
Occasionally one hears the term Parker’s Cement, so called from the name 
of the discoverer in England. 

LE CHATELIER’S CLASSIFICATION OF NATURAL CEMENTS 

In France there are several classes of Natural cement. Mr. H. Le 
Chatelierf classifies Natural cements as those obtained “by the heating of 
limestone less rich in lime than the limestone for hydraulic lime. They 
may be divided into three classes: 

“ Quick-setting cements, such as Vassy and Roman (Ciments a 
prise rapide, Vassy, romain); 

“Slow-setting cements (Ciments a prise demi-lente); 

“ Grappiers cement (Ciments de grappiers). 

“Vassy Cements are obtained by the heating of limestone containing 
much clay, at a very low temperature, just sufficient to decarbonate 
the lime. They are characterized by a very rapid set, followed afterwards 
by an extremely slow hardening, much slower than that of Portland ce¬ 
ments.” 

“They differ from Portland cements by containing a much higher per¬ 
centage of sulphuric acid, which appears to be one of their essential ele¬ 
ments, and a much lower percentage of lime. 

♦Professional Papers, No. 28, U. S. Army Engineers, p. 33. 

fProcedes d’Essai des Materiaux Hydrauliques, Annales des Mines, 1893. 


5o 


A TREATISE ON CONCRETE 


“ Slow-Setting Cements, by the high temperature of calcination, 
approach Portland cements, but the natural limestones never possess 
the homogeneity of artificial mixtures, so that it is impossible to avoid 
in these cements the presence of a large quantity of free lime.” The 
composition of these products varies from that of the Vassy cements to 
that of the real Portlands. 

“ Grappiers Cements* are obtained by the grinding of particles which 
have escaped disintegration in the manufacture of hydraulic limes. These 
grappiers are a mixture of four distinct materials, two of which, com¬ 
pletely inert, are unburned limestone and the clinkers formed by contact 
with the siliceous walls of furnaces, and two of which, strongly hydraulic, 
are unslaked lime and true slow-setting cement. It is necessary that 
the latter should predominate in the grappiers for their grinding to give 
a useful product. The grappier of cement is obtained regularly only 
by the heating of a limestone but slightly aluminous and containing 
about three equivalents of carbonate of lime for one of silica; its pro¬ 
duction necessitates a heating at high temperature. 

“These grappiers cements are even more apt to contain free lime than 
the Natural cements of slow set which are obtained by the heating of lime¬ 
stone containing much more alumina. Because of their constitution, also, 
the grappiers cements may vary greatly in composition since they are 
produced by the grinding of a mixture of grains of cement and of various 
inert materials. The cement grains have very nearly the composition 
of tricalcium silicate (Si 0 2 3 CaO).” 

PUZZOLAN OR SLAG CEMENT 

Puzzolan cement is the product resulting from mixing and grinding 
together in definite proportions slaked lime and granulated blast furnace 
slag or natural puzzolanic matter (such as puzzolan, santorin earth, or 
trass obtained from volcanic tufa). 

The ancient Roman cements belonged to the class of Puzzolans. They 
were made by mechanically mixing slaked lime with natural puzzolana 
formed from the fusion of natural rock found in the volcanic regions of 
Italy. In Germany, trass, a volcanic product related to Puzzolan, has 
been used with lime in the manufacture of cements. 

Blast furnace slag is essentially an artificial puzzolana, formed by the 
combustion in a blast furnace, and the puzzolan or slag cements of the 
United States are ground mixtures of granulated blast furnace slag, of 
special composition, and slaked lime. 

♦Cements essentially of the Grappiers class in the United States are termed “ Non-Staining 
Cements.” These may closely approach Portland cement in strength. 


CLASSIFICATION OF CEMENTS 


5i 

A Board of Engineers officers, U. S. A., presented in 1901 the following 
conclusions,* based, undoubtedly, on the exhaustive studies upon the sub¬ 
ject made by a previous Board| having the same chairman, Major W. L. 
Marshall: 

This term (slag or Puzzolan cement) is applied to cement made by in¬ 
timately mixing by grinding together granulated blast-furnace slag of a 
certain quality and slaked lime, without calcination subsequent to the 
mixing. This is the only cement of the Puzzolan class to be found in our 
markets (often branded as Portland), and as true Portland cement is now 
made having slag for its hydraulic base, the term “ slag cement ” should 
be dropped and the generic term Puzzolan be used in advertisements and 
specifications for such cements. 

Puzzolan cement made from slag is characterized physically by its light 
lilac color; the absence of grit attending fine grinding and the extreme 
subdivision of its slaked lime element; its low specific gravity (2.6 to 2.8) 
compared with Portland (3 to 3.5); and by the intense bluish green color 
in the fresh fracture after long submersion in water, due to the presence 
of sulphides, which color fades after exposure to dry air. 

The oxidation of sulphides in dry air is destructive of Puzzolan cement 
mortars and concretes so exposed. Puzzolan is usually very finely ground, 
and when not treated with soda sets more slowly than Portland. It 
stands storage well, but cements treated with soda to quicken setting be¬ 
come again very slow setting, from the carbonization of the soda (as well 
as the lime) element after long storage. 

Puzzolan cement properly made contains no free or anhydrous lime, 
does not warp or swell, but is liable to fail from cracking and shrinkage 
(at the surface only) in dry air. 

Mortars and concretes made from Puzzolan approximate in tensile 
strength similar mixtures of Portland cement, but their resistance to 
crushing is less, the ratio of crushing to tensile strength being about 6 to 
7 to 1 for Puzzolan, and 9 to n to 1 for Portland. On account of its 
extreme fine grinding Puzzolan often gives nearly as great tensile strength 
in 3 to 1 mixtures as neat. 

Puzzolan permanently assimilates but little water compared with Port¬ 
land, its lime being already hydrated. It should be used in comparatively 
dry mixtures well rammed, but while requiring little water for chemical 
reactions, it requires for permanency in the air constant or continuous 
moisture. 

Puzzolanic material has been suggested by Dr. Michaelis, of Germany, 
and Mr. R. Feret, of France (see Chapter XVI), as a valuable addition 
to Portland cement designed for use in sea water. 

♦Professional Papers No. 28, p. 28. 

f Re port of the Board of U. S. Army Engineers on Steel Portland Cement, 1900, p. 52. 


5 2 


A TREATISE ON CONCRETE 


HYDRAULIC LIME 

The hydraulic properties of a lime, — its ability to harden under water, 
— are due to the presence of clay, or, more correctly, to the silica contained 
in the clay. Hydraulic lime is still used to quite an extent in Europe, 
especially in France, as a substitute for hydraulic cement. The celebrated 
lime-of-Teil of France is a hydraulic lime. 

Mr. Edwin C. Eckel states* that “ theoretically the proper composition 
for a hydraulic limestone should be calcium carbonate 86.8%, silica 13.2%. 
The hydraulic limestones in actual use, however, usually carry a much 
higher silica percentage, reaching at times to 25%, while alumina and iron 
are commonly present in quantities which may be as high as 6%. The 
lime content of the limestones commonly used varies from 55% to 65%,.” 

Although the chemical composition of hydraulic lime is similar to Port¬ 
land cement, its specific gravity is much lower, lying between 2.5 and 2.8.f 

In the manufacture of hydraulic lime the limestone of the required com¬ 
position is burned, generally in continuous kilns, and then sufficient water 
is added to slake the free lime produced so as to form a powder without 
crushing. 

COMMON LIME 

The commercial lime of the United States is “quicklime,” which is 
chiefly calcium oxide (CaO). 

Lime is now manufactured by a continuous process. limestone of a 
rather soft texture, so as to be as free as possible from silica, iron and 
alumina, is charged into the top of a kiln which may be, say, 40 ft. high 
by 10 ft. in diameter. The fuel is introduced into combustion chambers 
near the foot of the shaft, and the finished product is drawn out from time 
to time through another opening in the bottom of the shaft. The tempera¬ 
ture of calcination may range from 1400° Fahr. (760° Cent.) to, at times, 
2,000° Fahr. (1,090° Cent.). The product (see analysis, p. 47), in ordi¬ 
nary lime of the best quality, is nearly pure calcium oxide (CaO). Upon 
the addition of water the lime slakes, forming calcium hydrate (CaH 2 0 2 ), 
and, with the continued addition of ivater, increases in bulk to twice 
to three times the original loose and dry volume of the lump lime 
as measured in the cask. In this plastic condition it is termed by 
plasterers “puttyor “paste.” 

The setting of lime mortar is the result of three distinct processes 
which, however, may all gc on more or less simultaneously. First, it 

* American Geologist , March, 1902, p. 152. 
fCandlot’s Ciments et Chaux Hydrauliq ues, 1898, p. 26. 


CLASSIFICATION OF CEMENTS 


53 


dries out and becomes firm. Second, during this operation, the calcic 
hydrate, which is in solution in the water of which the mortar is made, 
crystallizes and binds the mass together. Hydrate of lime is soluble in 831 
parts of water at 78° Fahr; in 759 parts at 32 0 and in 1136 parts at 140°. 
Third, as the per cent, of water in the mortar is reduced and reaches five 
per cent., carbonic acid begins to be absorbed from the atmosphere. If 
the mortar contains more than five per cent, this absorption does not go 
on. While the mortar contains as much as 0.7 per cent, the absorption 
continues. The resulting carbonate probably unites with the hydrate of 
lime to form a sub-carbonate, which causes the mortar to attain a harder 
set, and this may finally be converted to carbonate. The mere drying 
out of mortar, our tests have shown, is sufficient to enable it to resist 
the pressure of masonry, while the further hardening furnishes the neces¬ 
sary bond.* 

9 

Magnesian Limes evolve less heat when slaking, expand less, and set 
more rapidly than pure lime. A typical analysis is given on page 47. 

Hydrated Lime is the powdered product formed by slaking quick 
lime with the requisite amount of water. The material as it comes into 
commerce is a very finely divided white powder, and if properly prepared 
contains no unhydrated particles of lime. 

SUB-CLASSIFICATION OF PORTLAND CEMENTS 

In addition to the gray-colored cements for ordinary uses, Portland 
cements are made from raw materials low in iron so as to produce a light- 
colored cement, and also from raw materials low in aluminum and high in 
iron to produce a cement which better resists the action of sea water. 1 his 
leads to a sub-classification suggested by Mr. Eckel. I he distinction is 
somewhat arbitrary, since the classes grade into each other, while normal 
Portlands vary in the relative proportions of iron and alumina. 

(1) Normal Portlands. Containing, with the silica and lime, both alumina 
andiron oxide in appreciable quantity; usually fromqtoio per cent alumina 
with 1.5 to 5 per cent iron oxide. Product: the ordinary gray-colored 
commercial cement. 

(2) Low Iron Portlands. Containing relatively high alumina, with only 
1 per cent or less of iron oxide. Product; white or very light colored, quick 

setting, usually low in tensile strength. 

(3) High Iron Portlands. Containing relatively high iron, with less 
than 2 per cent of alumina. Product: slow setting, high tensile strength in 
long time tests,, resistant to sea and alkaline waters. 

* The authors are indebted to Mr. Clifford Richardson for this paragraph. 


54 


A TREATISE ON CONCRETE 


CHAPTER VI 

CHEMISTRY OF HYDRAULIC CEMENTS* 

BY SPENCER B. NEWBERRY 

INTRODUCTION 

Hydraulic cements are compounds consisting chiefly of lime, silica, and 
alumina, which have the property, when mixed to a paste with water, of 
hardening to a stone-like mass. They may be classified as follows: 

1. Portland cement, made by calcining at high heat an artificial mixture 
of carbonate of lime and clay or slag, in exactly correct proportions, and 
grinding the resulting clinker to powder. 

2. Natural cement, made by burning at low heat limestone containing 
excess of clay and usually much magnesia, and grinding the product to 
powder. 

3. Hydraulic lime, obtained by burning limestone containing a small 
amount of clay, slaking by sprinkling with water, and bolting the product. 

4. Puzzolan or slag cement, consisting of a mixture of certain kinds of 
volcanic scoria, or of blast furnace slag, and slaked lime, ground together. 

Each of these classes of cement shows peculiar qualities, and each may 
have advantages for certain purposes. Puzzolan cement is that used by 
the Romans, and many striking examples of its durability are seen in 
ancient structures. Slag cement, a mechanical mixture of slag and slaked 
lime, is made to a considerable extent in this country, and finds extended 
use for mortar and in work in which the greatest strength and hardness are 
not required. Hydraulic lime is made chiefly in France, and is but little 
known in the United States. Natural cement is manufactured on a vcrv 
large scale from limestones containing a large proportion of clay. It is 
usually quick-setting, and the better qualities gain very good strength at 
long periods. Owing to its cheapness it is extensively used, chiefly as 
mortar for brickwork and masonry. All these earlier hydraulic materials, 
however, have gradually given way before the advance of Portland cement, 
as this product has been improved in quality and manufactured on a con¬ 
stantly increasing scale. 

Portland cement was first made in England in 1827, and named from the 

*The authors are indebted to Mr. Newberry for this chapter, which has been especially pre¬ 
pared by him for this Treatise. 


CHEMISTRY OF HYDRAULIC CEMENTS 


55 

resemblance in color of the hardened cement to the building stone quarried 
at the Island of Portland. 

MATERIALS* 

As above stated, hydraulic lime and natural cements are made by burning 
natural limestones containing suitable amounts of clay. Portland cement, 
on the other hand, is made from an artificial mixture of materials, of ex¬ 
actly correct composition. Limestones containing clay are of frequent 
occurrence. If a deposit of stone containing exactly the right amount of 
clay, and of exactly uniform composition, could be found, Portland cement 
could be made from it simply by burning and grinding. For good results, 
however, the composition of the raw material must be exact , and the pro¬ 
portion of carbonate of lime in it must not vary even by one per cent. No 
natural deposit of rock of exactly this correct and unvarying composition 
is known or likely ever to be found; therefore Portland cement is always 
made from an artificial mixture, usually, if free from organic matter, con¬ 
taining about 75% carbonate of lime and 25% clay. 

For the manufacture of Portland cement the materials chiefly used are 
limestone, chalk or marl, and clay. In southeastern Pennsylvania and 
western New Jersey occurs an unlimited deposit of cement rock , which 
consists of a slate-like limestone containing usually rather more clay than 
is required for a correct mixture. This is largely used for Portland cement 
manufacture, and is generally ground with a small amount of purer lime¬ 
stone to bring it to correct composition. At some of the factories in that 
section a correct mixture is obtained by grinding together, in suitable pro¬ 
portions, the upper and lower layers of the quarry. In the Central States, 
pure limestone, or marl (a soft and finely divided form of carbonate of 
lime) and clay, are the materials employed. Whatever the materials used, 
the first stage of the process is the preparation of an intimate and finely 
ground mixture of carbonate of lime and clay, of a certain definite compo¬ 
sition, and if this is accomplished the resulting cement will be the same, 
whatever the original materials may have been. Success in Portland 
cement manufacture depends, more than upon all other features of the 
process, in extremely fine grinding of the raw materials. Most of the 
faults found in inferior Portland cement are due to neglect in this regard. 
Either the wet or dry process may be used in preparing the mixture. The 
material is then dried and calcined at white heat, generally in revolving 
cylindrical kilns, from which it issues in the form of small, black, rounded 
fragments of clinker. By grinding this clinker to fine powder the finished 
Portland cement is obtained. 

*The materials for cement and the manufacture of cement are also treated in Chapter NXX. 


5 6 


A TREATISE ON CONCRETE 


Magnesia in Portland cement, beyond a small percentage, has generally 
been considered objectionable. But little positive evidence on this point 
is, however, available. A committee of the German Portland Cement 
Manufacturers Association, many years ago, reported that magnesia up to 
8 per cent, is harmless. Dyckerhoff, a member of the committee, presented 
a minority report stating that he had found more than 4 per cent, injurious. 
The subject was referred to another committee, in 1896, but this committee 
laid out a program of work which proved impracticable to complete, and 
nothing further has been accomplished. Van Blaese, in the Tlionindus- 
triezeitung, 1899, page 213, published a long series of tests of cements con¬ 
taining variable proportions of magnesia, which show that cement contain¬ 
ing 8 per cent, is faultless, while that containing 15 per cent, is defective. 
The writer has made a similar series of experiments and has found that 
properly prepared cement with 9 per cent, magnesia passes the boiling test 
perfectly, while that with 15 per cent, magnesia shows expansion* cracks 
after several hours boiling. Comparative tests of tensile strength and 
expansion of bars of these cements, over long periods, are now in progress. 
From the evidence now available it appears that the presence of magnesia 
up to 8 per cent., in a properly prepared Portland cement, is no disadvan¬ 
tage. > 

Sulphate of lime, in quantities exceeding about 2 per cent., is objectionable 
in the raw material, owing to liability of reduction to sulphide, causing the 
cement to turn dark blue in hardening and to give poor tests, especially 
with sand. This fault is more frequent with cement burned in vertical 
kilns than in those of the rotary type, since the former are more liable to 
imperfect draft and consequent reducing action. 

Clay for Portland cement manufacture should be highly siliceous and 
practically free from coarse sand. Siliceous clays, in which the silica i$ 
from 2.5 to 3.0 times the sum of alumina and iron oxide, give mixtures 
which stand the high heat of the kiln without fusing, produce a clinker 
which is comparatively easy to grind, and yield slow-setting cements which 
show steady gain in strength over long periods. More aluminous clays 
give hard, fusible clinker and quick-setting cement, and are in many re¬ 
spects troublesome to use. Highly aluminous cements are believed to be 
especially severely attacked by sea water. 

Alkalies (potash and soda) appear to exert very little influence, in the 
small amounts present in ordinary clays, on the character of burning or 
quality of the resulting cement. Excess of alkalies is. believed to make 
cement unsound. 


CHEMISTRY OF HYDRAULIC CEMENTS 

PROPORTION OF INGREDIENTS 


57 


Although Portland cement has been manufactured since 1827, definite 
rules for proportioning the ingredients have only lately been established, 
and are yet by no means generally accepted. In Germany it has been 
customary to adjust the ingredients, as recommended by Michaelis, so that 
the “hydraulic modulus,” the ratio by weight of lime to silica, alumina 
and iron oxide, shall be from 1.8 to 2.2. It has, however, become gen¬ 
erally recognized by cement chemists that much more lime combines with 
silica than with alumina or iron oxide. The “hydraulic modulus” is 
therefore a variable, and must be much higher in the case of siliceous 
materials than with those high in alumina and iron. 

A clear explanation of the composition of Portland cement clinker was 
first given by Le Chatelier in 1887. From microscopic examination of 
clinker and hardened cement he came to the conclusion that the chief 
constituent of Portland cement is tri-calcium silicate, 3Ca0.Si0 2 , which 
is the active element in the hardening. This tri-silicate is produced by 
chemical precipitation from a mass of a multiple silico-aluminate which 
serves as a vehicle for the silica and lime and permits their combination, 
but remains inert during the hardening. Le Chatelier stated that the lime 
and magnesia in Portland cement should not exceed a maximum, 

CaO + MgO , N 

- 5 -<3 (1) 

Si 0 2 +A 1 2 0 3 

nor be less than a minimum, 

CaO + MgO (2) 

Si 0 2 —A 1 2 0 3 — Fe 2 0 3 — A 

These formulas represent chemical equivalents and not weights. 

The best brands of modern Portland cement approach pretty closely to 
the above maximum formula, while one corresponding to the minimum 
formula would be so greatly over-clayed as to be practically useless. 

The hardening of cement, according to Le Chatelier, consists in the de¬ 
composition of the tri-silicate by water, with the formation of crystalline 
calcium hydrate and hydrated mono-silicate. 

Since the publication of the above researches the constitution of clinker 
and hardened cement have been investigated by numerous experimenters, 
and a great number of new theories have been propounded. It cannot be 
said, however, that any of Le Chatelier’s important statements have been 
disproved, nor that any material advance has been made upon the theory 
which he proposed. At the present time Portland cement clinker is re- 




A TREATISE ON CONCRETE 


58 

garded by nearly all cement chemists as a crystalline mass of tri-calcium 
silicate, imbedded in a non-crystalline magma consisting of a fusible com¬ 
pound of silica and lime with practically all the alumina and iron oxide. 

Le Chatelier’s formulas are inconvenient in form and incomprehensible 
except to those familiar with chemical formulas. The writer published in 
1897 {Journal 0} the Society of Chemical Industry, Nov. 30, 1897) a paper 
on the constitution of hydraulic cements, containing an account of a series 
of experiments based on the work of Le Chatelier. It was found that the 
maximum of lime which could be brought into combination to produce a 
sound cement is three molecules for each molecule of silica present, and 
two molecules for each molecule of alumina. The composition of cement 
containing the maximum of lime would therefore be expressed by the for¬ 
mula 

X( 3 Ca 0 .Si 0 2 ) + Y( 2 Ca 0 .Al 2 0 3 ) (3) 

It is understood that this formula is merely empirical, representing the 
relative proportions present, since the aluminate remains for the most part 
in the magma in combination with part of the silica and with other sub¬ 
stances. 

Substituting weights for equivalents, the above formula may be expressed 
as follows: 

Lime = silica X 2.8 + alumina X 1.1. 

It should be remembered that this formula represents the maximum of 
lime which a Portland cement, burned in the usual manner, may contain 
without showing unsoundness. This maximum can be reached only by 
extremely fine grinding of the raw material. This formula, also, by no 
means represents the composition of finished cement, since the ash of the 
fuel lowers the lime and raises the silica and alumina, above that calcu¬ 
lated from the raw material, by at least 2 per cent. 

In the laboratory, using gas as fuel, it will be found practicable to prepare 
sound cements corresponding to the above formula. In actual manufac¬ 
ture it is safer to reduce the lime slightly, to counterbalance possible defec¬ 
tive grinding of raw material or unavoidable variations in composition. 
It will be found that the raw material at factories where the best Portland 
cements are made rarely falls below the composition, 

Lime = silica X 2.7 + alumina X 1.0. (4) 

This may be taken as a safe practical formula for commercial use. 
With fine grinding of the raw material it will invariably yield sound cements, 


CHEMISTRY OF HYDRAULIC CEMENTS 


59 


while the use of a lower proportion of lime will be likely to produce quick¬ 
setting cement, low in tensile strength. As already explained, commercial 
cements are considerably lower in lime, owing to change in composition 
produced by the fuel-ash. 

The writer’s experiments have shown that magnesia forms with clay no 
products having hydraulic properties It should therefore be disregarded 
in calculating cement mixtures, the composition of which should be calcu¬ 
lated on the basis of the silica, alumina and lime only, without regard to 
the magnesia present. Iron oxide, also, in the quantities usually met with 
in ordinary clays, plays an insignificant part so far as the proportions of 
the constituents are concerned, and may be disregarded in the calculation. 

As a practical example of the use of the above formula, let us suppose 
that we wish to make cement from limestone and clay of the following 
composition: 



Limestone 

Clay 

Lime. 

Z2.6 

2.2 

Magnesia .. 

0.7 

1.0 



Silica . 

X.2 

6 s *4 

•\himina.. 

1.0 

16. z 

Tron 0 \-irle ...... 

cm 

6.1 

1 nss on ignifion } etc. ..._ ............................... 

42 2 

7-9 


100.0 

100.0 


The silica and alumina in the limestone will require 
3.2 X 2.7 + 1.0 = 9.6% lime, leaving 52.6 — 9.6 = 43-0% li me avail¬ 
able for combination with clay. 

The silica and alumina in 100 parts clay will require 
65.4 X 2.7 + 16.5 X 1.0 = 193.1 parts lime. Subtracting the lime con¬ 
tained in the clay we have 

— 2.2 = 190.9 parts lime required for 100 parts clay. 

As the 100 parts stone contain 43 parts available lime, that amount of 
stone will require 

43 X 100 

-- =22.5 parts clay. 


190.Q 






















30 A TREATISE ON CONCRETE 

The composition of the charge and of the resulting cement may be tabu¬ 
lated as follows: 



100 

STONE 

22 .5 

CLAY 

122.5 

MIX ' 

78.52 

CEMENT 

100 

CEMENT 

Lime... 

52.60 

O.5O 

53 -i° 

53 -i° 

67.63 

Magnesia. 

O.7O 

•43 

I * I 3 

i-i 3 

1.44 

Silica... 

3.20 

14.71 

47 *9 1 

17.9 1 

22.8l 

Alumina. 

I.OO 

3 - 7 i 

4.71 

4.71 

6.00 

Iron Oxide. 

O.3O. 

i -37 

1.67 

1.67 

2.12 

Loss, etc... 

42.20 

1.78 

43 - 9 8 

.... 

.... 


100.00 

22.50 

122.50 

CO 

100.00 


As stated above, the ash of the fuel will change the composition of the 
resulting cement materially; analysis of the product, burned with coal, will 
probably show about 65 per cent, lime and perhaps 24 per cent, silica. 
This fuel-ash is, however, not uniformly distributed through the product, 
but attaches itself chiefly to the surfaces of the clinker. It is not, therefore, 
found practicable to materially raise the proportion of lime to counter¬ 
balance the silica and alumina of the ash. 

It will be noted that in the above calculated analysis of raw mixture and 
cement the 

Lime—alumina 

-= 2.7 

silica 

The writer proposes to call this figure the lime jactor of the mixture. 
Adoption of this factor will give cements of practically maximum quality 
with any materials, whether siliceous or aluminous, provided the mix is 
finely ground and properly burned. Owing to the influence of the ash of 
the fuel, as above explained, the factor of finished cements will be found 
about 0.2 lower than that of the raw material. The best commercial ce¬ 
ments generally show a factor of 2.5 to 2.6, though made from mixtures 
with a factor of 2.7 to 2.8. 

The following analyses, taken from a paper by the writer in Cement and 
Engineering News , November, 1901, show the influence of the fuel-ash on 
the composition of the clinker. The samples of clinker were taken one 




























CHEMISTRY OF HYDRAULIC CEMENTS 61 

hour later than those of raw material, since the passage through the kiln 
required about one hour. 


Lehigh Portland Cement Co ., Allentown, Pa. 



Mix 

Clinker, 
calculated 
from mix 

Clinker 

found 

Si 0 2 . 

14*33 

4 * 3 2 

1.46 

42.69 

1.81 
35*14 

22.18 

6.68 

2.26 

66.08 

2.80 

• • • • 

22.96 

6.78 

2*54 

^ 3*95 

2.94 

AI2O3. 

FC2O3... 

CaO. 

MgO and SO3. 

Loss. 

Factor AI2O3 

99*75 

100.00 

2.68 

99.17 

2.49 

SiCL 


Sandusky Portland Cement Co., Syracuse, Ind. 


• 

Mix 

Clinker, 
calculated 
from mix 

Clinker 

found 

SiOo . 

13 * 5 ° 

3*43 

1.27 

40.76 

3*27 

3 8 * 3 ° 

22.02 

5.6° 

2.07 

66.49 

3.82 

22-33 

5*53 

3.28 

64.40 

3.61 

AI2O3................................... ..... 

FeoOo . 

CaO. 

MgO and SO3. 

Loss. 

Factor CaO — AI2O3 

100.53 

100.00 

2.76 

99* I 5 

2.63 

Si 0 2 


Comparison of the above analyses of mix and clinker shows how greatly 
the ash of the fuel affects the composition. In commercial cement a still 
further reduction in the proportion of lime is caused by the addition of 
gypsum and the absorption of moisture and carbonic acid from the air. 
It will be readily seen, therefore, that analysis of finished cement gives but 
little indication of the true proportion of ingredients or of the quality of the 
product. 






















































62 


A TREATISE ON CONCRETE 


EFFECT OF COMPOSITION ON QUALITY 

Too high proportion of lime (lime factor of mix above 2.8) will give a 
slow-setting cement which will fail in the boiling test. If the excess of lime 
is great, pats of cement kept in cold water will show radial expansion 
cracks at the edges after a certain time, perhaps even within a few’ days. 
The same defects result from imperfect grinding of the raw material , and 
are far more often due to this cause than to excess of lime. Cement which 
is unsound and shows expansion from either cause may be improved and 
perhaps made sound by storage or by exposure to air. It is not, how r ever, 
safe to rely greatly on this remedy. Lack of soundness is in all cases due 
to faulty manufacture, since well-burned cement made from suitably pre¬ 
pared raw material will invariably pass all soundness tests when fresh from 
the grinding mills. Consumers are advised to accept no cement which 
fails to pass a reasonable boiling test, as they w r ill thus err, if at all, on the 
safe side, and will influence careless manufacturers to improve their pro¬ 
cess. 

Too low proportion of lime, giving an over-clayed mixture, produces a 
fusible clinker, liable to overburning. This is especially the case w r ith 
aluminous materials. If hard-burned, such mixtures give a fused clinkei 
liable to fall to dust on cooling, hard to grind, and yielding skrvv-setting 
cement of poor hardening properties. If light-burned, an over-clayed mix¬ 
ture yields soft brownish clinker, grinding to a brownish, quick-setting 
cement of inferior strength. 

Overburning rarely occurs except with over-clayed mixtures or in conse¬ 
quence of the fluxing action of the fuel-ash or the brick lining of the kiln 
Properly proportioned mixtures stand a very high heat without injury 

Underburning, as stated above, in the case of an over-clayed mixture, 
yields quick-setting and weak cement. Normal mixtures, when under¬ 
burned, usually give cement w r hich fails in soundness tests. Light burning 
is generally indicated by heating of the cement on mixing with v’ater. 
This behavior generally accompanies quick setting, and may be so marked 
as to be quite apparent to the touch of the fingers. Some cements, though 
slow-setting when first made, become very quick-setting on storage. Cases 
are on record in which this change has taken place within a few days. 
After longer periods the original slow-setting quality may return. The 
cause of this phenomenon has not been determined; it may be said, how¬ 
ever, that troubles of this class, including quick setting and heating will 
water, are especially characteristic of cements made from aluminous ma¬ 
terials. 


STANDARD CEMENT TESTS 


63 


CHAPTER VII 

STANDARD CEMENT TESTS 

The tests which are regarded as most suitable for the selection and ac 
ceptance of cement for important concrete construction are as follows: 

Chemical analysis. 

Specific gravity. 

Fineness. 

Activity, or time of setting. 

Tensile strength of neat cement and sand mortars. 

Soundness or constancy of volume. 

The French Commission* in 1893, in addition to these tests, gave 
standard rules for testing weight, homogeneity (with the microscope), 
compressive strength, bending strength, yield of paste and mortar (rende- 
ment), porosity, permeability, decomposition, and adhesion, one or more 
of which tests may be desirable under certain conditions. As these are 
usually of minor importance, however, special mention of them is reserved 
for the following chapter. 

In unimportant construction it is often safe to use a first-class American 
Portland cement without testing, and in other cases the test for soundness 
is the only one which need be actually made. Under almost all circum¬ 
stances, however, when purchasing cement, full specifications (see Chapter 
III, p. 28) are advisable, so that if the cement does not work satisfactorily 
it may be more carefully examined and unused portions rejected. 

In this chapter are presented, in addition to the description of the methods 
of making cement tests, complete lists of apparatus for a large and a small 
laboratory (p. 80), formulas and tables for determining the quantity of 
water in cement mortars (p. 85), comparisons of American and European 
practice in cement testing, a discussion of the causes of unsoundness and 
the results of soundness tests (p. 101), curves showing the growth in strength 
of typical cements and cement mortars (p. 99), and other information with 
reference to the qualities and testing of Portland cement. 

STANDARD METHODS OF CEMENT TESTING 

The following recommendations for testing are reprinted, with comments 
by the authors, from the preliminary or Progress Report of Special Com- 

*Commission des Methodes d’Essai des Materiaux de Construction, 1894, Vol. 1, p. 235. 


A TREATISE ON CONCRETE 


64 

mittee on Uniform Tests of Cement of the American Society of Civil 
Engineers,* as presented in 1903 and amended in 1904 and 1909. I he 
methods are designed particularly for the testing of Portland cement, but 
are applicable to Natural (and also to Puzzolan), with the exception of para¬ 
graphs 5, 6, 68, (2), 71, and 74. 

The standards which should be attained by first-class Portland and 
Natural cements are presented in the Standard Specifications in 
Chapter III, page 28. 

Sampling. 1. Selection oj Sample. — The selection of the sample for 
testing is a detail that must be left to the discretion of the engineer; the 
number and the quantity to be taken from each package will depend largely 
on the importance of the work, the number of tests to be made and the 
facilities for making them. 

2. The sample shall be a fair average of the contents of the package; it 
is recommended that, where conditions permit, one barrel in every ten be 
sampled. 

3. Samples should be passed through a sieve having twenty meshes per 
linear inch, in order to break up lumps and remove foreign material; 
this is also a very effective method for mixing them together in order to 
obtain an average. For determining the characteristics of a shipment of 
cement, the individual samples may be mixed and the average tested; where 
time will permit, however, it is recommended that they be tested separately. 

4. Method of Sampling. — Cement in barrels should be sampled through 
a hole made in the center of one of the staves, midway between 
the heads, or in the head, by means of an auger or a sampling iron 
similar to that used by sugar inspectors. If in bags, it should be 
taken from surface to center. 

A sampling iron is illustrated in Fig. 8. 

With the usual packing of Portland cement, four bags to the 
barrel, one bag in forty is equivalent to one barrel in ten. 
There is no necessity because of the smaller size of the packages 
for testing a larger proportion of the total weight. 

The practice of mixing samples taken from a number of 
packages is by many authorities not considered advisable except 
for the purpose, suggested above, “of determining the charac- 
of a shipment.” A mixture of samples will not reveal 
irregularities in quality. 

Chemical Analysis. 5. Significance. — Chemical analysis may render 
valuable service in the detection of adulteration of cement with considerable 

*Proceedings, January, 1907. 



Fig. 8. 

Sampling 

Iron. 

(See p. 64.) 

teristics 







STANDARD CEMENT TESTS 


65 

Amounts of inert material, such as slag or ground limestone. It is of use, 
also, in determining whether certain constituents, believed to be harmful 
when in excess of a certain percentage, as magnesia and sulphuric anhy¬ 
dride, are present in inadmissible proportions. 

6. The determination of the principal constituents of cement — silica, 
alumina, iron oxide and lime — is not conclusive as an indication of quality. 
Faulty character of cement results more frequently from imperfect prepara¬ 
tion of the raw material or defective burning than from incorrect proportions 
of the constituents. Cement made from very finely ground material, and 
thoroughly burned, may contain much more lime than the amount usually 
present and still be perfectly sound. On the other hand cements low in 
lime may, on account of careless preparation of the raw material, be of 
dangerous character. Further, the ash of the fuel used in burning may so 
greatly modify the composition of the product as largely to destroy the sig¬ 
nificance of the results of analysis. 

7. Method. — Asa method to be followed for the analysis of cement, that 
proposed by the Committee on Uniformity in the Analysis of Materials for 
the Portland Cement Industry, of the New York Section of the Society for 
Chemical Industry, and published in Engineering News, Vol. 50, Page 60, 
1903, and The Engineering Record, Vol. 48, Page 49, 1903, is recom¬ 
mended.* 


An exceedingly simple test for determining adulteration with raw or 
partially burned rock, is the treatment of the cement with muriatic acid 
as described in the purity test on page 4. It does not furnish the 
percentage of foreign ingredients, but the black precipitation of the 
adulterant darkens the color of the yellow jelly to a degree depending 
upon the quantity of adulteration. 

Specific Gravity. 8. Significance. — The specific gravity of cement is 
lowered by adulteration and hydration, but the adulteration must be 
in considerable quantity to affect the results appreciably. 

9. Inasmuch as the differences in specific gravity are usually very small, 
great care must be exercised in making the determination. 

10. Apparatus and Method. — The determination of specific gravity is 
most conveniently made with Le Chatelier’s apparatus. This consists of a 
flask (D), Fig. 9, of 120 cu. cm. (7.32 cu. in.) capacity, the neck of which 
is about 20 cm. (7.87 in.) long; in the middle of this neck is a bulb (C), 
above and below which are two marks (F) and (E); the volume between 
these marks is 20 cu. cm. (1.22 cu. in.). The neck has a diameter of about 
9 mm. (0.35 in.), and is graduated into tenths of cubic centimeters above 

the mark (E). 

11. Benzine (62° Baume naphtha), or kerosene free from water, should 
be used in making the determination. 

♦Printed in Appendix I of this Treatise. 


66 


A TREATISE ON CONCRETE 


12. The specific gravity can be determined in two ways: 

(i) The flask is filled with either of these liquids to the lower mark (E), 
and 64 grams (2.25 oz.) of powder, cooled to the temperature of the liquid, 
is gradually introduced through the funnel ( B) [the stem of which extends 
into the flask to the top of the bulb (C)], until the upper mark (F) is reached. 


B 



Fig. 9. —Le Chatelier’s Specific Gravity Apparatus. {See p. 65.) 


The difference in weight between the cement remaining and the original 
quantity (64 g.) is the weight which has displaced 20 cu. cm. 

13. (2) The whole quantity of the powder is introduced, and the level 
of the liquid rises to some division of the graduated neck. This reading 
plus 20 cu. cm. is the volume displaced by 64 grams of the powder. 

14. The specific gravity is then obtained from the formula: 


Specific Gravity = 


Weight of Cement in grams 
Displaced Volume, in cubic centimeters 


































































































































































































STANDARD CEMENT TESTS 


67 

x 5- The hask, during the operation, is kept immersed in water in a jar 
(A), in order to avoid variations in the temperature of the liquid. The 
results should agree within 0.01. The determination of specific gravity 
should be made on the cement as received; and should it fall below 3.10, a 
second determination should be made on the sample ignited at a low red heat. 

16. A convenient method for cleaning the apparatus is as follows: The 
flask is inverted over a large vessel, preferably a glass jar, and shaken ver¬ 
tically until the liquid starts to flow freely; it is then held still in a vertical 
position until empty; the remaining traces of cement can be removed in a 
similar manner by pouring into the flask a small quantity of clean liquid 
and repeating the operation. 

r 7. More accurate determinations may be made with the picnometer. 

The usual specific gravities of different classes of cement are given on 
page 81. 

Le Chatelier’s apparatus, suggested above as most convenient, was also 
recommended by Mr. E. Candlot after experiments for the French Com¬ 
mission,* in which he employed for comparison the Mann, Keate, Schu¬ 
mann, and Candlot, as well as the Le Chatelier apparatus. 

Mr. Daniel D. Jacksonf has more recently devised an apparatus 
with which temperature corrections can be made more readily than with 
the older types. 

Fineness. 18. Significance. — It is generally accepted that the coarser 
particles in cement are practically inert, and it is only the extremely fine 
powder that possesses adhesive or cementing qualities. The more finely 
cement is pulverized, all other conditions being the same, the more sand it 
will carry and produce a mortar of a given strength. 

19. The degree of final pulverization which the cement receives at the 
place of manufacture is ascertained by measuring the residue retained on 
certain sieves. Those known as the No. 100 and No. 200 sieves are recom¬ 
mended for this purpose. 

20. Apparatus. — The sieves should be circular, about 20 cm. (7.87 in.) 
in diameter, 6 cm. (2.36 in.) high, and provided with a pan, 5 cm. (1.97 in.) 
deep, and a cover. 

21. The wire cloth should be of brass wire having the following diameters: 

No. 100, 0.0045 xn d No. 200, 0.0024 in. 

22. This cloth should be mounted on the frames without distortion; the 
mesh should be regular in spacing and be within the following limits: 

No. 100, 96 to 100 meshes to the linear inch. 

No. 200, 188 to 200 “ “ 

23. Fifty grams (1.76 oz.) or 100 g. (3.52 oz.) should be used for the test, 
and dried at a temperature of ioo° Cent. (212 0 Fahr.) prior to sieving. 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 15. 

•fSee Engineering Record, July 16, 1904, p. 82. 


68 


A TREATISE ON CONCRETE 


24. Method. — The Committee, after careful investigation, has reached 
the conclusion that mechanical sieving is not as practicable or efficient as 
hand work, and, therefore, recommends the following method: 

25. The thoroughly dried and coarsely screened sample is weighed and 
placed on the No. 200 sieve, which, with pan and cover attached, is held in 
one hand in a slightly inclined position, and moved forward and backward, 
at the same time striking the side gently with the palm of the other hand, 
at the rate of about 200 strokes per minute. The operation is continued 
until not more than one-tenth of 1% passes through after one minute of 
continuous sieving. The residue is weighed, then placed on the No. 100 
sieve and the operation repeated. The work may be expedited by placing 
in the sieve a small quantity of large steel shot. The results should be 
reported to the nearest tenth of 1 per cent. 

Laboratorv scales for weighing the samples and the residue are illus¬ 
trated in Fig. 10. 


Fig. 10.—Delicate Laboratory Scales. (See p. 68.) 

A table is given on page 84 for comparing American and European 
sieves, and the effect of the fineness of cement upon its strength is discussed 
on page 82. 

It is impracticable to sift cement through a sieve finer than 200 meshes 
per linear inch. The particles which will just pass a No. 200 sieve are 
about 0.10 millimeter (0.004 in.) in diameter*. For still further sepa¬ 
rating the cement, some method based on the principle of suspension in 
liquid is employed as described on page 85. 

Normal Consistency. 26. Significance. — The use of a proper percent¬ 
age of water in making the pastesj* from which pats, tests of setting and 
briquettes are made, is exceedingly important, and affects vitally the results 
obtained. 

27. The determination consists in measuring the amount of water re¬ 
quired to reduce the cement to a given state of plasticity, or to what is 
usually designated the normal consistency. 

28. Various methods have been proposed for making this determination, 
none of which has been found entirely satisfactory. The Committee 
recommends the following: 

*Allen Hazen in Report Massachusetts State Board of Health, 1892. 

•(•The term “ paste ” is used in this report to designate a mixture of cement and water, and 
the word “mortar” a mixture of cement, sand and water. 


























STANDARD CEMENT TESTS 


69 

29. Method. Vicat Needle Apparatus. — This consists of a frame {K) x 
Fig. ii, bearing a movable rod (L), with the cap (. 4 ) at one end, and at the 
other the cylinder (B), 1 cm. (0.39 in.) in diameter, the cap, rod and cylinder 
weighing 300 grams (10.58 oz.). The rod, which can be held in any desired 
position by a screw (F), carries an indicator, which moves over a scale 
(graduated to centimeters) attached to the frame (K). The paste is held 
by a conical, hard-rubber ring (/), 7 cm. (2.76 in.) in diameter at the base, 
4 cm. (1.57 in.) high, resting on a glass plate (/), about 10 cm. (3.94 in.) 
square. 

30. In making the determination the same quantity of cement as will be 
subsequently used for each batch in making the briquettes (but not less 
than 500 grams) (17.64 oz.) are kneaded into a paste, as described in Para¬ 
graph 58, and quickly formed into a ball with the hands, completing the 



Fig. ii.—V icat Needle. (See p. 69.) 


operation by tossing it six times from one hand to the other, maintained 
6 in. apart; the ball is then pressed into the rubber ring, through the larger 
opening, smoothed off, and placed (on its large end) on a glass plate and 
the smaller end smoothed off with a trowel; the paste, confined in the ring, 
resting on the plate, is placed under the rod bearing the cylinder, which is 
brought in contact with the surface and quickly released. 

317 The paste is of normal consistency when the cylinder penetrates to a 




























































































































7 ° 


A TREATISE ON CONCRETE 


point in the mass io mm. (0.39 in.) below the top of the ring. Great care 
must be taken to fill the ring exactly to the top. 

32. The trial pastes are made with varying percentages of water until 
the correct consistency is obtained. 

33. The Committee has recommended, as normal, a paste, the consist¬ 
ency of which is rather wet, because it believes that variations in the amount 
of compression to which the briquette is subjected in molding are likely 
to be less with such a paste. 

34. Having determined in this manner the proper percentage of water 
required to produce a paste of normal consistency, the proper percentage 
required for the mortars is obtained from an empirical formula. 

35. The Committee hopes to devise such a formula. The subject proves 
to be a very difficult one, and, although the Committee has given it much 
study, it is not yet prepared to make a definite recommendation. 

Formulas of Mr. R. Feret for determining the percentage of water for 
sand mortars, and an approximate table, are presented on pages 86 and 88. 

The Boulogne Method for determining the proper consistency of neat 
paste was formerly in general use in France, and is still the best guide for 
determining the correct consistency of paste when the Vicat apparatus is 
not available. The Vicat needle, however, should be included in every 
well equipped cement laboratory, experiments by Messrs. P. Alexandre 
and R. Feret for the French Commission* showing that it gives much more 
uniform results than the Boulogne method. 

The Boulogne method requires that the paste shall be firm but well 
bonded, shining and plastic, and shall satisfy the following conditions: 

1. The consistency shall not change if it is worked 3 minutes longer 
than the original 5 minutes.j* 

2. If dropped 50 centimeters (20 in.) from a trowel, it should leave 
the trowel clean, and fall without losing its shape or cracking. 

3. Light pressure in the hand should bring water to the surface, and 
the paste should not stick to the hand. If a ball thus formed falls from 
a height of about 50 centimeters (20 in.) it should retain its rounded form 
without showing cracks. 

4. The proportion of water should be such that more or less will produce 
opposite effects from those just described for the proper consistency. 

Time of Setting. 36. Significance. — The object of this test is to de¬ 
termine the time which elapses from the moment water is added until the 
paste ceases to be fluid and plastic (called the “initial set”), and also the 
time required for it to acquire a certain degree ot hardness (called the 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 49. 

fThe original working for the U. S. Standard tests is H minutes (see paragraph 58). 


STANDARD CEMENT TESTS 


7i 

final” or ‘‘hard set”). The former of these is the more important, since, 
with the commencement of setting, the process of crystallization or harden¬ 
ing is said to begin. As a disturbance of this process may produce a loss 
of strength, it is desirable to complete the operation of mixing and molding 
or incorporating the mortar into the work before the cement begins to set. 

37. It is usual to measure arbitrarily the beginning and end of the set¬ 
ting by the penetration of weighted wires of given diameters. 

38. Method. — For this purpose the Vicat Needle, which has alreadv 
been described in Paragraph 30, should be used. 

39. In making the test, a paste of normal consistency is molded and 
placed under the rod (L), Fig. n, as described in Paragraph 31; this rod, 
bearing the cap ( D ) at one end and the needle ( H ), 1 mm. (0.039 i n 0 in 
diameter, at the other, weighing 300 g. (10.58 oz.). The needle is then 
carefully brought in contact with the surface of the paste and quickly re¬ 
leased. 

40. The setting is said to have commenced when the needle ceases to 
pass a point 5 mm. (0.20 in.) above the upper surface of the glass plate, and 
is said to have terminated the moment the needle does not sink visibly into 
the mass. 

41. The test pieces should be stored in moist air during the test; this is 
accomplished by placing them on a rack over water contained in a pan, and 
covered with a damp cloth, the cloth to be kept away from them by means 
of a wire screen; or they may be stored in a moist box or closet. 

42. Care should be taken to keep the needle clean, as the collection of 
cement on the sides of the needle retards the penetration, while cement on 
the point reduces the area and tends to increase the penetration. 

43. The determination of the time of setting is only approximate, being 
materially affected by the temperature of the mixing water, the temperature 
and humidity of the air during the test, the percentage of water used, and 
the amount of molding the paste receives. 

For practical purposes in ordinary construction where laboratory ap¬ 
paratus is unavailable, the setting qualities of a cement or mortar may 
often be examined by making up pats from a number of the packages and 
trying their hardening by pressure of the thumb. When the thumb nail 
fails to indent the surface the paste or mortar may be considered to have 
reached its final set. 

The Gillmore needles, described on page 89 and there compared with 
the Vicat apparatus, were formerly the U. S. standard. 

Standard Sand. 44. The Committee recognizes the grave objections V 
the standard quartz now T generally used, especially on account of its high 
percentage of voids, the difficulty of compacting in the molds, and its lack 
of uniformity; it has spent much time in investigating the various natural 
sands which appeared to be available and suitable for use. 

45. For the present, the Committee recommends the natural sand from 


7 2 


A TREATISE ON CONCRETE 


Ottawa, Ill., screened to pass a sieve having 20 meshes per linear inch and 
retained on a sieve having 30 meshes per linear inch; the wires to have 
diameters of 0.0165 an< ^ 0.0112 in., respectively, i. e., half the width of the 
opening in each case. Sand having passed the No. 20 sieve shall be con¬ 
sidered standard when not more than one per cent, passes a No. 30 sieve 
after one minute continuous sifting of a 500-gram sample.* 



Photographs of 
the grains of 
Ottawa and o f 
crushed quartz 
sand are shown on 
page 175. 

European is 
compared with 
U. S. standard 
sand on page 90. 

Form of Bri- 
quette. 46. 

While the form of 
the briquette 
recommended by 
a former Commit¬ 
tee of the Society 
is not wholly sat- 
isfactory, this 
Committee is not 
prepared to sug¬ 
gest any change, 
other than round¬ 
ing off the corners 
bv curves of J-in. 
radius, Fig. 12. 

The Germ a n 
standard "bri¬ 
quette is sketched 
on page 92. 


Molds. 47. The molds should be made of brass, bronze, or some 
equally non-corrodible material, having sufficient metal in the sides to pre¬ 
vent spreading during molding. 

48. Gang molds, which permit molding a number of briquettes at one 

* The Sandusky Portland Cement Company, of Sandusky, Ohio, has agreed to undertake the 
preparation of this sand, and to furnish it at a price sufficient only to cover the actual cost of 
preparation. 















STANDARD CEMENT TESTS 


73 


time, are preferred by many to single molds; since the greater quantity of 
mortar that can be mixed tends to produce greater uniformity in the re¬ 
sults. The type shown in Fig. 13 is recommended. 

49. The molds should be wiped with an oily cloth before using. 



Mixing. 50. All proportions should be stated by weight; the quantity 
Df water to be used should be stated as a percentage of the dry material. 

51. The metric system is recommended because of the convenient rela¬ 
tion of the gram and the cubic centimeter. 

52. The temperature of the room and the mixing water should be as 
near 21 0 Cent. (70° Fahr.) as it is practicable to maintain it. 

53. The sand and cement should be thoroughly mixed dry. The mixing 
should be done on some non-absorbing surface, preferably plate glass. If 
the mixing must be done on an absorbing surface it should be thoroughly 
dampened prior to use. 

54. The quantity of material to be mixed at one time depends on the 
number of test pieces to be made; about 1,000 gr. (35.28 oz.) makes a con¬ 
venient quantity to mix, especially by hand methods. 

55. The Committee, after investigation of the various mechanical mixing 
machines, has decided not to recommend any machine that has thus far 
been devised, for the following reasons: 

(1) The tendency of most cement is to “ball up” in the machine, thereby 
preventing the working of it into a homogeneous paste; (2) there are no 
means of ascertaining when the mixing is complete without stopping the 
machine, and (3) the difficulty of keeping the machine clean. 

56. Method . — The material is weighed and placed on the mixing 
table, and a crater formed in the center, into which the proper percentage 
of clean water is poured; the material on the outer edge is turned into the 
crater by the aid of a trowel. As soon as the water has been absorbed, 
which should not require more than one minute, the operation is completed 
by vigorously kneading with the hands for an additional 1 minute, the 
process being similar to that used in kneading dough. A sand-glass affords 
a convenient guide for the time of kneading. During the operation of 
mixing^ the hands should be protected by gloves, preferably of rubber. 

The apparatus required for mixing briquettes consists of a piece of i-inch 
plate glass at least 24 inches square, counter scales (preferably 
metric system), recording from 10 grams to kilograms, a 250 


















74 


A TREATISE ON CONCRETE 


cubic centimeter graduated measuring glass, rubber gloves, one 8-inch 
mason’s trowel, one 4-inch pointing trowel, Fig. 14, and a 
thermometer. 

Fig. 14. European standards specify mixing five minutes instead 

(See p. 74 .) 0 f one and a half minutes. This difference in time is due 
to the methods of manipulation, in Europe the materials being mixed 
with a trowel or spoon. Experiments by the authors tend to show that 
a denser mixture can be obtained by kneading one and a half minutes 
than by mixing five minutes with a trowel, so that the American method 
is both quicker and better. 



Molding. 57. Having worked the paste or mortar to the proper con¬ 
sistency, it is at once placed in the molds by hand. 

58. The Committee has been unable to secure satisfactory results with 
the present molding machines; the operation of machine molding ’is very 
slow, and the present types permit of molding but one briquette at a time, 
and are not practicable with the pastes or mortars herein recommended. 

59. Method .—The molds should be filled immediately after the mixing 
is completed, the material pressed in firmly with the fingers, and smoothed 
off with a trowel, without mechanical ramming; the material should be 
heaped up on the upper surface of the mold, and, in smoothing off, the 
trowel should be drawn over the mold in such a manner as to exert a 
moderate pressure on the excess material. The mold should be turned 
over and the operation repeated. 

60. A check upon the uniformity of the mixing and molding is afforded 
by weighing the briquettes just prior to immersion, or upon removal from 
the moist closet. Briquettes which vary in weight more than 3% from the 
average should not be tested. 


The method of introducing the paste or mortar into the molds exercises 
considerable effect upon the strength of the specimen. If a comparatively 
dry mixture is employed and it is packed in thin layers into the mold, a 
denser mass results and the strength is higher, especially on short-time 
tests, than with specimens of a wet or plastic consistency. Results from 
plastic cements and mortars, however, show greater uniformity. 

Although the French Commission in 1893 specified the method of using 
dry mortar, they recommended that after an international agreement 
standard plastic mortars be employed for all tests. 

Experiments by Air. R. Feret, made for the French Commission,* which 
are summarized in an article by the authorsf on Variation in Strength oj 
Mortars , give the comparative strengths of specimens beaten with a spatule 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1895, V°l- 4 V, p. 73. 

\Cement. July, 1903, p. 165. 


1 











STANDARD CEMENT TESTS 


75 

(the German method), pressed with a hand rammer, rammed in the Tet- 
majer apparatus, and rammed with the Bohme rammer (an alternate 
German method). 

Storage of the Test Pieces. 61. During the first 24 hours after molding, 
the test pieces should be kept in moist air to prevent them from drying out. 

62. A moist closet or chamber is so easily devised that the use of the 

damp cloth should be abandoned if possible. Covering the test pieces 

with a damp cloth is objectionable, as commonly used, because the cloth may 
dry out unequally, and, in consequence, the test pieces are not all main¬ 
tained under the same condition. Where a moist closet is not available, a 
cloth may be used and kept uniformly wet by immersing the ends in water. 
It should be kept from direct contact with the test pieces by means of a 
wire screen or some similar arrangement. 

63. A moist closet consists of a soapstone or slate box, or a metal-lined 

wooden box — the metal lining being covered with felt and this felt kept 
wet. The bottom of the box is so constructed as to hold water, and the 

sides are provided with cleats for holding glass shelves on which to place 

the briquettes. Care should be taken to keep the air in the closet uniformly 
moist. 

64. After 24 hours in moist air, the test pieces for longer periods of time 
should be immersed in water maintained as near 21 0 Cent. (70° Fahr.) as 
practicable; they may be stored in tanks or pans, which should be of non- 
corrodible material. 

A moist closet and storage pans designed by Mr. Richard L. Humphrey 
are shown in Fig. 15, page 75, and Fig. 16, page 76. 

Tensile Strength. 65. The tests may be made on any standard ma¬ 
chine. A solid metal clip, as shown in Fig. 17, is recommended. This 




























































76 


A TREATISE ON CONCRETE 



clip is to be used without cushioning at the points of contact with the test 
specimen. The bearing at each point of contact should be J in. wide, and 
the distance between the center of contact on the same clip should be i| 
in. 

66. Test pieces should be broken as soon as they are removed from the 
water. Care should be 'observed in centering the briquettes in the testing 
machine, as cross-strains, produced by improper centering, tend to lower 
the breaking strength. The load should not be applied too suddenly, as 
it may produce vibration, the shock from which often breaks the briquette 
before the ultimate strength is reached. Care must be taken that the clips 
and the sides of the briquette be clean and free from grains of sand or dirt, 
which would prevent a good bearing. The load should be applied at the 
rate of 600 lb. per minute. The average of the briquettes of each sample 
tested should be taken as the test, excluding any results which are mani¬ 
festly faulty. 

Testing machines and their operation are discussed and illustrated on 
page 93. The actual tensile strength of neat cement and sand mortar is 
treated on page 99. 




































































































































STANDARD CEMENT TESTS 77 

Tests have shown that for the highest and most uniform results briquettes 

should not be removed from the 
water until, as specified, just before 
they are broken. 


Constancy of Volume.* 67. Sig¬ 
nificance. — The object is to develop 
those qualities which tend to destroy 
the strength and durability of a ce¬ 
ment. As it is highly essential to de¬ 
termine such qualities at once, tests of 
this character are for the most part 
made in a very short time, and are 
known, therefore, as accelerated 
tests. Failure is revealed by crack¬ 
ing, checking, swelling or disintegra¬ 
tion, or all of these phenomena. A 
cement which remains perfectly 
sound is said to be of constant 
volume. 

68. Methods. — Tests for con¬ 
stancy of volume are divided into 
two classes: (1) normal tests, or 
those made in either air or water 
maintained at about 21 0 Cent. (70° 
Fahr.) and (2) accelerated tests, or 
those made in air, steam or water at 
a temperature of 45 0 Cent. (113 0 
Fahr.) and upward. The test pieces 
should be allowed to remain 24 hours 
in moist air before immersion in 
water or steam or preservation in air. 

69. For these tests, pats, about 7^ 



{See p. 75 .) 


cm. (2.95 in.) in diameter, 1} cm. (0.49 in.) thick at the center, and 
tapering to a thin edge, should be made, upon a clean glass plate [about 
10 cm. (3.94 in.) square], from cement paste of normal consistency. 

70. —Normal Test. — A pat is immersed in water maintained as near 
21 0 Cent. (70° Fahr.) as possible for 28 days, and observed at intervals. A 
similar pat, after 24 hours in moist air, is maintained in air at ordinary tem¬ 
perature, and observed at intervals. 

71. Accelerated Test .—A pat is exposed in any convenient way in an 
atmosphere of steam, above boiling water, in a loosely closed vessel, for 
5 hours. The apparatus recommended for making these determinations is 
shown by Fig. 18, Page 78. 

72. To pass these tests satisfactorily, the pats should remain firm and 
hard, and show no signs of cracking, distortion or disintegration.! 

*Soundness. 

•[See page ioi. 






































78 


A TREATISE ON CONCRETE 


73. Should the pat leave Ihe plate, distortion may be detected best 
with a straight-edge applied to the surface which was in contact with 
the plate. 

74. In the present state of our knowledge it cannot be said that cement 
should necessarily be condemned simply for failure to pass the accelerated 
tests; nor can a cement be considered entirely satisfactory, simply because 
it has passed these tests. 

Submitted on behalf of the Committee, 


Committee. 

George S. Webster, 
Richard L. Humphrey, 
George F. Swain, 
Alfred Noble, 

Louis C. Sabin, 

S. B. Newberry, 
Clifford Richardson, 
W. B. W. Howe, 

F. H. Lewis. 


George S. Webster, 

Chairman 

Richard L. Humphrey, 

Secretary. 


i 


December 28, 1908. 



Fig. 18.—Steaming Apparatus. (See p . 77. 1 


































































STANDARD CEMENT TESTS 


79 


ELEMENTARY DIRECTIONS FOR TESTING SOUNDNESS 

Soundness tests, which are of greater importance than any other one 
test, may be made by those unskilled in laboratory practice, with no 
apparatus except a piece of plate glass at least ^ inch thick and 12 by 18 
inches square, pieces of window glass 4 inches square, and a small trowel. 
Take samples at random from several barrels or bags, as described on 
page 64. From each sample make three pats of neat cement, requiring 
for the three, about 8 ounces (250 grams) or one cupful of dry cement. 

Cements of different classes and degrees of fineness require different 
percentages of water. The consistency must be such that the cement can 
be readily kneaded without crumbling and formed into a smooth pat with 
a thin edge, when pressed upon the piece of glass provided for it, without 
running or losing its shape.* Approximate amounts may be taken for the 
first trial of any cement, as, — 

Portland Cement. 20% of water by weight 



Natural 

Puzzolan 


If these quantities after kneading give too wet or too dry a mixture, the 
paste should be thrown away and the trial repeated with less or more water 
until the desired consistency is attained. The percentage thus determined 
may generally be used in the remaining tests of the same shipment of 
cement. 

Place a sample of the dry cement upon the plate glass in the form of a 
mound, and with the small trowel make a depression in the center. Weigh, 
or measure, a quantity of water which has been found by trial to give the 
proper consistency, and pour it into the depression, allowing it to soak into 
the cement, and then turn the material on the edges into the water with a 
trowel. As soon as the water is absorbed, the paste is kneaded for 1^ 
minutes with the hands, which should be protected with rubber gloves. 

A piece of window glass about 4 inches square is required for each pat. 
A portion of the paste is made into a ball and pressed upon one of 
these pieces of glass so as to form a circular pat about 3 inches in diameter 
and J inch thick in the center, tapering to a thin edge. For the first 24 
hours, to prevent the surface from drying too quickly, the pats must be 
kept under a cloth moistened and suspended above the pats, with its ends 
immersed in water to keep it wet. The temperature of the air while 
mixing, and of the water for mixing and storage, should be maintained as near 
as possible to 70° Fahr. (21 0 Cent.). At the end of 24 hours one pat should 


♦See also Boulogne method, d. 70 . 





8o 


A TREATISE ON CONCRETE 


be placed in water and another in air, to be observed at intervals for a 
period of 28 days, and the third pat placed upon some sort of a frame in a 
loosely covered vessel over boiling water, and kept there, with the water 
boiling, for 5 hours. The possible defects which are mentioned above in 
paragraphs 74 and 75 are described at length on page 103. 

APPARATUS FOR A CEMENT TESTING LABORATORY! 

(The apparatus is designed for one experimenter. Where the number 
of pieces is not stated, their number depends upon the quantity of cement 
to be tested.) 

*One piece plate glass, one inch thick, 24 by 24 inches square; 

*Two or more gangs of 4 or 5 molds each — A. S. C. E. standard (see 
Fig- 13. P- 73 ); 

*One metric counter scale recording from 10 grams to ij kilograms. 
*One No. 100 sieve (96 to 100 meshes to the linear inch) about 20 centi¬ 
meters (7.87 ins.) in diameter and 6 centimeters (2.36 in.) high, made 
of woven brass wire cloth, with wires 0.0045 inches diameter; 

*One No. 200 sieve (188 to 200 meshes to the linear inch) of similar size to 
the No. 100 sieve, and made of woven brass wire cloth, with wires 
0.0024 inches diameter; 

*One measuring glass graduated to 250 cubic centimeters; 

*One 8-inch mason’s trowel; 

*One 4-inch pointing trowel (see Fig. 14, p. 74); 

*One-half dozen pairs rubber gloves; 

*Pieces of window glass 4 inches square for soundness tests; 

*One tensile testing machine (see Figs. 22 to 27, pp. 94 to 98); 

*Air thermometer; 

*Standard sand; 

Two or more gangs of 4 molds each for 2-inch cubes (see Fig. 43, p. 119); 
Two or more molds for transverse specimens 1 by 1 by 6 inches (see Fig. 44, 
p. 121); 

io-pound tin cans with covers for holding samples; 

One special scale for weighing cement in ascertaining fineness (see Fig. 10, 

p. 68); 

One pan of same diameter as the sieves and 5 centimeters (1.97 in.) deep, 
with cover, for holding sieve when shaking it; 

One measuring glass graduated to 100 cubic centimeters; 

*An asterisk designates the apparatus required for a temporary laboratory on construction 
work. 

fThis list has been criticised and approved by Mr. Richard L. Humphrey. 


STANDARD CEMENT TESTS 


&i 

One cement sampler 24 inches long (see Fig. 8, p. 64) 

One and one-half minute sand glass; 

One moist closet (see Fig. 15, p. 75); 

Galvanized iron waste cans; 

Apparatus for steaming and boiling specimens (see Fig. 18, p. 78); 
Tanks for immersing specimens (see Fig. 16, p. 76); 

Vicat needle apparatus (see Fig. 11, p. 69); 

One compression testing machine (adapted also to transverse tests), capac¬ 
ity 50,000 lb. (see Figs. 41 and 42, pp. 117 and 118); 

Chemical thermometer; 

Specific gravity apparatus (see Fig. 9, p. 66); 

Microscope with 1^ inch objective; 

Set of sieves, about 8-inch diameter, for analyzing sands, sizes No. 4, 8, 
20, 50-100 (the number corresponds to the number of meshes to the 
linear inch) (see p. 159a); 

Mechanical shaker for sifting sand (see Fig. 68, p. 195). 

SPECIFIC GRAVITY OF DIFFERENT CEMENTS 

The specific gravity test, by determining whether a cement is thoroughly 
burned, supplements the chemical analysis, since the latter does not indicate 
the degree of calcination. A Puzzolan cement may be distinguished from 
a true Portland because its specific gravity is usually between 2.7 and 2.9, 
while that of Portland ranges from 3.05 to 3.15. The adulteration of 
Portland cement lowers its specific gravity, because the substances used, 
— powdered sand, limestone, trass or slag, — are lighter than particles of 
pure cement. The test will not detect a small adulteration nor adulteration 
with a material of high specific gravity. 

Natural cement usually has a specific gravity above 2.75, ranging from 
this sometimes as high as 3.1,* thus overlapping the inferior limit given 
for Portland cement. 

The specific gravity of cement is lowered by exposure, because of the 
absorption of water and carbonic acid, hence the necessity of drying it 
at ioo° Cent. (212 0 Fahr.) before determining. Even this temperature 
may not always be sufficient to restore old cements to their original con¬ 
dition, j* 

A neat little device for dropping fine material into a specific gravity 
apparatus so as to prevent the entraining of air has been devised by Mr. 
Thomas H. Wiggin. A thin wooden board with a circular hole in it is 

t 

*Tests of Metals, U. S. A., 1901, p. 476. 

•f-See experiments in Tests of Metals, U. S. A., 1901, p. 476, and Dr. H. Kupfender in Thonirt- 
dustriezeitung , translated in Cement, March, 1903, p. 23. 


82 


A TREATISE ON CONCRETE 


placed above the apparatus and a paper funnel fitted into the hole and 
filled with dry cement. An electro-magnet, such as is used with an 
ordinary electric door-bell, is connected with its storage battery and ar¬ 
ranged so that the clapper, instead of striking a bell, strikes a metal 
plate attached to the corner of the board. The constant tapping jars 
the funnel so that the grains fall slowly into the apparatus without re¬ 
quiring the attention of the operator. 

ADVANTAGES OF FINE GRINDING 

The effects of fineness of grinding upon cements are to make them,— 

Stronger when tested with sand; 

Weaker when tested neat; 

Quicker setting; 

Capable of producing a larger volume of paste; 

Less affected by free lime. 

Fineness is expressed by the percentage of the total weight of the cement 
retained on each sieve. 

A recognition of the value of extreme fineness has led to the adoption of 
higher standards than formerly, and manufacturers have accordingly im¬ 
proved the quality of their product in this respect. As an illustration of 
this, in 1875 it was a common requirement for Portland cement that 85% 
should pass, or not more than 15% be retained on, a sieve having 50 
meshes per linear inch; in 1893 Max Gary gave the German standard as 
90% to pass, or not more than 10% to be retained on, a sieve having 76 
meshes per linear inch, while in 1904 specifications for first-class work 
required not more than from 6% to 10% to be retained on a sieve having 
100 meshes per linear inch, and not more than 20% to 35% on a sieve 
having 200 meshes per linear inch. Some American factories are equipped 
to grind even finer than this, shipping cement of which less than 10% is 
retained on a No. 200 sieve. Standard requirements for different cements 
are given in the specifications on pages 30 and 31. 

Strength affected by Fineness. With the same proportions of sand 
higher tensile and compressive strength is obtained from finely ground 
than coarsely ground cements. Conversely, a larger proportion of sand 
can be used with fine ground than with coarse ground cement, with the 
same resulting strength. 

The chief cementing value of a cement lies in the grains which are 
fine enough to pass a sieve having 200 meshes per linear inch. Photo¬ 
graphs of thin sections of sand briquettes several years old made by 


STANDARD CEMENT TESTS 


83 

Mr. E. W. Lazell show very clearly the coarser grains of cement which 
have never been penetrated and chemically changed by the water. 

Tested neat, a coarse cement may give higher strength than the same 
cement after regrinding. This is chiefly due, in the opinion of the authors, 
to the fact that the fine cement requires more water in gaging to produce 
the same consistency of paste, so that the same weight of cement produces 
a larger volume of paste, which therefore has less density and consequently 
lower strength. When sand is added, on the other hand, less influence is 
exerted by the water, because in any case a smaller volume of it is required 
in proportion to the dry materials, and besides this the very fine grains, 
which also have higher cementing qualities, fit more readily into the voids 
in the sand. The relation of the density of a mortar to its strength is dis¬ 
cussed in Chapter IX, page 132. 

The effect of the fineness of cement upon its strength was brought to 
general notice by Mr. John Grant* in 1880, who quotes experiments made 
in Gerrfiany by Dyckerhoff. In 1883 Mr. I. J. Mannf illustrated the 
small cementing value of the coarse particles by substituting for them 
grains of sand of the same size, with but little reduction in the resulting 
strength. 

The following table from tests reported in 1885 by Mr. Eliot C. ClarkeJ 
illustrates the effect of the fineness of cement on paste and mortars. All 
of these cements would be reckoned as coarse in modern practice, but the 
relative results are still of interest. 


Tensile Strength of Mortar Affected by Fineness of Cement. 
By Eliot C. Clarke. 


' PORTLAND CEMENT 

ROSENDALE CEMENT 

Proportions 
of cement 
to sand 

STRENGTH IN POUNDS PER 
SQUARE INCH 

Proportions 
of cement 
to sand 

STRENGTH IN POUNDS PER 
SQUARE INCH 

Ordinary cement 
35% retained 
on No. 120 sieve 

Finely ground 
cement 

12% retained on 
No. 120 sieve 

Coarse cement 
17% retained on 
No. 50 sieve 

Fine cement 
6% retained on 
No 50 sieve 

I : O 

403 

3°4 

1 : 0 

98 

9 2 


io 5 

0 

00 

M 

1. ij 

29 

41 

i : 5 

68 

96 

i: 2 

16 

25 


*Proceedings Institution of Civil Engineers, Vol. LXII, p. 149. 
•{•Proceedings Institution of Civil Engineers, Vol. LXXI, p. 254. 
^Transactions American Society of Civil Engineers, Vol. XIV, p. 158. 





















8 4 


A TREATISE ON CONCRETE 


Mr. D. B. Butler* in England has made extended tests to determine the 
value of coarse particles in cement and the effect of regrinding. A sum¬ 
mary of one of his tables, illustrating also the effect of fineness upon the 


Effect of Regrinding Coarse Particles and of Substituting Sand. 


By David B. Butler. 


CEMENT, 

« 

HOW TREATED 

Fineness resi¬ 
due per cent 
on sieves of 
meshes per 
linear inch 

Setting 

Proper¬ 

ties 


180 

76 

5 ° 

Initial set 
min. 

Final set 
min. 

As received. 

33-7 

15-5 

4.6 

13 

90 

Reground. 

Sand substituted for coarse 
particlesf. 

i -3 

0.0 

0.0 

2 

20 


TENSILE STRENGTH IN POUNDS PER 
SQUARE INCH 


Neat cement 

I 

part cement to 3 
parts sand 

7 

days 

28 

days 

3 

mo. 

6 

mo. 

12 

mo. 

7 

days 

28 

days 

3 

mo. 

6 

mo. 

12 

mo. 

504 

580 

641 

702 

7 i 7 

194 

262 

354 

404 

4 21 

497 

478 

518 

489 

504 

326 

411 

53 i 

59 i 

618 

414 

480 

606 

660 

702 

164 

217 

290 

354 

387 


time of set, gives the average of his results from four brands of Portland 
cement. 

The fine grinding of commercial cements, by accelerating the setting, has 
been one of the causes for the necessity of adding gypsum or plaster 
during manufacture. 

American vs. European Sieves. Standard sieves recommended by the 
American Society of Civil Engineers^ and the French Commission§ are 
tabulated below with English and Metric equivalents. 


American Sieves. 


No. 

of 

sieve 


ioo 

200 


U. S STANDARD 


Meshes 

per 

linear 

inch 


IOO 

200 


Meshes 

per 

square 

inch 


IO ooo 
40 000 


Diam. 

of 

wire 

in. 


O.OO45 

0.0024 


Width 

of 

openings 

in. 


0.0045 

0.0026 


Meshes 

per 

cm. 


39 

79 


METRIC EQUIVALENTS 


Meshes 

per 

sq, cm. 


1 55° 

6 200 


Diam. 

of 

w T ire 

mm. 


0.114 
0.061 


Width 

of 

openings 

mm. 


0.140 

0.066 


♦Proceedings Institution of Civil Engineers, Vol. CXXXII, p. 343, and Butler’s Portland Cement, 
±899, p. 169. 

fAll particles not passing No. 180 sieve (averaging 33.7% by weight) were removed from the 
original cement as received, and sand having grains of similar size substituted for them. 

JSee p. 67. 

§Commission des Methodes d’Essai des Materiaux de Construction, 1894, Vol. I, p. 248. 


































































STANDARD CEMENT TESTS 85 


French Sieves. 


FRENCH STANDARD 

ENC'TSH EQUIVALENTS 

Meshes 

per 

cm. 

Meshes 

per 

sq. cm. 

Diam, 

of 

wire 

mm. 

Width 

of 

openings 

mm. 

Meshes 

per 

linear 

inch 

Mesnes 

per 

square 

inch 

Diam. 

of 

wire 

in. 

Width 

of 

openings 

in. 

18 

3 2 4 

0.20 

0.36 

46 

2 120 

0.0078 

0.0124 

30 

900 

c.15 

O.18 

76 

5 7 So 

0.0059 

0.0071 

70 

4 900 

0.05 

0.09 

00 

M 

31 680 

0.0020 

0.0035 


Separating Material Passing No. 200 Mesh Sieve. The high 
cementing value of the grains of cement passing a No. 200 sieve leads 
in elaborate tests to still finer separations. In studies for soil analysis 
chiefly, the various methods of separating the different sized grains have 
been developed. They are fully described in Wiley’s Principles and 
Practice of Agricultural Analysis , Vol. I, pages 171 to 281. The same 
principles are applicable to cement determinations, except that some 
liquid other than water must be employed. 

Separation may be made by a winnowing device* in which a blast of 
air is directed against falling grains of cement; by settlement through 
water at rest, which in its simplest form may be accomplished by allow¬ 
ing the material to settle in a beaker, for a certain length of time and 
then decantingf; and by means of a liquid in motion, as illustrated in 
the Schone apparatus, and, with still greater exactness, by Hilgard’s 
churn elutriator.f The Schone apparatus has been adapted by Dr. W. 
Michaelis to cement, and has also been employed by Mr. J. B. Johnson.§ 

QUANTITY OF WATER FOR NEAT PASTE AND MORTAR 

The quantity of water used in gaging affects the results of tests, es¬ 
pecially in the determination of the time of setting and of the strength. 
(See p. 151.) Different cements even of the same class require different 
proportions of water to produce the same consistency, chiefly because of 
differing degrees of fineness, the cement containing the largest proportion 
of fine particles requiring the largest percentage of water by weight. 

For chemical combinations alone about 8 per cent of water to the weight 
of the cement is customarily assumed to be required, but in practice the 
percentage must be much greater. 

*Tests of Metals, U. S. A., 1901, p. 474. 

■j-Allen Hazen in Report Massachusetts State Board of Health, 1892. 

jWiley’s Principles and Practice of Agricultural Analyses, 1894, Vol. I, p. 226. 

§ Johnson’s Materials of Construction, 1903, p. 412. 























86 


A TREATISE ON CONCRETE 


Percentage of Water f i Mortar of Normal Consistency. The fol¬ 
lowing table, based on the formula of Mr. Feret given on page 88, which 
is strictly applicable only to French sands and French methods, has 
been suggested provisionally by the Committee of the American 
Society for Testing Materials (1904), for the percentage of water 
for mortars of consistency corresponding to that of normal neat 
paste. To use the table select from the first column the percentage of 
water required for the neat paste of the selected cement and read in 
column of the desired proportions the percentage of water required for 
the mortar in terms of the sum of the weights of the cement and sand. 


Percentage of Water for Cement Mortars of Normal Consistency. 


Ut 

V 

- t -> 4-1 

$ a 
*! 


PERCENTAGE OF WATER 

TO CEMENT PLUS SAND 


°8 

bo+i 

5 s 

C (3 

Proportions cement to sand by weight 

<v^ 

Cl, 

i : 1 

1: 2 

1:3 

1:4 

i: 5 

i8 

12.0 

IO.O 

9.0 

8.4 

8.0 

X 9 

12.3 

10.2 

9.2 

8-5 

8.1 

20 

12.7 

IO.4 

9-3 

8.7 

8.2 

21 

13.0 

IO.7 

9-5 

8.8 

8-3 

22 

I 3-3 

IO.9 

9-7 

8.9 

8.4 

2 3 

i 3-7 

I I .1 

9.8 

9 - 1 

8-5 

24 

14.0 

11 -3 

10.0 

9.2 

8.6 

2 5 

14.3 

11.6 

10.2 

9-3 

8.8 

26 

T4.7 

11.8 

10.3 

9-5 

8.9 

27 

15.0 

12.0 

10.5 

9.6 

9.0 

28 

x 5 -3 

12.2 

10.7 

9-7 

9 - 1 

29 

x 5-7 

12.5 

10.8 

9.9 

9.2 

3 ° 

16.0 

12.7 

11.0 

10.0 

9-3 

3i 

16.3 

12.9 

11.2 

10.1 

9.4 

32 

16.7 

x 3 - x 

11 *3 

10.3 

9-5 


Percentage of water 
for neat cement 

PERCENTAGE OF WATER 

TO CEMENT PLUS SAND 

Proportions cement to sand by weight 

1: 1 

1: 2 

1:3 

1:4 

1:5 

. 33 

17.0 

T 3-3 

11 *5 

10.4 

9.6 

34 

x 7-3 

13.6 

11 *7 

10.5 

9-7 

35 

17.7 

13.8 

11.8 

10.7 

9.9 

36 

18.0 

14.0 

12.0 

10.8 

10.0 

37 

18.3 

14.2 

12.2 

10.9 

10.1 

38 

18.7 

14.4 

12.3 

11 .i 

10.2 

39 

19.0 

14.7 

I2 -5 

11.2 

10.3 

40 

x 9-3 

14.9 

12.7 

11 -3 

10.4 

41 

19.7 

I 5- 1 

12.8 

11 -5 

10.5 

42 

20.0 

x 5*3 

13.0 

11.6 

10.6 

43 

20.3 

15.6 

13.2 

n.7 

10.7 

44 

20.7 

15.8 

i3-3 

11.9 

10.8 

45 

21.0 

16.0 

x 3-5 

12.0 

11.0 

46 

21.3 

16.1 

T 3-7 

12.1 

11.1 


Weights of Cement and Sand for Different Proportions. 



1:1 

1:2 

1: 3 

Cement. 

500 

333 

250 


Sand. 

500 

666 

75° 



1:4 


200 

800 


i: 5 

167 

8 33 


The Engineers of the U. S. Army* advocate a dryer mixture than most 

^Professional Papers, No. 2.8. 


































































STANDARD CEMENT TESTS 87 

authorities, and the following percentages suggested by them may there¬ 
fore be taken as representing minimum quantities. 


Portland Cement. 


Neat.20% of water by weight. 

1 cement: 3 sand. i2 l / 2 % “ “ 


Natural Cement. 


Neat.30% of water by weight. 

1 cement: 1 sand.17% “ “ 


Puzzolan Cement. 


Neat.18% of water by weight. 

1 cement: 3 sand.10% “ “ 


French Determination of Consistency of Neat Paste. The Vicat 
needle apparatus has been selected in America as well as in France as the 
standard appliance for determining normal consistency. The apparatus 
is shown in Fig. n on page 69, and the U. S. standard method of applying 
the test is there described. 

A plastic paste is preferred to one of dryer consistency. The French 
Commission* advised a softer consistency than the American standard, 
the French requiring for normal consistency the penetration of a needle 
one centimeter (0.39 in.) in diameter and weighing 300 grams (10.58 oz.) 
through a disc of cement 40 millimeters (1.57 in.) thick to within 6 milli¬ 
meters (0.23 in.) of the bottom, making a total depth of penetration of 
34 millimeters (1.33 in.), while the American Society recommend the 
penetration of a similar needle into a like mass to a depth of 10 millimeters 
(0.39 in.) below the surface. 

Feret’s Formulaf for percentage of water for mortar of normal consis¬ 
tency was evolved from a very interesting series of experiments. J He found 
that it was impracticable to determine with the Vicat needle the proper 
consistency of a mortar of cement and sand, and therefore based his deter¬ 
mination upon the average judgment of several operators, plotting the 
consistencies designated by them upon cross-section paper. 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1894, Vol. I, p. 270. 

fCommission des Methodes d’Essai des Materiaux, 1895, Vol. IV, p. 103. 

^Methods of Mr. Feret’s investigations are described and illustrated in an article by the authors 
on “Quantity of Water to Use in Gaging Mortars” in Cement and Engineering News 
(Chicago), November, 1903. 








88 


A TREATISE ON CONCRETE 


His formula is: 

For mortars of plastic consistency,* 

2 P 

W= — —— + 6.0 (i) 

3 5 + 1 

For mortars of dry consistency,* 

2 P f x 

M = — 7 T— + 4-5 ( 2 ) 

3 S + i 

Where 

W = percentage of water for mortar in terms of weight of the mixture of 
dry materials; 

P = percentage of water required for neat cement of normal consistency; 
S = parts of sand by weight to one part cement. 

Mr. Richard L. Humphrey! states that from formula (2) he has ob¬ 
tained very uniform results with U. S. standard sand, although slight 
modifications are necessary for a mortar containing more or less than 
three parts of sand. 


ARBITRARY PERIODS OF SETTING 


The methods employed in mixing and depositing the mortar or concrete 
and the character of the construction form a guide to the necessary re¬ 
quirements for the time of setting of the cement. 

The setting of cement is due to chemical reaction, as described by Mr. 
Spencer B. Newberry on page 57. The process is a gradual one, but 
may be arbitrarily divided into three periods: 

Initial set. 

Final set. 

Hardening. 

The dividing line between these periods is arbitrary, but the division is 
based upon the fact that after water is added the paste remains plastic for 
a certain period, and then commences to “stiffen” or crystallize. This is 
called the time of initial set. The setting process continues rapidly, and 
when a point is reached that the paste will withstand a certain pressure, 
Arbitrarily fixed in practice, it is said to have reached its final set. The 


*The original formula of Mr.Feret corresponding to formula (2) is E — — NA-\-60 and to formula 
/\- F _ 2 .. . . .3 

(. 3 / 1S ^ ~~ “-^^+ 45 ) in which E— weight of water in grams required for one kilogram of dry mix¬ 


ture of cement and sand, N= weight of water in grams required for one kilogram of neat cement, 
and A= weight in kilograms of cement in one kilogram of the dry mixture. The change in the form 
of the formula permits the direct use of percentages, 
fjournal Franklin Institute, 1901-2. 





STANDARD CEMENT TESTS 89 

process of hardening now continues more slowly, and proceeds with in¬ 
creasing slowness for an indefinite period. 

Those unfamiliar with cement construction must bear in mind that a 
cement which has reached its final “set” is not hard nor is it capable of 
bearing a load. Natural cement, for example, usually reaches its initial 
and its final set much earlier than Portland cement, but it hardens more 
slowly, and Natural cement masonry will not bear loading nearly so 
quickly as Portland cement masonry. 

EUROPEAN METHODS FOR DETERMINING SET 

The French and German requirements are similar to the American 
(p. 70) except that in them the commencement of the set is taken as the 
time when the needle can no longer penetrate entirely to the bottom of the 
box instead of limiting it to a penetration to a depth of 5 millimeters above 
the bottom surface. 

For sand mortars the French Commission designate the final set as the 
moment when the surface of the mortar can support pressure of the thumb 
without indentation. As an alternate method, they use the Vicat apparatus 
with a needle one centimeter (0.39 in.) in diameter and weighing 5 kilo¬ 
grams (11.02 lb.). The preliminary reports of Mr. R. Feret and Mr. P. 
Alexander in Commission des Methodes d’Essai des Materiaux de Con¬ 
struction, 1895, Vol. IV, pp. hi and 139, describe experiments with different 
apparatus. 

Comparison of Vicat and Gillmore Needles. The Gillmore needles, the 
former American standard, were first used by General Totten in 1830.* 

By these needles the initial set of Neat cement is the time at which a wire 
one-twelfth-inch diameter, loaded to a | pound, is just supported by the 
mass without appreciable indentation. The final set is taken as the time 
when a wire one-twenty-fourth-inch diameter, loaded to weigh one pound, 
is supported without appreciable indentation. 

The diagram in Fig. 19, page 90, from experiments made at the 
Watertown Arsenalf upon various cements (designated by letters) shows 
the difference in the nominal time of setting when measured by the 
Gillmore needle and the Vicat needle, employing with the latter the 
German method. (See above.) The diagram also shows the variation 
in time of set of Portland cement occasioned by varying the proportion 
of water, and the effect of leaving out the usual “restrainer” of plaster 
of Paris or gypsum. 

*Gillmore’s Treatise on Limes, Hydraulic Cements and Mortars, p. 80. 

■{■Tests of metals, U. S. A., 1901, p. 492. 


9° 


A TREATISE ON CONCRETE 


THE RATE OF SETTING 

The rate of setting of cement, that is, the process of hardening, has 
been studied by the French Commission* in France and by Prof. Edgar 
B. Kay in the United States. The diagram, Fig. 20, page 91, shows 
curves of setting made with a machine of Prof. Kay’s design and the 
corresponding tensile strength of briquettes of the same cement. Prof. 
Kay calls attention to the positive change from the plastic to the granular or 
crystalline structure which in the cement shown occurred between the 
periods of 35 and 40 minutes. The elongation of the briquette when 
being broken gradually changed from f inch at the 5-minutes period to 
0.15 inch at 40 minutes, while at 200 minutes, or one hour before the 
initial set was completed, the elongation was not measurable. 


PORTLAND 

CEMENTS 

WATER 

PER 

CENT 

TIME OF SETTING-HOURS 

NATURAL 

CEMENTS 

WATER 

PER 

CENT 

TIME OF SETTING-HOURS 








0 

2 



6 f 

3 










0 

2 



f 


8 








20 





0 — 

•— 

-A 












30 





0 - 

-0 





L' 




A 




25 






0 -' 

f- 









L 



35 



















30 








- 

' 









40 






0 . 


— 




















""r 




























20 









3F 









30 



O- 

.... 









— 



— 



25 








0 — 

. ,L_ 

L 

0 





M 



35 



O 


... 

0 









30 










L._ 

... 








40 




' 

1 


— 

O 

















































20 





0 — 


-0 


V 










30 




0 


— 

3 







r 

c 




25 







0- 

—« 








N 



35 





°l— 

— 

> 





V* 

_ 

ITH PLASTE 
kGE 42 DAYS 

R 

30 








0- 







. 




40 






T 

TV 

-O 














































20 



CO 















30 



O 


— 

— 0 









c 

_ 

PL 

D 

AS! 

AYS 

'ER 

25 



O- 













O 



35 



>- 









WM 

_, 

‘HOUT 
VGE 4: 

3 0 








0 -.. 



—0 








40 



u 

—.. 


-- 

















































20 




0- 

— 

— 

—■ 

-0 











35 



0 

-O 











D 




25 







0 — 

=31 







P 



40 



0 

— 


— 0 













30 








3—• 

— 

•O 









45 




O. • 

... 


-O 












































— 






20 



O- 


— 

— 

— 0 












40 




0 


— 

■O 





E 




25 







0— 


— 0 







R 

_ 


45 






3 







— 

— 





30 








O 

— 


) 








50 






O 





- 

- • 




































- NOTE —FULL LINES SHOW .TIME OF SETTING BY VICAT NEEDLE 

-DOT & DASH “ “ ' “ “ “ “GILLMORE “ - 


Fig. 19.—Time of Setting of Typical Cements,— and comparison of Vicat and Gill- 
more’s Needles. (Tests of Metals, U. S. A., 1901.) (See p. 89.) 

AMERICAN AND EUROPEAN STANDARD SANDS COMPARED 

The character of the sand has so great an effect upon the strength of a 
mortar that for comparing different brands of cement or specifying re¬ 
quirements of strength a sand of standard size and quality is essential. 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vo!. TV., p. j 11. 






















































































































































































































120 180 240 300 360 410 

Fig. 20.—Rate of Setting and Corresponding Tensile Strengm of Portland Cement Paste. (See p. 

(Especially prepared by Prof. Edward B. Kay /or this treatise ! 



O — Ni 01 '' J 00 'Co — fo u> 

TENSILE STRENGTH LB. PER SQ. IN. 


TIME OF SETTING IN MINUTES 


























































































001 


9 2 


A TREATISE ON CONCRETE 


The U. S. Standard Sand recommended by the Committee of the Amer¬ 
ican Society of Civil Engineers, as specified on page 71, is a natural sand 
from Ottawa, Ill., screened to pass a sieve having 20 meshes per linear inch, 
and retained on a sieve having 30 meshes per linear inch. 

The change in America from artificial to natural sand is in accord with 
recent practice abroad. 

The English Standard Sand is obtained from a pit at Leighton Buzzard,* 
and the screens are the same as in the United States. 

The German Standard Sand is a natural quartz retained between sieves 
having respectively 20 and 28 meshes per linear inch. 

The French Standard Sand , a natural sand from Leucate, France, is 
simple or compound. Simple standard sand must pass a screen having 
holes 1.5 millimeters (0.059 i n 0 * n diameter, and be retained on a screen 
having holes one millimeter (0.039 in.) in diameter. Compound stand¬ 
ard sand is made by forming a mixture of equal weights of the following: 

(1) Grains passing holes of 2 mm. 
(0.079 i n -) and retained by 1.5 
mm. (0.059 in-)* 

(2) Grains passing holes of 1.5 mm. 
(0.059 in.) and retained by 1 
mm. (0.039 in.). 

(3) Grains passing holes of 1 mm. 
(0.039 in-) and retained by 0.5 
mm. (0.020 in.). 



THE FORM OF BRIQUETTE FOR 
TENSILE TESTS 

Mr. John Grant in 187if presented 
results of a series of experiments 
with different forms of briquettes and 
sizes of section. Ten years laterf he 
adopted the form now used in Eng- 

FlG V 2 J i-- The German Standard Briquette land which j s substantial i y the g 
(dimensions are in millimeters). J 

{See page 92.) as that recommended by the American 

Society of Civil Engineers in 1884, 

and, with a very slight alteration, in 1903. (See Fig. 12, p. 72.) 

The German Standard Briquette, also adopted by the French Commission 

♦Butler’s Portland Cement, 1899, p. 200. 

fProceedings Institution of Civil Engineers, Vol. XXXII, p. 282. 

^Proceedings Institution of Civil Engineers, Vol. LXII, p. 137. 










STANDARD CEMENT TESTS 


93 


iii 1893, is shown in Fig. 21. The section is 5 square centimeters (0.78 
sq. in.). Results with this form of briquette are lower per unit of area than 
those of the American pattern. Prof. Jerome Sondericker* in studying the 
quality of strength and uniformity of breaking of different forms, found that a 
groove in the sides of the specimen lowered the unit strength about 13%. 

M. Feretf found that briquettes of 5 square centimeter section gave 46% 
higher strength per unit of area than briquettes of 16 square centimeter, and 
attributed this difference to lack of homogeneity throughout the section. 

TO CONVERT METRIC UNITS OF STRENGTH TO ENGLISH UNITS 

To convert values of kilograms per square centimeter (kg. per sq. cm.) 
to pounds per square inch (lb. per sq. in.), multiply the former by 14.2.J 
To convert values of pounds per square inch (lb. per sq. in.) to kilo¬ 
grams per square centimeter (kg. per sq. cm.), multiply the former by 
0.07.§ 

MACHINES FOR TESTING TENSILE STRENGTH 

A testing machine should be so designed that the strain can be applied 
to the briquette at a definite rate without irregularity or jar. The clips 
should be suspended from pivoted bearings to avoid friction, and should be 
stiff, so that they will not spread. The contact surfaces should hold the 
briquette firmly without crushing it. 

Effect of Eccentricity in Placing Briquettes. One of the causes of 
irregularity in tests of similar briquettes is careless adjustment of the 
briquette in the clips of the machine, that is, placing it so that it is not 
exactly central. Prof. J. B. Johnson|| has discussed this theoretically, and 
concludes that 

if h = width of specimen, 

and a = eccentricity of loading, 

then — represents the percentage of increase in stress due to ec- 
h 

centricity. 

“Thus if a cement briquette one inch thick be placed in the clips 0.01 inch 
out of center, its strength will be reduced by 6%. This assumes perfect 
freedom of motion of the clips at the surface of contact, which they do not 

^Journal Association of Engineering Societies, January, 1899, p. I. 

fSee p. 136. 

jMore exactly, 14.2234. 

§More exactly 0.07031. , 

|| 1903 Edition, p. 446. 



g4 A TREATISE ON CONCRETE 

have. Experiments made at the Massachusetts Institute of Technology 
have shown that a displacement of one-sixteenth inch decreased the tensile 
strength by from 15% to 20%.” 

Rate of Applying Strain. The selections of the standard rate of 60c 
lb. per minute by the committee of the American Society of Civil En- 



Fig. 22.—Shot Testing Machine. (See p. 95.) 


gineers (see p. 76) is based on an extensive series of tests from which 
it was found that the breaking load increases with the speed up to a 
rate of at least 800 lb. per min., but that between the rates of 400 and 
600 lb. the variation is slight. Mr. E. S. Wheeler’s* experiments lend 
to confirm this conclusion. 

^Report Chief of Engineers, U. S. A., 1895, p. 2916. 











Fig. 23.—Shot Testing Machine. (See p. 95.) 

break occurs. The breaking load is determined from the weight of the 
shot. 

(b) The simple or compound lever machines apply their load by a 
sliding weight operated by hand or by power. A compound lever power 
machine is illustrated in Fig. 24, page 96. 


STANDARD CEMENT TESTS 95 

Types of Testing Machines. There are three most common types of 
tensile testing machines. 

(a) The shot machine, originally designed by Dr. Michaelis and shown 
in its American patterns in Figs. 22 and 23, applies the load by the dis¬ 
charging of a stream of shot whose flow is automatically shut off when the 











A TREATISE ON CONCRETE 


96 

(c) The spring balance machine, which was originally designed and 
used by Mr. Henry Faija in England, transmits the strain from the crank 
to the briquette through a spring balance which records the load upon the 
dial. (See Fig. 25, p. 97.) 

Johnson’s Ring Testing Machine. A machine devised by Mr. A. N. 

Johnson for testing the tensile strength of cement and mortars is based on 
an entirely different principle from the clip machines just described 



Fig. 24.—Compound Lever Testing Machine (See p. 95.) 


The cement or mortar instead of being formed into standard briquettes is 
molded in the shape of rings. The apparatus is shown in Figs. 26 and 27, 
page 98. A cylinder A filled with water or other liquid contains a piston oper¬ 
ated by a handwheel F. The pressure exerted by lowering the piston is 
transmitted by the liquid to the closed cylinder B, a section of which 
consists of rubber tubing which is expanded by the pressure from within 
until it bursts the ring of cement which encircles it. The pressure is alee 





























































STANDARD CEMENT TESTS 


97 


transmitted to the gage whose reading for a certain diameter and thickness 
of ring of cement or mortar bears a definite ratio to the circumferential 
tensile stress upon the ring. Brass molds of special design for forming 
the rings are constructed either single or in gangs of five. 

TENSILE TESTS OF NEAT CEMENT AND MORTAR 

Tests of tensile strength are made primarily to determine whether the 
ingredients of the cement and the process of its manufacture are such that 
a continued and uniform hardening may be expected in the work, and 

whether its actual strength in mortar or 
concrete is so high that it can be depended 
upon to withstand the strain placed upon it. 
Tensile tests must be combined with other 
tests, most particularly the test for sound¬ 
ness, to arrive at correct conclusions on 
these points. 

The dates which have been universally 
selected for making tensile tests to deter¬ 
mine the quality of the cement are 7 days 
and 28 days after molding. In each case 
the briquettes remain for the first 24 
hours in moist air, and the balance of 
the time in water at the standard tem¬ 
perature of 21 0 Cent. (70° Fahr.). For 
arriving at a quicker knowledge of the 
quality, standard specifications require 
one-day tests, the briquettes being broken 
after 24 hours in moist air. Longer 
periods than 28 days are useful for deter¬ 
mining the rate of permanent hardening, 
although the rate of growth is different in 
neat cements, mortars and concretes. The 
growth in tensile strength is not strictly 
comparable with its growth in compressive strength. 

A cement giving an extremely high test at a very short period may be 
regarded with suspicion, although if future tests show a good increase, no 
fault can be found. Specifications occasionally limit the strength of the 
one-day or the 7-days test. Others require a definite increase in strength 
between periods. The engineers of the New York Rapid Transit Com- 



Fig. 25.—Spring Balance Testing 
Machine. (See p. 96.) 






















9 8 


A TREATISE ON CONCRETE 




D 

Fig. 27.—Machine after a Test with the Top Cap Removed, Showing the Broken 
Cement Ring and Distended Rubber Cylinder or Tube. (See p. 96.) 


Fig. 26.— Machine with Cement Ring in Position ready for a Test. (See 


p. 96.) 












STANDARD CEMENT TESTS 


99 

mission require, for example, “a specific ratio of increase,” 15% in tensile 
strength from 7 to 28 days, and furthermore that a cement showing as 
high as 750 lb. at the earlier stage should be generally refused as unlikely 
to give good results in long-time tests.”* Manufacturers consider this 
a very severe requirement for Portland cement tested neat. 

Specifications for tensile strength are given on pages 30 and 31. A 
comparison of these with the actual strengths of different cements as 
furnished by manufacturers will show that on the average the tensile 
strength of Portland cement as now manufactured is largely in excess of 
the specifications. In comparing these figures, however, it must be 
recognized that specifications are not for average strength, but are in¬ 
tended to cover the lowest limit which can be allowed on the work, and 
to provide for lack of uniformity in testing as well as in real quality. 


GROWTH IN STRENGTH OF PORTLAND AND NATURAL 
CEMENTS AND CEMENT MORTARS 

The curves in Fig. 28, for which we are indebted to Mr. W. Purves 



Fig. 28. —Growth in Tensile Strength of Neat Portland Cement and Portland Cement 
.Mortars with Different Proportions of Standard Sand. (See p. 99.) 

(Compiled for this treatise by W. Purves Taylor.) 


Taylor, illustrate the growth in strength of neat Portland cement and 
Portland cement mortars. The tests from which the curves are drawn 
were made under his direction at the Philadelphia Municipal Laboratories. 

*Report of New York Board of Rapid Transit Commissioners, 1900-01, p. 258. 







































































































































































































































































































































































































































































IOO 


A TREATISE ON CONCRETE 


The neat and i: 3 (i. e., one part cement to 3 parts sand by weight) curves 
are averaged from over 100,000 briquettes, while the other curves are each 

based on tests of 300 to 500 briquettes. 

The cements included a number of brands, American brands largely 
predominating. The sand was crushed quartz, the former U. S. standard. 
The Philadelphia records include tests of much longer time than one year, 
and there is a noticeable falling off in the observed tensile strength after 
the one-year period. This is most noticeable with neat cement of rotary 
kiln brands, but also occurs to a less degree with sand mortars. With 
cements from stationary kilns it is less marked. The falling off in tensile 
tests is generally attributed to the brittleness of the small sized speci¬ 
mens, which tends to irregularity of results with the ordinary testing 
machine, and to the unequal hardening of the surface and interior of the 
specimen, rather than to actual deterioration in the cement. 

The average growth in strength of neat Natural cement and Natural 
cement mortars is illustrated in Fig. 29 from data kindly prepared by 



Fig. 29.—Growth in Tensile Strength of Neat Natural Cement and Natural Cement 
Mortars with Different Proportions of Standard Sand. (See p. 100.) 

(From data by Richard L. Humphrey and A. W. Munsell.) 


Mr. Richard L. Humphrey from Philadelphia tests, and by Mr. A. W. 
Munsell from tests made for the Baltimore & Ohio R. R. Cements from 
seven different sections of the United States are included in the averages 
from which the curves are drawn, representing the Akron, Cumberland, 
James River, Lehigh Valley, Louisville, Milwaukee, Rosendale and Utica 
districts. 






























































































































































































































IOl 


STANDARD CEMENT TESTS 

SOUNDNESS OR CONSTANCY OF VOLUME 

The term “ soundness ” is more commonly used in America and England 
than the expression ‘‘constancy of volume” suggested by the Committee 
of the American Society of Civil Engineers, or “deformation” as employed 
in France. The purpose of the test is to determine in advance whether a 
cement is in danger of disintegrating, that is, crumbling, or of expanding 
or contracting so as to cause distortion or cracking in the masonry. 

If a cement satisfactorily passes the tests for soundness, it will in all 
probability withstand the effect of the elements without swelling or disin¬ 
tegration, and will continue to harden for an indefinite period. Failure, 
on the other hand, to pass the tests for soundness, especially the hot test, 
is not positive proof of inferiority, for a cement which fails to pass may 
possibly, through subsequent exposure to the air before being used, or 
because of mixing with sand or other aggregate, produce durable masonry. 
We may, however, with safety adopt the following conclusion: 

If a Portland cement passes the hot test it may be used immediately 
with reasonable certainty of its ultimate soundness. If it fails to 
pass, it should be regarded with suspicion and thoroughly tested. 

Causes of Unsoundness. Disintegration, or crumbling, of work in 
Portland cement properly mixed and laid, is usually due to an excess of 
lime in a form which can be attacked by the elements. This may come 
about in two entirely distinct ways, either (i) by the use of too high a 
proportion of lime in the raw materials from which the cement is made, 
(2) by under-burning the cement, or (3) by too coarse grinding. 

The presence of magnesia in excess in a thoroughly burned cement may 
produce a gradual expansion which will disintegrate the mortar or con¬ 
crete after several years. This action, brought to notice by tests of Mr. 
H. Le Chatelier,* is generally recognized, but opinions differ as to the 
limit to the percentage of magnesia which may occur in Portland 
cement without deleterious effect. Le Chatelier’s experiments led him to 
consider 5% as injurious. The Association of German Cement Manu¬ 
facturers first placed the limit at 3^%, and later raised it to 5%. Mr. 
Spencer B. Newberry states (page 56) that recent experiments made by 
himself and by Van Blaese show that cements containing 8% or 9% of 
magnesia will pass the boiling test, while those with 15% magnesia will 
expand. The limit of 4% recommended by the Committee of the Amer¬ 
ican Society for Testing Materials in 1904 (see p. 30) is undoubtedly 
conservative. Natural cement, which is burned at a lower temperature, 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 229. 


102 


A TREATISE ON CONCRETE 


may contain a much larger quantity of free lime and of magnesia without 
injury. 

The expansion caused by an excess of free lime is due to the hydration 
or slaking of the calcium oxide (CaO). This is readily understood from 
the expansion of common lime, which in slaking with water will produce 
a bulk of paste from 2 to 3 times greater than the volume of the loose 
powder. The presence of lime in a free or loosely combined state must 
not be confounded with other compounds of calcium. A thoroughly 
slaked lime paste, or pow’der, that is, one which is completely hydrated, 
may in fact be added to a Portland cement mortar without injurious 
results, to lengthen its time of setting or to produce a more water-tight 
mixture. 

The small amount of free lime which frequently occurs and sometimes 
produces unsoundness in first-class Portland cement, tested when fresh, 
may be hydrated and rendered harmless by air-slaking after, say, two or 
three weeks’ storage, or after spreading the cement out in the air. 

Adulteration with slag may cause a cement containing an excess of 
free lime to pass the boiling test. 

Tests for Soundness. The presence of ingredients which will render a 
cement unsound, that is, which will cause it to expand or disintegrate, is 
determined by the eye, or by measuring appliances in specimens which 
have been exposed under conditions which as nearly as possible produce 
the same effect as the practical effects of time and the elements. 

There is apparently no reliable method for determining the presence of 
free lime by chemical analysis. Mr. E. Candlot* says that “ there is in fact 
no method for finding the percentage of free lime in the cement,” and 
Dr. Schuman* concurs in this view in the following statement* 

I do not know a method for finding out the percentage of free lime in 
Portland cement. I do not think there exists such a method, and I am 
myself of the opinion that chemists will never find out one; the solutions 
capable of taking away the free lime from the cement will always work in 
a more or less strong degree on the cement itself. 

This inability to detect free lime by chemical analysis necessitates a 
resort to physical tests. Specimens for testing soundness are generally 
circular pats tapering toward the edges, so that the expansion of the mass 
will tend to enlarge the circumference and thus produce cracks at the edges. 

^Quoted by W. \V. Maclay in Transactions American Society of Civil Engineers, Vol XXVII, 
p. 448. 


STANDARD CEMENT TESTS 


103 


Egg-shaped specimens and also briquettes are sometimes used. Both 
of these show deterioration by the appearance of the surface. 

Appearance of Soundness Specimens. Cracks which appear on pats 
are not always caused by unsoundness. Expansion cracks, which reveal 
an unsound cement, are distinguished from shrinkage cracks, which usually 
appear during setting instead of after the cement is set, in Figs. 30 to 37. 
Hair cracks also sometimes appear upon specimens, and in practice upon 
neat cement or very rich mortar, where so large an excess of water has 
been employed in mixing that it does not dry off until the cement has set, 
and causes the deposition of a very thin coating of partially decomposed 
cement which had remained in suspension in the water. An unsound 
cement in air or in water at the ordinary temperature will generally show 
defect within 28 days, although in very exceptional cases several months 
or even years have been known to elapse before signs of deterioration 
appear in specimens which have not been subjected to heat. 

Photographs of pats illustrating the appearance of defective specimens 
which have been subject to the boiling test are shown in Figs. 38 and 39, 
pages 108 and 109. Figs. 30 to 37, pages 104 and 105, are sketches* 
employed in the Philadelphia Municipal Laboratories for distinguishing 
harmless appearances in neat pats from evidences of unsoundness. Mr. 
Taylor describes the pats as follows: 


Fig. 30 represents a normal pat in good condition. 

Fig. 31 represents shrinkage cracks. These cracks are ordinarily due to 
the use of a too wet mixture or to too quick a drying out. If the pats are 
left exposed to dry air during setting these cracks are often developed. 
Shrinkage cracks ordinarily, therefore, indicate only a lack of care in 
manipulation, and not dangerous properties in the cement. 

Fig. 32 shows cracks caused by the expansion of the cement and the 
curling of the edges of the pat from the glass while the pat still adheres, 
which is often coincident with the expansion. In the air pats these cracks 
are developed in nine-tenths of the pats adhering to the glass, and unless 
very decidedly marked are not dangerous. They should not exist in the 
water pats. If they do exist, however, to an appreciable extent, it denotes 
the presence of a too great proportion of expansives, which ordinarily is 
sufficient to condemn the sample. 

Fig. 33 shows blotching, a pat which is usually indicative of either adul¬ 
teration or under-burning. This condition in itself should not necessarily 
mean rejection, but should always induce an investigation of the causes 
producing it, which may or may not be sufficient to warrant rejection. 

Fig. 34 shows pats which have left the glass (/l) by mere lack of ad- 
nesion, ( B ) by contraction, and (C) by expansion. ( A ) is never dangerous 

♦Presented to the authors by Mr. W. Purves I aylor. 


104 


A TREATISE ON CONCRETE 




Fig. 32. —Expansion Cracks, Harmless in Air Pats.* 




Fig. 33.—Blotches Requiring 
Investigation.* 


FtG. 34.—Pats which have left Glass.* 



*See pp. 103 and 106. 

















STANDARD CEMENT TESTS 


io 5 




Fig. 35. —Cracked Glass (pat removed.)* 




Fig. 36.—Incipient Disintegration.* 



Fig. 37.—Complete Disintegration* 
*See pp. 103 and 106. 
















io6 


A TREATISE ON CONCRETE 


in either air or water. ( B ) and (C) are dangerous only when existing in 
a marked form. A curvature of about a quarter of an inch can be con¬ 
sidered about the limit of safety in a 3-inch pat. Case (C) rarely, if ever, 
occurs in water. 

Fig. 35 shows a peculiar condition in which the pat is perfectly sound and 
hard, but the glass on which it is made is badly cracked.* This has often 
been laid to chemical action, but this conclusion is doubtless erroneous. 
It is probably due entirely to expansion of the pat, when the adhesive 
strength of the cement to the glass exceeds the strength of the glass itself. 
It is only found in the water pats, and is not usually indicative of dangerous 
qualities of the cement. 

Fig. 36 shows the radial cracks of incipient disintegration. These are 
the danger marks to be looked for in the normal pat tests, and are always 
sufficient to warrant rejection. 

Fig. 37 shows cases of complete disintegration, which almost invariably 
begins merely by showing radial cracks, as in Fig. 36. 

Accelerated or Hot Tests. The object of all forms of hot tests is to 
produce in a few hours the results which at a normal temperature require 
several days or perhaps months. Engineers are by no means agreed as to 
the value of accelerated tests, the chief objection to their use being that 
some cements which fail in these tests prove satisfactory in construction. 

An argument for the hot test lies in the fact that Portland cement 
manufacturers are coming to recognize it as the very best test for 
them to use in determining whether their own cement will fulfil the 
requirements of permanent construction. In a recent letter to the authors 
the superintendent, of one of the largest factories in the United States 
writes, “So far as we are concerned, we consider the hot test of the greatest 
importance. If this shows up well, we feel quite satisfied that all other 
tests will show up properly.” Those desiring to investigate the various 
opinions upon the subject are referred to References, Chapter XXXI. 

Mr. W. Purves Taylor, in a paper read before the Cement Section of the 
American Society for Testing Materials, at the Sixth Annual Meeting, 
1903,1 gives the results of a large number of accelerated tests made 
at the Philadelphia Testing Laboratory by boiling balls or pats (after 
24 hours in moist air) for three or four hours, and the results of some 
of the conclusions there given are quoted as follows: 

“The condition in a cement most affecting the result of an accelerated 
test is its age or the amount of seasoning it has undergone. Every cement, 

*Similar causes may produce one or two cracks in the glass. 

fProceedings American Society for Testing Materials, 1903, Vol. Ill, p. 374, also printed 
Engineering News, July 23, 1903, p. 81. 


STANDARD CEMENT TESTS 


io? 

no matter how well proportioned and burned, will contain at least a small 
amount of free or loosely combined lime, which will usually cause un¬ 
soundness if used or tested at once. This lime, however, will hydrate in a 
very short time on exposure to air, thus rendering it inert and preventing 
any expansive action. It will, therefore, be found in a large majority of 
cases that if a cement failing in the accelerated tests be stored for two or 
three weeks, this unsoundness will disappear, and the cement pass the 
test with ease.” 

This is illustrated in the following table and in Fig. 38, page 108, the 
first three photographs also showing various conditions which may be 
expected in specimens which fail to pass accelerated tests. 

Effect of Age of Cement on Results of Boiling Test. 


By W. Purves Taylor. {See p. 107.) 




TENSILE STRENGTH 


[normal pat tests 


Age of 
cement 
when 
tested 


Neat 


1:3 

sand 

BOILING TEST 

>> 

d 

M 

7 days 

28 days 

7 days 

C/3 

d 

00 

<N 

28 days in air 

28 days in water 

i week 

550 

7 6 5 

762 

171 

225 

Curled and soft. 

Slightly 

checked. 

Partly disin¬ 
tegrated. 

2 weeks 

548 

67 

771 

170 

246 

Slightly curled. 

Slightly curled. 

Checked and 
cracked. 

3 “ 

49 2 

718 

7 6 3 

182 

244 

“ O. K.” 

“ O. K.” 

Slightly 

checked. 

5 “ 

427 

692 

747 

l § 3 

249 

“ O. K.” 

“ O. K.” 

Sound. 


“Coarseness of grinding is also a frequent cause of unsoundness for the 
reason that the larger particles are not readily susceptible to hydration, and 
contain for a long period of time expansive elements which very rapidly 
develop a disintegrating action when treated in the accelerated tests.” 

“A large number of tests on different cements were made and the time 
at which failure occurred was observed. In these tests it was found that 
of those samples which did not pass the test, 22% failed in the first half 
hour, 57% failed in the first hour, 85% failed in two hours, 96% in three 
hours and 99% in four hours,” “thus showing generally that a test piece of 
cement standing three or four hours of boiling will almost invariably stand 
a much greater* length of time, and also that at least three or four hours 

should always be allowed for the test.” 

“Pats of cement allowed more than about twelve hours to harden will, 
if unsound, fail when tested by boiling at almost any time in the future.” 

“We now come to the very important question of the relation of the 
boiling tests to the other tests foi soundness and strength as made in the 


























io8 


A TREATISE ON CONCRETE 


laboratory. No one who has had much experience with the boiling test 
questions that, although it is by no means infallible, the results obtained 
from it are generally corroborated by either the tensile tests or the normal 
tests for soundness. The writer has recently compiled some data in re¬ 
gard to this point, covering over a thousand tests on many varieties of 
cement, with the following results: 

“Of all samples failing to pass the boiling test, 34% of them developed 
checking or curvature in the normal pats — or a loss of strength in less than 
twenty-eight days. Of those samples that failed in the boiling test but re- 




One Week Old. 


Two Weeks Old. 


Three Weeks Old. . Five Weeks Old. • 

Fig. 38.—Specimens showing the Effect of the Age of the Cement upon its Soundness. 

(See p. 107.) 

mained sound at twenty-eight days, 3% of the normal pats showed checking 
or abnormal curvature in two months, 7% in three months, 10% in four 
months, 26% in six months, and 48% in one year; and of these same sam¬ 
ples, 37% showed a falling off in tensile strength in two months, 39% in 
three months, 52% in four months, 63% in six months, and 71% in one 
year. Or, taking all these together, of all the samples that failed in the 
boiling test, 86% of them gave evidence in less than a year’s time of pos¬ 
sessing some injurious quality. 

“On the other hand, of those cements passing the boiling test, but one- 
half of 1% gave signs of failure in the normal pat tests," and but 13% 
showed a falling off in strength in a year’s time. 










STANDARD CEMENT TESTS 


109 

u This certainly makes a very strong showing in favor of the boiling test, 
at least considered from a laboratory standpoint. 

“In order to show the great value sometimes obtained from the results 
of the boiling test, several examples are given in the table on page ito of 
tests of cements occurring in the regular routine work of the laboratory.” 

The air and water pats of sample 2 of this table are shown in Fig. 39 
at the age of four months. These pats were sound at twenty-eight days. 

In conclusion Mr. Taylor lays special emphasis upon the fact that many 
cements which do not pass the boiling test will give excellent results in 



Fig. 39.—Examples of Unsound Pats at 4 months which were sound at 28 days. 

(See p. 109.) 


practice. He gives as the probable reason for this that the test for sound¬ 
ness is generally made immediately upon the receipt of a shipment, while 
the cement used in construction has opportunity to season, and upon the 
fact “that the disintegrating action of a cement is always far greater when 
mixed neat than when mixed with an aggregate, and the greater the amount 
of the aggregate the less the tendency to unsoundness.” It is often good 
policy before rejecting a cement which fails to pass the hot test to hold it 
for a week or two so that it may further season and then retest it. 

Methods of Making Accelerated Tests. The methods of conducting 
accelerated tests are numerous, the object of all of them being to hasten 







Evidences of Failure in Cement Indicated by the Boiling Test. HO 

By W. Purves Taylor. (See p. 109.) 


♦ 


tuO 

P 


O 

PQ 


£d 
C 03 
. 3 ! -*-> 

C/3 Cj 


P &> p 


id 

c 13 

C/3 ccj c/3 Ctf 

■ ~■ >-1 •4 

M P M 


d 
C « 


03 

C 33 
.3 -M 
c /1 03 
•r; 4 

P bo 




■M d’ „ 

.2-2- d ' 0 

c /3 cd o 3 aj 

P & W l 5 


A! 

o 


'g 44 

g 2 

03 (J 

43 

U 


d 

c 

Cd rQ 

33 

33 


44 

<J 

<U 

u 


Gj 

4 

O 


d 

33 

44 

O 

33 

43 

U 


d 

33 

44 

<J 

33 

43 

u 


c/i 

H 

cn 

W 

H 

4 

< 

Pc 

4 

< 

a 

« 

o 

z 


< 


t/i 

>. 

cj 

73 

00 

01 


c/i 

43 

C 

O 

£ 

7 - 


C/3 

cj 

73 

00 

01 



\ 













X) 

T3 

-d x) 

T3 

x) 

T3 

-v 















03 

03 

03 03 

03 

03 

03 

03 


C/3 

£ 

1 

<L> 

'd 

i 

T3 

1 

a; 

4-» 

t 5 

1 

<u 

4-» 

T3 

1 

<D 

4-» 

-d 

i 

-d 

p 

44 

O 

1-3 

Tl 

2 

44 

U 

7^ 

^3 

44 

(J 


cl 

0 

g 

a 

*55 

<V 

4 -* 

cj 

• S 

*55 

<L> 

4 -* 

cj 

co 

<V 

4-» 

cj 

13 

• r-H 

C/2 

<D 

cj 

.s 

*s 

a; 

4-» 

*^ 

4-» 

c3 

0 

03 

43 

(J 

'dxi 
x 0 

u 

03 

43 

03 

a 

03 

43 

0 

u 

<L) 


Q 

bo 


bo 

P 

bO 

P 

bn 

Q 

bo 

p 

bJ3 

cd 

T 1 


nd 

cj 


nd 

cj 

T3 

c3 














PQ 

a 

c 3 

« S 

PQ 

a 

cj 

pq 

S 3 

cj 


C/3 

C/3 

ccj 

r —' H 

b 0 


33 

P 


C/3 

C/3 

PS 

lab 


33 

P 


o 


w 

o 


o 


M 

o 


o 


o 


o 


M 

o 


<4H 

O 

«4H 

O 

<4-H 

O 


«+H 

O 

O 

<+H 

O 

<4-» 

O 

mh 

O 

C/2 

C/2 

C/2 


C/2 

C/2 

C^ 

C/2 

C/2 

-d'd' 

*d d‘ 

dT d' 

. 

73 d* 

dd 1 

73 d‘ 

to d“ 

•dd* 

03 43 

03 43 

03 43 

(U 

+-> 

03 43 

03 43 

03 43 

03 43 

03 43 

T1 g 

4 g 

4 g 

Tl g 

T g 

4 g 

T g 

7H g 

0 2 

13 3 

4» 2 

p 3 

cj 

)h 

biD 

02 

3! § 

O 4 

u 2 

<J 4 

3 § 
O 4 

3 3 
0 2 

u 

03 

0 

O 

0 

CJ 

O 

0 

b^'d 

b^dl 

b^d) 

4-» 

b-.’d 

b^-d 

b-.'d 

b-,70 

b^d 

1§ 

'd § 

cj 

'B S 

cj 

• pH 

C/2 

• H 

1« 

1 § 

is 

'd S 

Cj 03 

d g 

pq 

pq 

pq 

P 

pq 

pq 

pq 

pq 

pq 

• •> 

. rv 

• 

. r, 



• #s 

« PS 

. PS 

X3 

TJ 

T3 

"d 



•d 

73 

d 

03 

03 

03 

03 



03 

03 

03 

7H 


7H 

’ JJ 



id 

7d 

72 

31 


31 

33 



3 

3 

3 

u 

U 

03 

03 



03 

0 

03 


o 

C/3 


d 

JO 

3 

o 


3 


3 

4 

o 

>,-o 

1 § 
pq 


-i-> C/3 

43 

bfij^ 

=3 “ 
b| 

03 — 1 

> 


^ , 

C/2 

43 3 
b 0 j 3 

33 b£> 

M -m 

4 ^ 
03 


4-> C/3 ’Zj C/3 

43 5 « 43 ^ 

bcJ2 boJ 5 


43 bJD 

C/3 

03 

> 


CO 


bo 


CP 33 
33 
> 


CO 

CO 

'm 


03 

P 


CO 

co 

P 5 

W> 


03 

P 


. 

+q co 

r- CO 

bbp* 

33 bJD 

CO 

-t-> 

dS 

03 ^ 

> 


>n 


co 


43 w 43 co 

_bcp 5 w)_2 


bJD 

(JJ 
>A C *~' 

4 

03 —' 

> 


CO 


bo 


4 33 
03 ^ 
> 


CO 

CO 

Hb 


03 

p 


w 

H 

o 

z 

W 

35 

4 

C/3 

W 

4 

HH 

CO 

Z 

w 

H 


73 

a 

cj 

CO 

CO 


aj 

£ 


CO 

43 

-*-* 

C 

o 

£ 

t- 


<N 

lO 


4- 

7j- 


Ov 


7 " 

CN 


M 

0O 


r^. 

7 - 


3'- 


10 

vO 


no 

Ov 


C /3 











cj 


CM 

M 


CM 


M 


0 

W 

"O 


GO 

no 


IO 

M 


rt* 

w 

co 

00 

cs 

<N 


CM 

CM 

CM 

CM 

CM 

<N 

CM 

CM 











w 











cj 

0 

Tt* 

C 20 

vO 

ro 

OO 

O 

CM 

uo 

ON 

ON 

no 

O 

CM 

00 

On 

01 

M 

M 

M 

CM 

M 

M 

CM 

M 

M 


4 months 

Disinte 

grated. 

Disinte 

grated. 

Disinte 

grated. 

ro 

CM 

CM 

M 

202 

94 

O 

01 

no 

C/2 










cj 


VO 

0 


no 


O 

no 

CM 

73 

Ov 

OO 

0 


O 

M 

CM 


CM 

OO 


vo 

J>- 


vO 


VC 

l'- 


CM 










c /2 










>> 

no 

CM 

CM 


H 


no 


On 


Ov 


vO 



CM 

OO 

vO 

CM 



OO 




CO 

OO 

OO 

OO 

>» 

cj 

CM 

no 

OO 



no 

CM 


CM 

■a 

CM 

O 

Ov 


CM 

O 

Ov 

no 

0 

M 

LO 

vo 




10 


10 

10 


03 

T 3 

a 3 


O 

(3 

CO 

-«-> 

CO 

03 


03 

03 

£ 


03 

T3 

c3 

S 

■i-i 

O 

13 


co 

03 


03 


Note.—A ll of these cements were normal in specific gravity, time of setting, and fineness. 









































STANDARD CEMENT TESTS 


in 


the hardening of the cement so as to produce in a few hours results which 
under ordinary conditions require weeks or months. Boiling the speci¬ 
mens, instead of steaming them as recommended by the Committee of the 
American Society of Civil Engineers, while more common, is more severe. 
Other methods are employed in Europe. 

The Steam Test, recommended by the Committee of the American So¬ 
ciety of Civil Engineers, requires, as already described (p. 77), that the 
pat after twenty-four hours in moist air shall be placed in an atmosphere 
of steam above boiling water. 

The Boiling Test was originated by Prof. Tetmajer in Germany. After 
twenty-four hours in moist air, or until it is thoroughly set, the specimen 
is placed in cold water, which is raised to and then maintained at the 
boiling point for several hours. Three or four hours is the time specified 
by Mr. W. Purves Taylor, and often used in the United States, although 
some cement factories boil for twenty-four hours. Dr. Michaelis ad- 
vocates six hours’ boiling, and this period is specified by the French 
Commission. 

Combined Boiling and Tensile Test. A regular test at many Portland 
cement factories consists in testing the tensile strength of briquettes which 
have been subjected to the hot test. A briquette of neat cement after 
twenty-four hours under a damp cloth is placed in an atmosphere of 
steam over boiling water for an hour or two, and then immersed in water 
at about the boiling point and boiled for about twenty-four hours, when 
it must show a certain tensile strength. 

The Hot Water Test, as adopted by Mr. Efenry Faija in England, and 
advocated there by Mr. David B. Butler, consists in subjecting a newly 
mixed pat to a moist heat of ioo° to 105° Fahr. (38° to 40° Cent.) for six 
or seven hours, or until thoroughly set, and then placing it in warm water 
at a temperature of 115 0 to 120° Fahr. (46° to 49 0 Cent.) for the re¬ 
mainder of the twenty-four hours. Mr. Deval in France employed a 
temperature of 176° Fahr. (8o° Cent.) for a period of six days. 

Other Accelerated Tests which have been employed in Europe are oven 
tests, where the specimen is heated in an oven; glow tests, where a ball is 
heated over a gas flame, and Prussing disc tests, where discs are formed 
under heavy pressure and then exposed to hot water. 

Measurement of Expansion. Appliances have been devised for testing 
the soundness of cement by measuring the amount of expansion or def¬ 
ormation which it undergoes in different periods of time. The principal 
of these are the long bar apparatus, devised by Messrs. Durand-Claye and 


II2 


A TREATISE ON CONCRETE 


Debray, which was recommended by the French Commission, Bauschin- 
ger’s caliper apparatus, and Le Chatelier’s tongs.* 

The Chimney Expansion Test , in which a small quantity of neat cement 
is solidly pressed into a straight lamp chimney with the idea that an un¬ 
sound cement will break the glass, is worthless, as all first-class cements 
expand to a greater or less degree. 

♦Described in Spalding’s Hydraulic Cement, 1903, p. 166. 


SPECIAL TESTS OF CEMENT AND MORTAR 


11 3 


CHAPTER VIII 

SPECIAL TESTS OF CEMENT AND MORTAR 

The most important tests for comparing the qualities of different cements 
and for determining their practical value have been described in the pre¬ 
ceding chapter. Certain other tests are often made to investigate special 
qualities of a cement or mortar, or for scientific research. 

Such special tests may be enumerated as follows: 

Color. 

Weight. 

Microscopical. 

Compressive. 

Transverse. 

Adhesive. 

Shearing. 

Abrasive. 

Porosity. 

Permeability. 

Yield of mortar. 

Rise in temperature. 

COLOR 

The color of a cement bears but slight relation to its quality, but a vari¬ 
ation of color in the same brand is sometimes an indication of inferiority. 
Natural cements made in different localities may often be distinguished 
from each other and from Portland cements by their color. 

Portland Cement. The chemical composition of Portland cements 
made by different processes is so uniform that the color of different brands 
varies less than that of Natural cements. 

The color of Portland cement is described as a cold blue gray. In 
England the term “foxy” is applied to ^ Portland cement of a brownish 
color. According to Mr. David B. Butler* this denotes “insufficient cal¬ 
cination or the use of unsuitable clay or possibly excess of clay.” He 
further states that if a Portland cement contains a large quantity of under¬ 
burned particles, on account of their lower specific gravity they tend to 
rise to the surface on troweling, thus forming a yellowish brown film which 
is noticeable in the section qf the briquette after fracture. 

*Butler’s Portland Cement, 1899, p. 255. 


A TREATISE ON CONCRETE 


114 

The dark color of the coarser particles of a Portland cement left as residue, 
on a screen is due simply to the fact that cement clinker is black, and pieces 
which are not finely ground retain the color of the clinker. 

Natural Cement. The color of Natural cement varies with the character 
of the rock and consequently with the locality in which it is produced. It 
ranges from the light ecru of the Utica (Ill.) cement to the dark grayish 
brown of the Rosendale (N. Y.). Samples received by the authors from 
various manufactories show the James River cement to be a light yellowish 
brown, the Akron (N. Y.) cement, ecru, the Milwaukee (Wis.) cement, drab, 
and the Louisville (Ky.) cement, a brownish gray. Certain other brands 
are similar in color to Portland. 

Puzzolan Cement. Puzzolan cement made from slag is of a light lilac 
shade, much lighter than Portland. After being kept under water it 
assumes, when freshly fractured, a bluish green tint. This green tint, 
which according to Candlot* is due to sulphide of calcium present in the 
cement, is especially noticeable in a sample kept in sea water, and fades 
on exposure to dry air. 

WEIGHT OF CEMENT 

Weight is no indication of quality. Formerly, nearly all specifications 
required that a cement should reach a certain standard of weight per 
struck bushel or per cubic foot, on the principle that, other things being 
equal, a thoroughly burned cement is heavier than one which is under¬ 
burned. But when, on the other hand, the degree of fineness was found 
to affect the weight much more than any difference in calcination, the 
worthlessness of this requirement became apparent, and the test for spe¬ 
cific gravity was substituted. 

The following table by Eliot C. Clarkef illustrates the difference in 
weight between cements of the same manufacture which contain different 
percentages of coarse particles. 

Weights of Cements Containing Varying Percentages of Coarse Particles. ( See p 114.) 

By Eliot C. Clarke. 


Percentage of cement retained 

Weight 

on No. 120 sieve 

per cu, ft. 

0 

75 

lb. 

IO 

79 

<< 

20 

82 

U 

30 

86 

U 

40 

90 

a 


♦Candlot’s Ciments et Chaux Hydrauliques, 1898, p. 159. 
fTransactions American Society of Civil Engineers, Vol. XIV, p. 144. 


SPECIAL TESTS QF CEMENT AND MORTAR 


11 5 

Mr. Henry F'aija’s experiments* arranged in the following table prove 
that the weight of a cement decreases with age. His explanation for this 
is that the lower specific gravity of the moisture and carbonic acid absorbed 
from the air tends to increase the bulk of the cement without correspond¬ 
ingly increasing its weight. 


Decrease oj Weight of Cement with Age. (See p. 115.) 

By H. Faija. 



Weight per 

Percentage of 


cu. ft. 

loss in weight 


lb. 

per cent. 

When received. 

88 


After one month. 

85^ 

2.7 

“ three months... 

79/4 

9.9 

“ six “ . 

78 

11.4 

“ nine “ . 

75/4 

14.2 

“ one year. 

74 

i 5-9 


Method of Weighing Cement. The apparatus finally recommended 
by the French Commission, after a series of tests by Mr. P. Alexandre,f 
was a circular funnel with screen, as shown in Fig. 40. The cement 
placed upon the screen is stirred with a wooden spatula 4 cm. (if in.) 
wide, and 25 cm. (10 in.) long, and falls through the screen into the 
cylindrical measure of one liter capacity (61 cu. in.). 



0 


/! 


spatule 

s 


<-\K> 

k. 


MICROSCOPICAL EXAMI¬ 
NATION OF PORTLAND 

CEMENT CLINKER 

The structure of Port¬ 
land Cement clinker can 
be clearly discerned with 
the aid of the microscope 
and polarized light by 
preparing thin sections of 
it in the same way as those 
of rocks made by petrog- 
raphers. 

Le Chatelier, a French 
engineer, and Tornebohn, 


Fig. 40. Funnel Used in Weighing Cement. 

(See p. 115.) 

♦Butler’s Portland Cement, 1899, p. 240. 

fCommission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 


21. 
































A TREATISE ON CONCRETE 


116 

a Swedish petrographer, some years ago identified two essential 
mineral entities, and tnree others oi less importance, as constituents 
of Portland cement clinker. Tornebohn denominated the two essen¬ 
tial constituents alite and celite. 

Mr. Clifford Richardson has within the last few years taken the sub¬ 
ject up very elaborately in this country, and his results go to show that 
optical methods of examining clinker will eventually prove of great in¬ 
terest, not only in determining the character of clinker, but also in 
pointing out means of improving the methods of production. 

COMPRESSIVE TESTS OF CEMENT 

Compression testing machines are coming into general use in America. 
For merely determining the quality of a cement, tensile tests are more con¬ 
venient because they can be made more quickly and require less powerful 
machines, but for comparing different sand aggregates and for its adapt¬ 
ability to testing concrete by compression or by transverse, i.e., beam, 
tests, the compression machine possesses great advantage. The 
French Commission recommend compression tests in addition to 
tension, and many engineers in the United States advise them in well 
equipped laboratories.* 

Types of Compression Testing Machines. Machines especially adapted 
for compressive tests are built with capacities ranging from 30 000 to 
400 000 lb., or even larger. The Emery Machine at the Watertown 
Arsenal, U. S. Army, is of 800 000 lb. capacity while the machine designed 
in 1908 for the structural materials laboratory of the U. S. Geological Sur¬ 
vey at St. Louis has a capacity of 10 000 000 lb. A machine with a 
capacity of not less than 40 000 lb. is required for 2-inch cubes of neat 
cement or mortar, while for 6-inch cubes of mortar or concrete a machine 
should run to at least 150 000 lb. 

A testing machine for general laboratory work driven by power is illus¬ 
trated in Fig. 41, in which the pressure is continuously applied by means of 
a screw pump. It may be operated either by hand or by power and is 
built for maximum capacities of 200 000 lb. and upwards. 

An American machine of about 40 000 lb. capacity of the same type as the 
German Amsler-Laffon compression testing machine is illustrated in Fig. 
42, page 118. The hydraulic power is applied by turning the hand wheel 
and the load is read directly from the pressure gage. 


* Proceedings American Society of Civil Engineers, April, 1900, p. 125. 


SPECIAL TESTS OF CEMENT AND MORTAR 117 

Form of Compression Specimens. Extended tests were made for the 
French Commission by Mr. P. Simeon,* in which he employed specimens 
of various shapes and sizes, and compared the results with those obtained 



Fig. 41. —Compression Testing Machine. (See page 116.) 


from crushing the halves of briquettes which had been broken in tension. 
Quoting from a discussion of Mr. Thompsonf upon the Report of the 
Cement Committee of the American Society of Civil Engineers: 

♦Commission des Methodes d'Essai des Materiaux de Construction, Vol. IV, 1895, p. 187. 
■(■Sanford E. Thompson in Proceedings American Society of Civil Engineers, August, 1903, p. 646. 










A TREATISE ON CONCRETE 


Fig. 42. Hydraulic Compression Testing Machine. (See page 116) 









SPECIAL TESTS OF CEMENT AND MORTAR 


ii9 

The Commission reached the conclusion that the briquettes which had 
been broken in halves by tension should be used for the compressive tests. 
The two halves of each briquette are crushed separately and the sum 01 the 
two results divided by the total area of the briquette, thus obtaining the com¬ 
pressive strength per unit of surface. The surface area of the United 
States standard briquette recommended by our Committee is almost 
exactly 4 sq. in. Instead of the halves of a briquette, a single cylinder 
having the same thickness and the same area of surface as a whole 
briquette may be used with substantially equivalent results. 

Specimens which are rough or uneven may be smoothed by gentle 
rubbing on a stationary grindstone. 

In breaking, the pressure should increase uniformly, and at such speed 
that it will require between one and two minutes to crush each specimen. 

For comparing the strength of cement paste or mortar, with that of 
other materials which cannot readily be molded in cement molds, the 
Commission recommends cubes having an area of 50 sq. cm. (7.75 sq. in.) 
on each face. For a United States standard, cubes 2 in. on an edge, that 
is, with all faces having an area of 4 sq. in., conform to most common 
usage, and are therefore best for this class of comparative tests. 

A mold for cubes is shown in Fig. 43. 



Fig. 43. —Gang Mold for Compression Cubes. (See p. 119.) 

Relation of Compressive to Tensile Strength. Mr. R. Feret* con¬ 
cludes, after an extended series of tests, that there is no constant relation 
between resistances to compression and tension. He also concludes that 
the rate of increase in strength varies with the different cements, so that 
“two different mortars having the same resistance to compression do not 
necessarily break under the same tension.” He claims that compression 
tests give better results than tension and furnish “the real measure” of the 
cohesion of mortars. These opinions are generally corroborated by cement 
experts. 

The ratio of compression to tension also varies with the character of the 
sand or other aggregate. With a larger proportion of cement the com¬ 
pressive strength increases faster than the tensile strength, thus giving a 
higher ratio. This law continues to hold with concrete of different pro¬ 
portions, that containing the largest proportion of cement showing the 
highest compressive strength in comparison to its tensile strength. 

* Bulletin de la Societe d’Encouragement pour Plndustrie Nationale, 1897, Series 5, Vol. II. 


120 


A TREATISE ON CONCRETE 


A comparison of the compressive and tensile strength of 1:3 mortars 
based upon tests at the U. S. Government Structural Materials Labora¬ 
tory at St. Louis, in 1908, gives a formula 

Compressive strength 

——— ---= 6.6 + 2.3. log. A , 

Tensile strength 

where 

A = age of the cement mortar in months. 

By this formula it will be seen that the ratio vario* from 6.8 on a one- 
month test up to 10.3 on a 12-months test. The formula is in the same 
form, but the ratios are somewhat greater than those obtained by Prof. 
J. B. Johnson* from Prof. Tetmajer’s tests at Zurich. 

TRANSVERSE TESTS OF CEMENT 

Transverse, or flexion, tests of beams or prisms while very convenient 
for concrete are now seldom used for testing the quality of cement, 
although Gillmore and other of the older experimenters largely employed 
this form of test. Transverse tests are of value in comparing the relation 
between fiber stress and tension, and with proper care may give as uniform 
results as tension tests. As is stated below, the fiber stress bears a definite 
relation to the tensile strength, but since there is no fixed relation between 
tension and compression, there can be no fixed relation between transverse 
strength and compressive strength. Compression testing machines (see 
Figs. 41 and 42, pages 117 and 118) may be adapted for transverse tests by 
a suitable arrangement of supports and knife edges. 

Size of Specimen. Mr. Durand-Clayef made for the French Com¬ 
mission an extended series of tests by flexion or bending. As a result of 
his report, the Commission adopted for this form of test square prisms 
t. 2 cm. (4.72 in.) long by 2 cm. (0.79 in.) on a side. 

rci ... ,-;,.«•• . *^ ... .» E 

In breaking, a prism is placed on its side — that is, on a face which has 
been in contact with the mold — upon two knife-edges, 10 cm. (3.94 in.) 
apart, and the load is applied at the center through a slightly rounded 
knife-edge. The load should be applied continuously at the rate of 1 kgr. 
(2.2 lb.) per second. The same number of specimens should be broken 
as in tensile tests, and the results averaged. 

• • ■' r— 

^Johnson’s Materials of Construction, 1903, p. 419. 

•{■Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 21 t. 

-i ' . . . : id 





SPECIAL TESTS OF CEMENT AND MORTAR 


121 


English measure will naturally change the dimensions of the specimen 
to i by i by 6 in., to be broken upon knife-edges 5 in. apart.* 



for Prism. 
{See p. 121.) 


A prism 2 by 2 by 8 in. was employed by General Gillmore in 
experiments described in his famous “Treatise on Limes, Hydraulic Ce¬ 
ments and Mortars,” and has been adopted by other 
American engineers, but with apparatus of sufficient 
delicacy there is no reason why the specimens need be 
larger in section than tensile specimens, and the dimen¬ 
sions of 1 by 1 by 6 inches suggested above are recom¬ 
mended for comparative tests of neat cements and mortars. 
A form of mold is shown in Fig. 44. 

Relation of Tensile to Fiber Stress. In the experh 
Fig. 44. —Mold nients mentioned above Mr. Durand-Claye compared ah 
of his tests for flexion with tensile tests of briquettes 
made and tested at the same time. As a result, he ob¬ 
tained as the ratio between the ultimate fiber stress in flexion and the ten¬ 
sile strength, 1.92 at 7 days and 1.86 at 28 days; or in round numbers, 
1.9 for both. That is, tensile fiber stress is 1.9 times the simple tensile 
stress of the same material. In this connection he calls attention to the 
fact that a briquette tested in tension gives a result less than the real resist¬ 
ance, while a prism tested in flexion gives a greater result. He judges that 
the real resistance may be approximated by taking the mean of the two 
results. 

Mr. Durand-Claye also found the mean error by the two methods of 
testing to be very similar, with tensile briquettes the variation being about 
2.02 % as compared with 2.52% variation in the flexion tests. In tests with 
mortar there was less variation with prisms than with briquettes. 

Prof. Edgar B. Kay states that in recent experiments he has obtained 
more uniform results with tranverse than with tensile tests. 

Comparative tests of Mr. R. Feret in tension, flexion, and compression 
are shown in the table on page 136. 


ADHESION TESTS OF CEMENT 

Mr. E. Candlotf made a large number of tests of adhesion for the Frencn 
Commission, and designed a mold adopted as the French Standard. 
With reference to such tests he says that since the adhesion of mortar to a 
stone depends upon the state of the surface and the nature of the cement, 

*Sanford E. Thompson in Proceedings Americ-'n Society Civil Engineers, August, 1903, p. 646. 
■{'Commission des Methodes d’Essai des Mater.^ux de Construction, 1895, Vol. IV, p. 281. 








122 


A TREATISE ON CONCRETE 


absolute tests are of little value, but comparative tests, if made under 
identical conditions, are of real interest to the builder. 

Thus, to cite several examples, the tests of adhesion prove that a mortar 
regaged after having set possesses a strength of adhesion much smaller than 
the same mortar gaged and put in place before its set, the resistance to 
tension and compression of these two mortars remaining, however, almost 
the same; that mortars gaged dry have a more feeble adhesion than mor¬ 
tars gaged slightly liquid; that mortars gaged with an excess of water have 
in tension a resistance less than their adhesive strength, etc. 

Method of Making Adhesion Tests. In the same report Mr. Candlot 

describes the forms of specimens suggested by Dr. Michaelis and others, 
and then presents a form which he considers to best meet the requirements. 
On account of the difference in section of the French standard briquette, 
the mold he describes is not suitable for making specimens to fit the clips 



B 


\ 
CO 

<q in 















=• — ■ 





il 



1 




n 


1 .02—> B' 

Fig. 45.—Mold for Adhesion Block. (See p. 122.) 


on American testing machines. To adapt his mold to American stand¬ 
ards, the authors have designed the mold shown in Fig. 45. The method 
of making tests is described by Mr. Thompson* as follows: 

Adhesion is considered by Mr. Candlot in two ways: First, with refer¬ 
ence to the relative adhesive qualities of different cements; and, second, 
with reference to the adhesion of the same cement mortar to other materials 
of different natures. The same general method is advocated in both cases. 

Briquettes are formed, as described below, of a shape which can be broken 
in an ordinary tensile testing machine. The European tensile briquette is 
of small section, 5 sq. cm. (0.775 sq* an d an inconvenient shape for 
molding in halves. The area of the breaking section is therefore doubled 
by the Commission, while the curves where the clips take hold remain the 
same, so that the distance between the two points of each clip is unchanged. 
The shape of the United States standard briquette is such that fewer changes 
have to be made in its outline, and the regular section of 1 sq. in. need not 
be altered. 

♦Proceedings American Society of Civil Engineers, August, 1903, p. 647. 





































SPECIAL TESTS OF CEMENT AND MORTAR 


123 


The Commission found that adhesion briquettes could not be molded 
satisfactorily in the manner used for tension briquettes. They advised 
finally a mold in which a half briquette could be made, and then when this 
had set, the same mold could be used for completing the other half. In 
Fig. 45 is shown the style of mold selected, but with the dimensions 
changed to adapt the briquette to the United States standard form of clip. 
It consists of a bottomless box, which divides vertically in the center on the 
line BB, so that the half briquette can be removed readily. The bottom is 
formed of a movable bronze plate, shown at A. 

For the first class of tests, to determine the relative adhesion of different 
cements, a normal adhesion block is formed of a mortar composed, by 
weight, of 1 part of highest quality Portland cement, which has passed a 
No. 75 sieve, and 2 parts of fine sand, gaged 9% of water. As soon as 
it is rammed into the mold, the mold is removed, and after remaining 
in moist air for 24 hours the half briquette is placed in water until it is re¬ 
quired. It must set for at least 28 days. When required for use, the block 
is dried and the surface polished with emery paper. The block is 
then placed on a table with the large end down, the half mold, with the 
disc A removed, set on top of it and filled with plastic mortar consisting of 
the cement which it is desired to test mixed with sand in the required pro¬ 
portions, thus completing the briquette. This briquette is treated and 
tested as an ordinary tension specimen. 

For the second class of tests, if the material can be molded, it is formed 
as a half briquette, and the specimen completed with the mortar to be tested. 
If solid, a plate of the material, several millimeters thick, having one smooth 
face, is prepared, and placed at the bottom of the mold, on top of the 
bronze plate, and the first half of the specimen is formed by filling the mold 
with neat cement. After setting, the half of the briquette is completed with 
the mortar which it is desired to test. 


Adhesive Strength of Mortar. The following table from tests of Mr. 
Candlot, presented to the French Commission,* shows the results of ad¬ 
hesive tests upon Portland cement mortars cemented to the normal adhe¬ 
sion block by the method described in the preceding paragraphs. It is 
noticeable that, in the same column, the values, each of which represents a 
single specimen, are fairly regular, but that there is a very great variation 
in the adhesive strength of mortars made F om different cements, and no 
uniform relation between the strength of mortars of different proportions. 

Adhesion of Mortar to Various Materials. The results of tests made 
by Professor Tetmajer in Germany, quoted by Mr. E. Candlot, are briefly 
as follows: 1:2 Portland cement mortars cemented to sandstone gave an 
adhesive strength after 28 days of from 5.5 to 8.8 kg. per sq. cm. (78 to 125 
lb. per sq. in.). To rough glass the adhesion was about 3.5 kg. per sq. cm 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1895* ^ r °^‘ P* 


124 


A TREATISE ON CONCRETE 


(50 lb. per sq. in.). Tests made at Boulogne-sur-Mer using blocks of 
marble showed, after 28 days, variations of 3.1 to 8.3 kg. per sq. cm. (44 
to 118 lb. per sq. in.). Regaged mortar showed about half the strength 
in adhesion of fresh mortar. 


Adhesive Strength 0 / Portland Cement Mortars in Pounds per Square Inch A 

By E. Candlot. 


Cement. 

A 

B 

C 

D 

Proportions of 
mortar. 

1: 3 

I: 3 

1:2 

1: 2 

i -3 

1: 2 

t -3 

1:2 

i :3 

1: 2 

Per cent, of 











water. 

12 

13-8 

9-5 

15 

12 

J 3 

15 

J 7 

12 

T 3 


lb 

lb. 

lb. 

lb. 

lb. 

lb 

lb. 

lb. 

lb. 

lb. 


107 

135 

142 

149 

36 

3 6 

3 6 

43 

60 

65 

7 day tests. 

195 

I 3 1 

r 45 

152 

36 

43 

38 

5 ° 

60 

65 


J 5 6 

I 35 

128 

28 

3 6 

38 

36 

57 

7 i 


156 

! 5 2 

i 35 


28 

50 


36 

67 

82 






3 6 




57 

107 

Average. ... 

147 

*43 

I 39 

J 43 

33 

4 i 

37 

4 i 

60 

78 


164 

192 

188 

178 

92 

142 

78 

95 

152 

95 


178 

206 

294 

J 5 2 

81 

114 

74 

78 

128 

88 

28 day tests. 

178 

220 

124 

192 

85 

114 

7 i 

117 

114 

74 


199 

220 

i8 5 

156 

60 

85 

81 

100 

107 







67 

102 


88 



Average. ... 

180 

209 

198 

169 

77 

hi 

76 

96 

125 

86 


Mr. E. S. Wheelerf has made several series of tests, inserting thin discs 
of different materials in the center of briquettes. Although the irregularity 
in the results cast considerable doubt upon his method of testing, the ex¬ 
periments tended to show that the adhesive strength to sawn limestone of 
Portland cement mortar in proportions 1: o to 1: 2 is about one-third the 
cohesive strength of the mortar alone. Mr. Wheeler concluded that groov¬ 
ing the surface of the stone has no appreciable effect on the adhesive 
strength. For the maximum adhesive strength more water is required than 
for the maximum cohesive strength even if the surface of the stone be satu¬ 
rated. The substitution of a small portion of lime for a part of the cement 
apparently increases the adhesive strength. 

^Molded upon normal adhesion blocks, see pp. 122 and 123. 

fReport Chief of Engineers, U. S. A., 1895, P- 3 OI 9 anc * 1896, pp. 2799 and 2834. 










































SPECIAL TESTS OF CEMENT AND MORTAR 


I2 5 

Mr. R. Feret* states that adhesion to stone increases as the stone be¬ 
comes more porous. He found, as did Mr. Wheeler, that irregularities of 
surface of the stone do not seem to affect the adhesive strength. With 
iron, however, roughening the surface increases the adhesion of the mortar. 
A dirty surface or insufficient moistening of the surface lowers the ad¬ 
hesion. 

The method adopted by various experimenters of crossing two bricks 
and cementing them together, then determining the loads required to sepa¬ 
rate them, is obviously inaccurate because of the difficulty of distributing 
the pull uniformly over the entire surface. 

The adhesion of mortar to iron or steel is of such practical importance in 
the use of iron or steel for reinforcement, and the setting of bolts in mortar 
and concrete, that the subject is discussed in connection with reinforced 
concrete in Chapter XXI. 

SHEARING TESTS OF CEMENT AND MORTAR 

Mr. R. Feret made a series of shearing tests upon different mortars 

which are quoted in column (20) of the table on page 
136. He employed for the shearing test the halves 
of small prisms which had been broken to determine 
the transverse strength, placing the specimens and 
loading them as is shown in Fig. 46. 


ABRASION 

Abrasion or wearing tests have been made by 
pressing the specimen against a grindstone, an emery 
wheel, or a cast-iron disc, the last requiring sand in 
definite proportions to be poured upon it to increase the friction. 

Tests by Mr. Eliot C. Clarkef tend to indicate that for Portland cement 
mortar the best proportions to resist abrasive forces are 1: 2 and for Natural 
cement mortar 1:1, the resistance of Portland cement mortar mixed with 
two parts of sand being nearly double that of both the richer 1: 1 mixture 
and the leaner 1: 2\ mixture. 

POROSITY TESTS 

r 

The determination of the porosity of a specimen is often necessary in 
scientific research and for comparing the relative absorptive properties of 

^Communication au Congres de Budapest, 1901. 
f Trans actions American Society of Civil Engineers, Vol. XIV, p. 167. 



1 

1 

1 

1 






r 

m 


Fig. 46.—Shearing 
Test. (See p. 125.) 












126 


A TREATISE ON CONCRETE 


building materials. Porosity is a passive quality referring to the actual 
voids, i.e., air and uncombined water in a substance as distinguished from 
permeability or percolation, the quality of a substance which permits the 
flow of a liquid or gas through it. 

Method of Testing Porosity. Messrs. P. Alexandre, P. Debray, and 
H. Le Chatelier* recommended a method for making the test for porosity 
which, with the units converted into English measure, is summarized by 
Mr. Thompson^ in his “ Discussion on the Report of the Committee of the 
American Society of Civil Engineers on Uniform Tests of Cement.” This 
method is suitable for testing the porosity of concrete as well as of mortar. 


The porosity of a mortar is expressed as the ratio or percentage of voids 
to the total volume. In measuring the voids all water in the mortar is 
included except that of crystallization. 

If 

V = total apparent volume of mortar; 
v = volume of solid portion of mortar; 
v' = volume of voids in mortar; 

then 


Porosity = 


v f 

y 


V—v 

V 


The size of specimen recommended is that having a volume of between 
0.3 and 0.5 liter (18 to 30 cu. in.). 

The solid volume, v, is found by the application of the principle of 
Archimedes, that the difference between the weight of a body in air and 
its weight when suspended in a liquid is equal to the weight of the liquid 
displaced. From the weight of the displaced liquid, its volume, which is 
manifestly the volume, v, of the mortar, can be readily calculated. 

In English measure, if 

P = weight of specimen after drying; 

P = weight suspended in water after saturation; 

W = weight of 1 cu. ft. of water; 
v = volume of solid portion of mortar; 

then 

p _ jj 

v (in cubic feet) = -C_. 

J W 


In order that the specimen may be thoroughly impregnated with water 
and all air driven from the pores when determining p , its weight in water, 
the specimen is first exposed for J hour in rarefied air at a pressure not 
greater than 25 mm. of mercury. Water is made to cover it, and then the 
atmospheric pressure is restored. It must now remain in the water 24 
hours before being weighed. If apparatus for rarefying the air is not at 

^Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. TV, p. 247. 

^Proceedings American Society of Civil Engineers, Aug. 1903, p. 648. 





SPECIAL TESTS OF CEMENT AND MORTAR 


127 


hand, and if the specimen will stand exposure to heat, an alternate method 
may be used. The specimen, after 48 hours in water, is placed in cold 
water, raised to boiling, and boiled for 2 hours, then allowed to cool for 
24 hours. The weight, P, used in this determination, is taken after ex¬ 
posing it to a heat of between 40° and 6o° Cent. (104° and 140° Fahr.), until 
there is no loss in weight, care being taken to prevent any access of car¬ 
bonic acid gas from the heating apparatus. 

The apparent volume, V, of the specimen, can be found by direct 
measurement, or by calculation from its loss of weight in water, using again 
the principle of Archimedes. To prevent saturation in the later proceed¬ 
ing, it can be covered with a thin coating of grease spread with the fingers. 
The weight in water must be taken before that in air. 

The standard test of porosity is made with 1: 3 mortars of normal 
plastic consistency, 28 days old. Other proportions and ages suggested 
are 1:2, and 1: 5, at 7 days, 28 days, 6 months and 1 year. 

The Porosity of Different Mortars. Porosity includes the voids or 
pores occupied by both air and water, the relative volumes of the two 
classes of voids varying with the freshness of the mortar. 

In different fresh mortars there is much less variation in the volume of 
air voids than is generally supposed. If we leave out of consideration 
mortars that are mixed to such a dry consistency that voids are apparent 
to the eye, we notice from column 10 of the table on page 136 that in mor¬ 
tars proportioned richer than 1: 5 the air voids rarely exceed 12%, and for 
most mixtures are in the neighborhood of 4% to 8%, that is, 4% to 8% by 
volume of air is entrained when gaging. Although experiments of Messrs. 
Candlot* and Alexandre show similar results, the authors, by mixing the 
materials with gloves, as recommended by the American Society of Civil 
Engineers, and using more water than required for standard consistency, 
— about, in fact, the consistency used by stone masons, — have obtained 
mortars in proportions of cement to either standard sand or bank sand of 
1:0, 1: 1 and 1: 2 with no appreciable entrained air, and leaner mixtures 
with 1% to 2% air. A few experiments carefully made tend to show that 
in larger batches thoroughly mixed to soft consistency these low percent¬ 
ages may be obtained. Such mortars require no ramming, in fact the 
volume cannot be reduced after it is carefully introduced into the measure, 
except that if a very wet mixture is used it will expel a portion of its surplus 
water when setting so that the volume set is less than the volume green. 
One would naturally expect a greater variation with different materials 
and different proportions of water, but as a matter of fact, in a fresh mor- 

*Candlot gives a range of from 2 or 3% for mortars of coarse sand, up to io^o with fine sand. 


128 


A TREATISE ON CONCRETE 


tar slightly softer than standard consistency, the spaces between the par¬ 
ticles of sand and cement are not occupied by air but by water. 

As the mortar dries after setting, the variation between different mortars 
is more appreciable, since the additional amount of water which is re¬ 
quired with mortars of fine sand partially evaporates and leaves air voids. 
It is evident from experiments by Mr. Alexandre that the percentage of air 
voids due to evaporation of water ranges from 7% with a very coarse sand 
to 18% with a very fine sand. Assuming a small allowance for entrained 
air in the fresh mortar, due to imperfect mixing, we may estimate a range 
of from 7% to 25% total air voids in mortar after setting and drying. An 
average mortar of Portland cement and fairly coarse bank sand, in pro¬ 
portions 1: 2 by weight or 1: 2\ by volume, from experiments of the authors, 
may be expected to contain about 10% of air voids after setting and 
hardening, and to have a total porosity of about 25%. The porosity of 
well proportioned concrete is much lower (see p. 339). The porosity is 
but slightly affected by the percentage of water used in gaging, because 
an excess of water rises to the surface. (See p. 338.) 

PERMEABILITY OR PERCOLATION TESTS 

The permeability of mortar and concrete is discussed and the laws which 
govern it formulated in Chapter XIX. page 338. Permeability is distin¬ 
guished from porosity on page 126. 

Method of Testing Permeability. When preparing its final report, the 
French Commission* first experimented with cylindrical blocks having in 

the center a truncated well into which a vertical tube 
was introduced for a short distance to convey the 
water under pressure. They finally recommended 
instead of this form a cube of cement or mortar with 
a pipe cemented to its upper surface. Quoting again 
from Mr. Thompson’s Discussion^ on Uniform Tests 
of Cement: 

The permeability of neat cement and mortars is 
expressed by the number of liters of water passed in 
one hour through a cubical block, 50 sq. cm. (7.75 sq. 
in.) on a face, the size used for compressive tests. The 
block is placed on its side, that is, with a face which 
has been against the mold uppermost ; this surface is 
carefully cleaned and a glass tube 3.5 cm. (1.38 in.) in diameter, and 11 

♦Commission des Methodes d’Essai des Materiaux de Construction, 1894, Vol. I, p. 313. 

fProceedings American Society of Civil Engineers, August, 1903, p. 649. 



Fig. 47.—French 
Test for Per¬ 
meability. (See 
p. 128.) 
















SPECIAL TESTS OF CEMENT AND MORTAR 129 

cm - ( 4-33 “}•) high is sealed vertically to it by means of neat cement, as 
shown in Fig. 47. For varying the pressure, a rubber pipe is attached to 
this tube, and its upper end connected with a reservoir. The height of 
pressure, according to the permeability of the mortar, may be 10 cm. (4 in.), 
1 m. (3 ft. 3 in.) or 10 m. (33 ft.). 

Before taking the test, the block is immersed in water for 48 hours, and 
remains in water during the test. The periods recommended are: 24 
hours, 7 days, 28 days, 3 months, etc. The standard test is made at 28 
days. Tests are made on three blocks, and an average taken of the two 
which most nearly agree. 

Logically, we should suggest for the block to be used for testing per¬ 
meability in this country, the size mentioned for compression, that is, a 
2-inch cube. Further investigation is considered necessary, however, 
before adopting either the size or shape as a standard. 

Since the publication of the above discussion, the authors have performed 
a series of tests on the relative permeability of concretes, as described on 
page 348, obtaining satisfactory relative results by cementing a short 
length of pipe to the surface of a solid block of concrete in a manner simi¬ 
lar to that adopted by the French Commission. 

YIELD TESTS OF PASTE AND MORTAR 

The French Commission* recommend the testing of cement paste and 
mortar to determine the volume occupied. The yield or rendement is 
the volume of mortar obtained by gaging to any given consistency a unit 
of weight of cement or of a mixture of cement and sand in the selected 
proportions. One kilogram of cement, or of the required mixture of 
cement and sand, gaged to the given consistency, is introduced into a 
graduated cylindrical glass test tube about 6 cm. (2.37 in.) in diameter, 
with care to avoid imprisonment of air, and its volume is noted. 

Another method, which they consider more accurate, is to allow the 
paste or mortar to harden and then determine the difference in weight in 
air and in water. 

Mr. R. Feret in his report to the French Commission-)* on the production 
and density of mortars considers that sands should be submitted to a 
thorough test. He advises determining their granulometric composition, 
as described on page 142, the proportion of gravel (that is, of particles 
remaining on a sieve with holes of 50 mm. (0.19 in.) diameter, the min- 
jralogical nature, and the form of the grains. Disregarding the yield test 
he would study the absolute volumes of the cement, the sand, the water, 


♦Commission des Methodes d’Essai des Materiaux de Construction, 1894, Vol. I, p. 307. 
fCommission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 243. 


130 


A TREATISE ON CONCRETE 


and the voids in a unit volume of fresh mortar, and would estimate the 
cost per cubic meter of mortar made with different sands, and its strength 
under various conditions, as is discussed at length in the following chapter. 


TEST OF RISE IN TEMPERATURE WHILE SETTING 

The determination of the rise in temperature which takes place in a 
cement while setting has often been suggested as an indication of its quality, 
but the increase in temperature is due to so many causes that it is of 
slight value as a test of the cement. 

Mr. Le Commandant Ribaucour* found that the temperature com¬ 
menced to rise at the commencement of the setting, and the rise was 
generally higher with quick-setting cements. 

Mr. J. E. Howard at the Watertown Arsenalf discovered that the 



Fig. 48.— Rise in Temperature in 12-inch Cubes of Cement and Mortar. 

(Tests of Metals, U. S. A., 1901.) {See p. 130.) 

temperature was largely dependent upon the size of the specimen, small 
cubes showing very slight increase. He therefore made a series of tests 
upon 12-inch cubes to determine the temperature acquired by different 
brands of cement and mortars during setting, and plotted his volumes in 
a series of curves. The curves for a first-class brand of American Port- 

*Commission des Methodes d’Essai des Materiaux de Construction, 1895, Vol. IV, p. 133. 
fTests of Metals, U. S A., 1901, p. 493. 
































































SPECIAL TESTS OF CEMENT AND MORTAR 131 

land cement with and without sand, and for a typical Natural (Rosen- 
dale) cement, are shown in Fig. 48. 

Mr. Howard found that while first-class American brands of neat 
Portland cement often reached a maximum temperature of ioo° Cent. 
(212 0 Fahr.); the maximum temperature of the various brands of Ameri¬ 
can Natural cement was generally from 35 0 to 40° Cent. (95 0 to 104° 
Fahr.), and was reached at a shorter time than the Portland cements. 
The rise in temperature of the German brands of Portland cements was 
in general less than that of the American Portlands. 

The rise in temperature in Portland cement concrete is less than in 
neat Portland cement, but in the interior of a large mass like a dam 
may reach nearly ioo° Fahrenheit. 

TESTS OF SAND FOR MORTAR 

Tests of sand for mortar and concrete are as important as tests of cement 
Methods of making tests are given on page 159. 


< 3 2 


A TREATISE ON CONCRETE 


CHAPTER IX 

STRENGTH AND COMPOSITION OF 
CEMENT MORTARS 

The following are the important conclusions in this chapter: 

(1) The strength of a mortar depends primarily upon (a) percentage of 
cement in a unit volume, and ( b ) density. (See p. 133.) 

(2) The strongest mortar for any given proportions, by weight, of cement 
to dry sand, is obtained from sand which with the given cement produces 
the smallest volume of plastic mortar. (See p. 148.) 

(3) The best sand is in general that which will produce the smallest 
volume of mortar of standard consistency when mixed with the given ce¬ 
ment in the required proportions. (See pp. 133 and 149.) 

(4) The density of a mortar is determined by calculating the absolute 
volumes of its ingredients. (See p. 138.) 

(5) The qualities of different sands may be studied by screening each 
into three sizes and comparing their granulometric compositions with 
Feret’s curves. (See p. 142.) 

(6) Sharpness of the sand grains is of slight importance. (See p. 154a.) 

(7) Coarse sand produces stronger mortar than fine sand. (Seep. 146.) 

(8) Fine sand requires more water than coarse sand to produce a 
mortar of like consistency, and consequently its mortar is less dense. (See 
P- I 45 -) 

(9) Mixed sand, i. e., sand containing fine and coarse grains, in mortars 
leaner than 1: 2, usually produces stronger and more impervious mortars 
than coarse sand. (See p. 146.) 

(10) Screenings from broken stone usually produce stronger mortars than 
sand because of their greater density. The relative value of screenings 
and sand may often be determined by comparing their densities or the 
densities of mortar made from them. (See pp. 150 and 153.) 

(n) Mixtures of fine and coarse sand or of sand and screenings often 
produce better mortar than either material alone. (See p. 149.) 

(12) The variation of the sand in different portions of the same bank 
may be utilized by requiring the contractor to mix two sizes without exact 
measurement, so that the material as delivered shall contain not less than 
a definite percentage of sand coarse enough to be retained on a certain 
sieve. (See p. 149.) 


STRENGTH OF CEMENT MORTARS 


i33 


( r 3 ) Mineral impurities in sand, such as clay, in small quantities, may 
strengthen a lean mortar, and weaken a rich mortar. (See p. 154b.) 

( I 3 a ) Organic impurities in sand, such as vegetable loam, even in minute 
quantities may destroy the strength of the mortar or concrete. (See p.i54b.) 

(14) Gaging with sea water does not affect the ultimate strength of mor¬ 
tars. (See p. 159b.) 

(15) The unit fiber stress in a cement or mortar beam is about the same for 
a prism 4 cm. (1.6 in.) on edge as for one 2 cm. (0.8 in.) on edge. (See p. 134.) 

(16) The unit fiber stress in bending is about 1.89 times the unit 
tensile strength of briquettes of 5 sq. cm. (See p. 134.) 

(17) The unit tensile strength of specimens decreases as the breaking 
area is enlarged. (See p. 134.) 

(18) The unit compressive strength of similar specimens of cement or 
mortar is not greatly affected by their size. (See p. 134.) 

Laws of Strength. There are two fundamental laws of strength which 
apply to mortars composed of the same cement with different proportions 
and sizes of sand. 

(1) With the same aggregate,* the strongest and most impermeable mor¬ 
tar is that containing the largest percentage of cement in a given volume 
of the mortar. 

(2) With the same percentage of cement in a given volume of mortar, 
the strongest, and usually the most impermeable, mortar is that which has 
the greatest density,f that is, which in a unit volume has the largest per¬ 
centage of solid materials. 

The first of these rules is understood by ordinary users of cement, but 
the second rule states a fact which is appreciated only by experts. 

The value of a first-class cement is universally recognized, the effects of 
impurities have been studied in various ways, and the variations in strength 
of mortars made from different sands or broken stone screenings have been 
recorded, but the fundamental law of the relation of the density of a mor¬ 
tar to its- strength, — a function nearly as important as the quality of the 
cement itself and explaining many of the seemingly paradoxical results of 
tests with different aggregates and different proportions of water, — is but 
vaguely comprehended by the majority of experimenters and most of the 
users of cement. 

The importance of this subject claims for it a full investigation, and its 
study is taken up on page 134* The application of these laws to concrete 
is discussed in Chapter XX. 

*The word aggregate is defined on page i. 

+The meaning of density may be understood by referring to the figures on pp. 172 and 173. 


134 


A TREATISE ON CONCRETE 

STRENGTH OF SIMILAR MORTARS SUBJECTED TO 

DIFFERENT TESTS* 


Mr. Rene Feret, Chief of the Laboratory of Bridges and Roads at 
Boulogne-sur-Mer, France, has made very extended tests of strength of 
mortars, studying his results scientifically, and in many cases formulating 
laws and formulas applicable to different conditions. The tests of one 
series in particular are of so wide a range in character and in proportions 
used that the authors have converted the values into English units, and 
reproduce the table in full on pages 136 and 137. 

After plotting the strengths in various ways, Mr. Feret reaches conclu¬ 
sions which may be summed up as follows: 

(a) The unit fiber stress for prisms 4 centimeters (1.6 in.) on an edge 
is about the same as for prisms 2 centimeters (0.8 in.) on edge. 

(b) The tensile strength per square centimeter of prisms having a break¬ 
ing area of 16 square centimeters (the strength of which he found to be 
similar to that of briquettes of the same section) is about two-thirds the 
strength per square centimeter of the normal briquettes which have an area 
of 5 square centimeters. This difference is attributed partly to the lack of 
homogeneity of the specimens, especially on their surfaces, but prin¬ 
cipally to the unequal distribution of the stress on the area of the section. 

( c) Resistance to flexion, that is, the unit fiber stress in bending, is 
about 1.89 times the tensile strength per unit of area of briquettes of 5 
square centimeters. 

(d) The form and dimensions of the specimen do not greatly influence 
the strength per unit of area in compression when the height and width of 
the block are approximately equal. 

(e) Resistances to flexion and tension are proportional to each other, 
and resistances to compression, shearing, and punching are proportional to 
one another, but there is no constant relation between the resistance to 
compression and the resistance to tension or flexion. 

THE RELATION OF DENSITY TO STRENGTH 

In the same paper from which we have quoted, Mr. Feret treats of the 
density and elementary volumetric composition of mortars, using in his 
studies the results given in the table just described. He calls particular 
attention to the fact that the properties of hydraulic mortar, such as dura¬ 
bility, permeability, porosity, and ability to resist the decomposing action 
of sea water, depend not only upon the quality of the cement, but “in a 
measure greater than is generally believed, upon the granular physical 

* A valuable series of tests has also been made by Messrs. Humphrey and Jordan at the U. S. 
Government Testing Laboratory at St. Louis, see Bulletin No. 331 U. S. Geological Survey, 1908. 


STRENGTH OF CEMENT MORTARS 135 

composition of the mortars, that is to say, upon the dimensions and rel¬ 
ative positions of the different elements entering into their composition.” 

The density ( compacite ) of a mortar is represented by the total volume 
of the solid particles, — exclusive of the water and the voids, — entering 
into a unit volume of mortar.* 

The “elementary volumes” in a unit volume of fresh mortar consist of 
the absolute volumes of the cement, sand, water, and voids, each ex¬ 
pressed in the form of a decimal. To illustrate, the u elementary vol¬ 
umetric composition” of the mortar in Item 8 of the table on page 136, 
which is mixed in proportions by weight of one part cement to if parts 
of natural sand, is: 

Cement (c) — 0.226 

Sand (s) = 0.499 

Water (w) = 0.234 

Air voids ( v ) = 0.041 

Total volume =1.000 

Expressing this in more familiar terms, 22.6% of the unit volume of the 
given mortar consists of solid particles of cement, 49.9% of particles of 
sand, 23.4% of water, and the remaining 4.1% of air voids. 

The porosity, represented by the sum of the water and air voids, is 27.5%,. 
The term voids is often employed to represent the porosity, that is, the sum 
of the air and water. 

It is obvious that 

c -f + 1; 

also that 

v = 1 — (e + $ + w), 

which is equivalent to the statement that the entrained air in any volume 
of fresh mortar is equal to the measured volume of the mortar minus the 
space occupied by the cement, sand, and water. 

The density of the mortar considered above is c + s, or, 0.226 + 0.499 = 
0.725 as given in column (n) of the table on pages 136 and 137. 

A thorough understanding of the use of these symbols is essential to the 
study of strength of concrete and mortar, for, as will be shown further 
on, practical tests of strength are of small value unless the density and 
exact mechanical composition of the specimens are clearly defined. 

*If the word density is applied to sand alone, it means the proportion of the measured 
volume of the sand, which is occupied by the solid sand grains; a sand, for example, having 
under certain conditions 40% voids, would have a density of 1.00—0.40 = 0.60. 


Strength and Composition of Portland Cement Mortars. 

By R. Feret. {See p. 134.) 

(Bulletin de la Societe d’Encouragement pour l’Industrie Nationale, 1897, Vol. II, p. 1593d 


I36 


AVERAGE 

STRENGTH 

d 

uoissoid 1 x 103 

OOOOOOOOOO OOOOOOOOOO 
kj LO o, M P-* M M LO M O' M CO CO kj O Ct 

WOO in tOfOH CM OxvO CO (CCMC fo 7- H *3 

h m -co kj to inO nO m m M co kj lonO 'O 

A 

X uotxap ^ • 

pUR UOISU3JL 

oo (noO^-nhOn^) MCNOCOOOO lowmc; 

IT) H o Cl CO CO CO N Cl O MCM^fO 

M (N C 4 CO CO FO FT) H C 4 01 CO CO ^ FO FO 'O 

f D 'o' • 

SuuR3qg 3^,5 

OOO OOO OOO O NO On O ooo ooo o 

<to® OOO co kj lonO rf to H to to toco kj 

h to O tO >c Mca'O NO O co 00 <n o r-. to to 

MMMMMCOCOCO MMMMC1MCOCO 

STRENGTH PER SQ. IN, AFTER 5 MONTHS IN 
FRESH WATER 

a 

_o 

"55 

cn 

u 

k, 

ft 

s 

o 

U 

/*N 

O' A 

ft, h£ 

OOOOOOOOOO OOOOOOOOOO 

OOoO'Ot'cONH m h tOOO N O CO conO >o 
H 00 1 C CO t w tocOM M roat 0 00 O Ot^to O 

M M CO kj LONO t->» t'- M CM M CO kj toO O'- 

A 

CO 

(ft 

OOOOOOOOOO OOOOOOOOOO 

kjOO Oi N 00 H co O l> O t IN r^NO tlON M 

co 0"0 nO nO to Tfoo to M CO OnnO h 00 to t COO to 

k-i M CO kj to to NO no MMM CO kj to to NO 

© 

P? ££ 

210 

840 

1340 

2060 

2840 

375 ° 

4690 

5720 

6400 

7 ° 5 ° 

270 

970 

1380 

1780 

2460 

313 ° 

4010 

5 2 3 ° 

5830 

6600 

d 

.2 
*c n 

d 

<u 

H 


to M O O NO H N H N M 1CN O' w lot LOCO O' CO 
NOioojNOctt^OtoO codOOktoOfONO toco kT 

H N W N)CO t t >C ic H N W ccio t f t 10 

CO /^N 

CO O' kf-NO to OnnO to t H N N W NO O N 00 

to M kj- 0 t N CMC O' to kf to M (N f PI O t" 

M H N N 0 , 01 CO CO MMMMMCOCOCO 

d 

o 

'fi 

JV 

E 

tC *2 

kjNO O H 00 N N O' O O OO H00 NO N too COO O 

co to r^ no no co O conO m ic t co n r^.00 ft >cn O 

H N (O t LONO COCnO m H co t 1C to NO r^ O' O 0 

M k-t MM 

co 

pC 

-— / 

kf l^CC CM^CO t to O O MOMNOCNkfM-fO O 

cooo m 0 aoi 0 cot n rfcotoMMONct onoo co 

h n t >C LONO 00 O' O O M CO kj- lonO NO 00 On O m 

MM MM 


0.0083 
0.0266 
0.0511 

0.0841 

0.1190 

°- I 537 

0.1772 

0.2034 

0.2304 

0.2530 

0.0092 

0.0289 

0.0524 

0.0724 

0.1109 

0-1325 

0.1576 

0.1945 

0.2190 

0.2460 

A;isuaQ 3 

0.700 

0.718 

0-733 

0.750 

0.758 

0.760 

0-745 

0.725 

0.695 

0.646 

0.631 

0.657 

0.673 

0.685 

0.703 

0.698 

0.690 

0.680 

0.649 

0.617 

ELEMENT ARY 

VOI.U METRIC 

COMPOSITION 

spiOA iiy > 2 

0.185 

0.150 

0.119 

0.087 

0.062 

0.044 

0.041 

0.041 

0.043 

0.048 

0.217 

0.172 

0.141 

0.119 
0.082 
0.075 

0.068 

0-055 

0.057 

0.054 

I3JRA\ & 3 

0.115 

0.132 

0.148 

0.163 

0.180 

0.196 

0.214 

0.234 

0.262 

0.306 

0.152 

0.171 

0.186 

0.196 

0.215 

0.227 

0.242 

0.265 

0.294 

°- 3 2 9 

pURg (C 00 

OcotooOMtoONONtot^ cr^-\c> CMCiC'OOO O m 
t^NO to t co O lOONMOO CNOO NO 1CN 00 N t kf 

OOnC nOnOO ictt Cl 10 to to to i-O to t t CC ci 

666 666 666 6 66 6 666 6 6 6 6 

IU3UI93 

O LO00 N N IC O O O ON C'ONOoOfCtNC'O 

CCtON O N1C00 NOO to CONO M tN O ICO 

OOO MMM mom CO OOO MMM MOCOCO 

666 666 66 6 6 066 606 066 6 

JRJ.IOUI JO ^ 

•pA'nOR JO 3JUJ 

c- ionO ONOr^Mk-j-TtioNCOONkj-too h 9 o> t 
cpON-^-OtOkHOONOr^-CO ONt^O t^-kj-O NNOl t 
N « co t t ic lonO I>"Cn m pi co co kf ic lonO tA CN 

COMPOSITION OF 
MORTAR BY WEIGHT 

jriioui qsaij jo . 

•pA - no R jo 

OiOOtOtONiCt MOONtootOkj-MONO 

O' N fO ic 1C M m Qn to O' MONOCOCN-t-r^-Otoco 
0 t to no r^oo 00 k N 03 m 0 kj- kj no no no r^.NO no 
cocococococococococo cocco cotOfO cococc co 

amjxiui Aip 

suinaS 3 

0001 aad w 

LO VO FO IO FO IO 

cnO v O h’cO 10 fO fO OOW 10 M !>. FO00 0 

ONNOOOOQ\OHr<)\0 C> ^ O Omw C4 ^O fo 00 

MMM M M MMM MMM M 

-\-o )3jnjxiui Aip 
suirjS b 

__' OC 

OOO l I UI JU3UI33 

MMNO O IQ N NlCft (N Mtor^NOMCOCOMOOOO 
lOO'N'OO'COOOiCtO IN-MNO ONkjcO comm kj 

M MMM M CO kj NO MM M M M CO t >C ^ 

Approxi¬ 

mate 

Propor¬ 

tions 

by Weight 

pURg ^ 

NO ON On M m M LOCO Cl t^- On O O M M to O kj ON lO 
00 On NO to kj co Mmm 6 MlN-tOkjcOM m’mO 6 

M M 

JU3UI33 ^ 

mmm mmm mmm m mmm mmm mmm m 

K31I 

m M CO kj to NO r^co ON / q' ^k-T^rdo "kj 5o'o' 'C-tp) ^C~. 

—' '— — y M 1-1 1-1 mmm m 

*-cinvs 

O m 








































































c* 

ci 


sQ 


vO 


0 

0 

OOO 

O 

0 0 

0 

O 

O O 

0 

fa(- 

CO 

tf Hf H 

O 

NO O 

w 

LO 

w M 

vf 

vo 

N 

CnOO i'>- 

O 

t'- vo 

M 

ro 

O 00 

NO 


M 

H <M to 

vo 

to NO 


CN 

^ fl - 

to 


O 

fl- 

o 



t^NO 

fl“ 

Cl 

1- 

NO 

0 

fl" 

X^» 

Hi 

00 

0 i 

00 

NO 

CO 

Cl 

NO 

Cl 

Hi 

0 

NO 

to 

M 


fl- 

ON 

Cl 

VO 

Hi 

VO 

0 



M 

Cl 

to 

CO 

fl- 

VO 

vo 

NO 

NO 

to 

fl- 

vo 

fl" 

NO 


NO 

O 1 

X) 

0 

0 

0 

0 

0 

0 

'o' 

0 

0 

0 


0 

0 



M 

to 

!>. 

lO 

x^ 


Cl 

Cl 

0 

x^. 


CO 


M 

to 

t'- 

fl- 

HI 

VO 

1>* 

0 

vo 

M 

V'- 

HI 

0 


NO 





HI 

Cl 

CM 

CM 

to 

to 

fl- 

HH 

to 

to 


to 


0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 


0 


to 00 

Cl 

Cl 

x>- 

0 

to 

x^ 

0 

M 

X^ 

W 

Cl 


w 


W 

fl- 

to 

HI 

HI 

HI 

CO 

0 

On 

HH 

vo 

VO 

O' 


HH 




w 

Cl 

to 

fl“ 

VO 

NO 

NO 

x^. 

Cl 

fl- 

fl- 


!>. 

A 


O 

0 

0 

0 

O 

O 

0 

0 

O 

0 

0 

0 

0 

0 

0 

00 

O 

VO 

On 

w 



Hi 

lO 

X^ 

to 

vo 


X^ 

vo 


Cl 

vo 

Cl 

O' 

On 

vo 

fl - 

fl* 

O' 

CO 

tooo 

00 

NO 

to 

'-- 



M 

rH 

Cl 

to 

fl- 

vo 

VO 

NO 

Cl 

to 

fl" 

to 

x^ 


0 

0 

0 

O 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 


NO 

0 

CO 

On 00 


VO 

10 

to 

0 

Cl 

fl- 

fl- 

0 

Cl 

Hi 

M 

NO 

O 

r^. 

to 

fl* 


r^NO 

fl- 

HH 

NO 

NO 

NO 

x^ 




HI 

HH 

Cl 

to 

fl" 

vonO 


CM 

to 

A" 

to 

CO 


Vi ti 

CLi <D 

a *-> 
<D 

1/3 £ 
(J 

fl o 

S3 

**-■ 3 
o <-> 

‘'’fa 

fa 

rt P< 
■3 U) 

fa (j 

« fl 

£ g 

a i *—i 


13? 


w 

t> 


to 


1-0 0) 00 MD 1" O 
'O <N O On 10 to 

H N OJ CO ft 


N OfO H 

O tt « X-~ 

VO IONO NO 


O vo to 

N h 
<0 Tf VO 


VO 

VO 

H" 


O 

NO 


On NO to to 
m On <0 <0 

M H N N 


CJ to M 
O t ^ t ^- 

to to to 


m On O-nO 
o to o <0 
H" M too 


to 

On 

CJ 


2 

a 

fa 

o 

X 

o 

tn 

fa 

rt 


--- fa 

VO o 
CO S 
fO ,, 


I* 

(N 

NO 


tn 

z 

s 

p 

p 

o 

o 

b 

o 

z 

o 

p 

< 

z 

< 

p 

fa 

X 

fa 


e 

"fl 
G O 
cd ,-Q 

in cd 


fl 

O 


fl 

CD 

“c S 
3 'tt: 

4=7- £ 
m-2 

• h r\ u-4 
<L> 0 

> Vi _ 

^ (DO 

CsO >• 
rt no • 
<u m £ 



A - 

Di¬ 

ed 

£- 

1/3 

U 

Hi 

O O 

M HI 

£ 

C/3 

03 

Hi 

A 

R- 

a 

d 

CO 



tn 

r- 0) 

C fl 

£ 

C/3 rr< 

•C-c 

in 

*n 

fti 

a 

^ T3 

fa c 

a 

<D 

PS rt 

rX 

£ c 

0 

Hi 

rt 

xr 

^HH H 

<i-« 

O W 

0 

C/3 rfl 

tn 

CJ CJ 

<D 

> fl 

>■ 

3 H 

’~ci 


ffi' 


o- 


rtp; 


to 

H 

<D 

bC 

ed 

a 

a 

o 

03 

, cr 

1 C/3 

fl 

CJ 

C/3 


CO 


S *2 

fl <D 
<D —* 

£ 2 
.£ c 

U • "- 

Rc 


c 

.2 

■*—> 

O o 

M fai CO C/3 1 

x x x • 

fl M fl fl 
X X X U t 
fl Cl fl ^ 

C/3 

»o 



l-H-H-H’Sci 

■" 00 tOtO C3 x. 
P X X X--V 
“ Nf (I « J 

rr fl m ci - 

^ 'To 

o m 

IT, v —' 


+ 

o. 

x 


O' 


h 



HI 00 

VO 

no tooo 

to 0 0 

0 

tooo HI 

0 

tn 
• fl 

•C w fa-d 
a U 



Hf tO 

HI 

O' tx 

no CNJ 00 

X^ 

CNJ O CO 

HH 

’a . 

-n a d 



HH CM 

fl - 

vonO 00 

QS H Cl 
HH W 

CO 

HH 

NO 00 ON 

VO 

HH 

03 

Hi 

cd 

c 0) r fl 

— fl U CJ 

<-fai 

0 


•*t t^OO NO <0 tt o o 
h tj- o r^OMCOO 

Hi CJ rtf VO X'-OO ON m 


O row O 
00 fat tf O' 
N NO 00 On 


Cj 

NO 

00 


CO <• 
cj r 



NO O' 

On 

CO 

CM 

NO 

HI CO 

HH 

0 

NO MO 

O' 

NO 

HH 


X'-nO 

CM 

M CO 

X^ 

00 

On 

to 

10 

CM 

fl" 

VO 

M 

O CJ 

vo 

CO 

0 

to 

NO 

On 

M 

vo 

NO O 

fl“ 

Cl 

00 

HI 

0 0 

0 

0 

HH 

HH 

HH 

HH 

CM 

CM 

O H, 

HH 

HH 

CM 


6 6 

6 

0 

O 

O 

0 

O 

0 

0 

0 6 

O 

d 

0 


w 

H 

O 


0 . 
tn 
a: 
pc 


NO 


o 

U 


£ 


in 

Cjz 

„ <D cj 

v £ fl 

faD .fl CD 

fl ° 
fl Q, 0 

52: 1/1 


a £ 


C/3 
<D 
•*—> 

-*—j _ 

<D C/3 

fl 73 fl 
Z, (j L 

>w> O _ C /3 - 

*n 3 *c 

P u B 


fa 

a 

vo to o »t) tr> >f> c 

H fa H tl M O 


o 

(J 


fa 

M 

rt 

fa 

fa 


!t. 

c 

u 


fa 

M 

rt 

1-. 

a> 


o 

O 


o to rr vovo i'co a o m 

^ fa fa fa H fa fa fa CJ CJ 


w 

N — X 

OJ vo 

0 0 

NO NO 

d d 

to 

O 

N°. 

o’ 

to rt- 1- 
OOO 
NO NO NO 

o’ o’ o’ 

VO 

0 

NO 

0’ 

CJ faf 

O 00 
NO vo 

d d 

x^ 

x^ 

vo 

6 

On On to 
OOO N 
X^NO NO 

o’ o’ d 

CO 

HH 

X^ 

6 

fl¬ 

ee 

vo 

6 


On On nO 

00 

CO 

O 


vo 

vo 

Cl 

fl- 

Cl 

On 

00 

Cl 

O 

Cl 

-n 

HH 

0 

000 

X^NO 

x^ 

NO 

VO 

vo 1" 

0 

vo 

M 

HH 

Hi 

HH 

HH 

O 

O 

O 

0 

0 

0 

0 

O 

O 

HH 

0 


d 

d 

O 

O 

O 

O 

O 

0 

0 

0 

0 

O 

O 

o’ 

d 


On NO 

HH 

ONCO 

X^ 

00 

to 

HH 

HH 

x^. 

On 00 

On 

fl" 

/^N 

NO 

x^oO 

CO 

On O 

HH 

to 1- 

NO 

to vo 

X^ 


HH 

's_x' 

Cl 

CM 

CM 

Cl 

Cl 

to 

to 

to 

to 

to 

Cl 

CM 

Cl 

HH 

fl* 


0 

0 

0 

0 

0 

0 

O 

0 

0 

0 

0 

d 

0 

d 

d 


1-00 

VO 

fl* 

On 0 

HH 

CM 

to 

HH 

x^ 

On 1- 


0 


NO 

Cl 

00 


0 

x^ 

tooo 

Cl 

VO 

0 

CO x^. 

vo 

0 

CO 

LO 

vo 

fl* 

fl" 

fl" 

to 

to 

CM 

CM 

HH 

NO 

vo 

fl- 

vo 

0 


O 

0 

o’ 

0 

0 

0 

0 

0 

0 

O 

0 

0 

o’ 

o’ 

0 


CO 

x^oo 

O' vo 

fl- 

fl- 

0 

HH 

NO 

CM 

0 

On 

NO 

fl* 


CO X^ 

w 

VO 

0 

to 

x^ 

Cl 

NO 

Cl 

0 

10 

On 

VO 

to 


0 

0 

HH 

HH 

HH 

Cl 

CM 

to 

to 

fl" 

HH 

HI 

Hi 

w 

VO 


0 

0 

O 

O 

O 

0 

0 

0 

0 

0 

O 

O 

o’ 

0’ 

O 


OnCO N 
1- to to 


NO 

CJ 


M CN1 tO *tt- 


CJ o N 
On On On 

VT; vo no rLoo 


ONCO 
O ON 


On 

fO 

o* 


Co 


00 

0 

Cl 

CO X— CJ 

00 

0 

VO 

vo 

0 CJ vo 

0 

Cl 

0 

x^ 

to NO 

W NO M 

vo 

HH 

On 

fl- 

VO 1 - 1 - 

Cl 

VO 


HH 

Cl 

CM 

CO co tJ- 

fl* 

VO 1- 

vo 

NO NO NO 

NO 

VO 

»s» 

to 

to 

to 

CO co co 

to 

to 

to 

to 

CO co co 

to 

to 

5 


vo 

r^oo O 

NO NO N 


M vo On 


vo 

itJO N 
00 On On 


CO 

O 


to NO 00 
N to Ht- 


On 


VO ‘ J 4 


Hf 

0) 


VOCO 
X^- ’ 3 " 


vo ON to On 

N C^NO CN| 

CM N totf 


O to ON 

O MO 
VO 10 NO 


w 1^. O to 
N O 10 to 
H N to 


o 

vo 

<N 


8 Q 

o * 


toco ic 'too to o o~ vo to o_ o o o 
WVotONMP mOO O VO to tv to 


W M M 


HI w to tt- VONO 
CJ 01 N N N N 


•t^OO O'* O hi 0 to 
CJ CJ Cl to to to to 


Tf vo 
to to 


Z O 


•piC "no aad 
3oud 

3 j-BuiTxoaddy 


m 


00 


O' 

it, 


•pX ‘no jad 
SJl{ 3 l 3 iW 
sj^aiixoaddy 


tj-t— 

‘5 g 

fa PS 

|-a 

O O 

3 ft 

|l 

(S u 


C/3 

<D fl 

•S 3 

[t v L-i 

^ bO 




\r t 

C' 

W 

M 

CO 

O 

00 

1 r, 


Cl 

Cl 

Cl 

Cl 

CO ’ 

Os 

0 

w 

Os 

d 

d 

6 


C/3 

<D 

rfl 

C/3 

<D 

£ 


O 

O 

c 

o 

fl 

o 

T 3 

<D 

fl 


£ tn 

• 5 .£ ^ 
■a s z 


<D 

§ 


fa 

teJO 


it) 

N 


O 

f'- 


o 

6 


fa tn 

S.S 

5 ts 

O fa 

CJ w> 


O 


vo 


o 

o 


stntuS jo utjoj 

Large 

and 

rounded 

Varied 

Fineand 

rounded 

Angular 

ptres jo 3-m)t:j\T 

Granitic 

Very 

shelly 

Strongly 

siliceous 

Quartz 


D 

z 

< 

tn 


« E? 

- 4 —> 3 

fl O 

fa 

C- 15 

2 fa 

•ic ts 

fa 

a 

t t 

fl fl 

00 g 

o 


fl 

a 


A 

CO 


o 

M 

fl 

rt 

CO 

CO 


C/3 

<D 

fl 

fl 

<D 

—» 

£ 

o 

Ih 

i__ 

H3 

fl 

fl 

CO 


i.S 

* N 
Lfa <D 

fl X 

&g 

CD 

u 

fl g 
o 03 

_*r"a 
O « 


<D 

U 

"fl 
fl 
_ fl 

C/3 

(D 

C/3 

£ fl 

vc 5 

CD 

3 c 


> H 

.2 B, 

c;j 

> c/3 
fl <D 

c a> 

8 £ ■ 
S ^ fl 

t-* f'O CD 
fa P 

• n 

£ rt CJ 
H 0"O 


3 ^- 

E j- 
c 


73 - 

ag u p: 

i— <D 


<N 

fl 


fl. 

fl 

o 

D 

c 

"fl 

in 

fl 

C 

•^3 

c 

fl 

fl 

o 

u 

# u 

‘fl 

a 

1 S 
c 


V C/3 


fl *-< 

s' 

2 o 






















































1 3 8 


A TREATISE ON CONCRETE 


In practice density of volumetric tests are of great value for comparing 
the relative values of different aggregates, and for determining the pro¬ 
portions for the most economical concrete. They are also useful for study¬ 
ing the effect of varying quantities of water. As is shown in the following 
pages, the density of mortars or concretes made from similar materials 
bears a definite relation to the strength, so that it is frequently possible to 
determine the best mixture as soon as the density tests are completed, 
instead of waiting for the tests of tensile or compressive strength. The 
test has been used by the authors in a practical way for comparing sands 
and for grading sands in special work, and also for concrete to fix on the 
best proportions when using merely one fine and one coarse aggregate, 
and in other cases to determine the proper proportions for a scientifically 
graded mix.* 

Density of Mortars and Concrete. The density of fresh mortars of 

ordinary proportions, as shown by tests of the authors, averages about 0.70 
(corresponding to 30% air plus water voids). Mortars of fine sands may 
run as low as 0.60 (40% air plus water voids), while by special grading or 
the use of an exceptionally good coarse sand the density may be as high 
as 0.75 (25% voids). The density of neat cement usually ranges between 
0.50 and 0.55. The density of concrete ranges^ from 0.76 to 0.88, depend¬ 
ing upon the grading of the aggregates and the cement. 

The values apply to the materials freshly mixed before setting. The 
chemical combination of the cement and water reduces the porosity further. 

Density or Volumetric Tests of Mortar.J To obtain accurate results, 
considerable care is necessary in making the experiments. An approxi¬ 
mate method suited to rough comparisons will be given first and this will 
be followed by more accurate methods advised for laboratory work. 

The rough volumetric test may be made in almost any vessel or 
mold so long as the capacity is readily computed and its dimensions 
such that the depth of mortar or concrete can be measured exactly. 
A deep mold is more accurate than a shallow one. The volume 

* See Chapter XI, p. 183. 

f From the “Laws of Proportioning Concrete,’’ by Wm. B. Fuller and Sanford E. Thompson, 
Transactions American Society Civil Engineers, Vol. LIX, 1907, p. 67. 

jThe French Commission determine the “yield” of a mortar (see p. 129) by measuring its 
volume green, that is, just after introduction into the molds, when an excess of water may affect 
the volume, and thus give misleading results with very wet mixtures. 

In his Report to the French Commission, 1895, v °l- FV, P- 2 43 > Mr. Feret also measures the 
mortar wet, but he employs a vessel of known capacity, — a cylindrical measure whose height 
and interior diameter are each about 8 centimeters, — and uses only a portion of the mortar which 
he mixes, calculating his percentages by ratio of the weight of mortar made to the weight of mortar 
introduced into the measure to fill it exactly. This method eliminates inaccuracies in measur¬ 
ing the level of the surface. 


STRENGTH OF CEMENT MORTARS 


138a 


of mortar and concrete of dry consistency will measure the same after 
setting as when green, but wet mixtures must be measured before setting, 
and again after they have become sufficiently hard to expel the surplus 
water. The measurement before setting is necessary in order to calcu¬ 
late the volume of air bubbles entrained in the wet mortar or concrete. 
The volume after setting, or partially setting, however, is the only one of 
real importance for studying the characteristics of strength, permeability, 
and cost. The sand is dried, or its moisture is determined by weighing 
and drying a sample of it. If stone of a porous nature is used the pores 
of its particles should be filled with water, but there should be no per¬ 
ceptible moisture on their surfaces. The quantities of dry materials for 
a single tube or mold are weighed in the required proportions, mixed 
with a known weight of water, and placed compactly in the mold, whose 
lateral dimensions have been exactly measured so that the volume of 
mortar in it may be obtained by measuring down from the top. The 
exact space occupied by the particles of each of the solid materials and 
. by the water is calculated, if the metric system is employed, by dividing 
their total weight by the specific gravity of each, or, if English units are 
used, by dividing the weight times 1728 (the number of cubic inches in a 
cubic foot) by the specific gravity multiplied by the weight of a cubic foot 
of water. After partially setting, the exact depth of the mortar in the 
mold is measured and its volume calculated. The percentage of each of 
the dry materials, which really determines the density,—which is repre¬ 
sented by the sum of the absolute volumes of the dry material,—is found 
by dividing the absolute volume of each material by the total volume of 
the set mortar or concrete. 

The specific gravity of cement which has been stored for a short time 
may be taken at 3.10 and the specific gravity of dry sand at 2.65. 

The following example from the authors’ note book illustrates the method 
of finding the density when the measurements are in English weights 
and measures: 

Example :—Find density of a mortar composed of Newburyport sand 
and Portland cement in proportions 1 : 2 by weight. 

Solution :—For the mold used, it was estimated that 8 lb. cement 
and 16 lb. dry sand would be required. Gaging these with 3 lb., 12.6 oz. 
(3.79 lb.) of water, the quantity necessary for the desired consistency, 
the volume of the mortar was found by measurement to be 348 cu. in. 
when green, and 336 cu. in. after setting and pouring off the surplus 


A TREATISE ON CONCRETE 


138 b 

water. The absolute volumes are expressed below, first in cubic inches and 
finally in terms of the density (c + s), of the set mortar. 


8 X 1728 

Cement — . . , 

3.1 X62.3 

= 71.6cu.1n. 

16 X 1728 

Sand — , , 

2.65 X 62.3 

= 167.4 cu.m. 

3.79 X 1728 


Water - , 

62.3 

= 105.1 cu. in. 

Absolute volume cement, sand and water, 

344 cu. in. 

Measured volume green mortar, 

348 cu - . in. 

Volume of entrained air, 

4 cu.in. 

Percentage of entrained air, 

1.2% 


Density of set mortar, c + 


71.6 167.4 

^36 + "336" “ 0,213 + 0,498 = 0,711 


Volumetric Tests of Mortar at Jerome Park Reservoir. The methods 
used by Messrs. Fuller and Thompson at Jerome Park Reservoir in tests 
for the New York Aqueduct Commission in 1906* have since been adopted, 
with slight variations, in the authors’ laboratory. The procedure is indi¬ 
cated in the blank form used in the tests, a copy of which filled out is here 
reproduced on page 139. While somewhat lengthy in appearance, it is 
arranged to correct almost automatically for the unavoidable losses due to 
free water and mortar sticking to the tools. The chief object of the test is 
to find the density of a fresh mortar, that is, the ratio of solid material 
in it to the total volume, and also to determine the elementary volumes of 
each ingredient. In the test illustrated, for example, the density is 0.696 
and the air plus water voids are therefore 30.4%. 

The apparatus used for density tests of mortar are a shallow pan about 
9 inches diameter, a small pointing trowel, scales to weigh to one-tenth 
gram, measuring glass or graduate about ij inches diameter and 250 cubic 
centimeters capacity, one or two beakers, and a stick for tamping the mortar 
in the glass. 300 or 400 grams of mixed cement and aggregate may be 
used in the tests. 

It has been found that the material which sticks to the tools is either 
cement or similarly fine aggregate, so that the weight of the aggregate which 
passes a No. 100 sieve should be recorded for use in the computations. 


* See paper by Messrs. Fuller and Thompson, Transactions American Society Civil Engineers, Yol. 
LIX, p. 67. 








STRENGTH OF CEMENT MORTARS 


139 


Volumetric test for Reservoir .File W. R. 

Cement B Aggregates Clean Sand .Date 4-26-06. 

Computed by Brown .Checked by T. 


(1) 

(2) 

(3) 

(4) 

(5) 

( 6 ) 

( 7 ) 

( 8 ) 

(9) 

(10) 

(11) 

(12) 

(13) 

(14) 

(15) 

C r 6) 

(17) 

(18) 

(19) 

(20) 

(21) 

(22) 

(23) 

(24) 

(25) 

(26) 

(27) 

(28) 

(29) 


Experiment No. 

Nominal proportions by volume 

Proportions by weight. 

Description of aggregate. 

Wt. of cement.. 

Total weight of aggregate. 


sieve 


U 

U 


u 

(( 


“ “ “ (after using) . . 

water used = (8) — (9) 


Percentage of water = 


( 5 ) + (6) 

Consistency.. 

Temperature water. 

Total weight mixed = (5) + (6) + (10) . . 

Weight tray and tools (after using). 

“ “ “ “ (before using). . . 

Weight mix adhering = (15)—(16) 
Weight measuring glass or graduate. . . . 

Weight glass + mix. 

Weight glass + mix — freewater. 

free water = (19 — 20) .. 

mix set = (14) — (17) — (21) . 

“ “ = (20) - (18). 

Discrepancy = (23) — (22). 

Time mixing completed. 

Volume of mix, in cu. cm. 

Time settling. 

Final volume of mix in cu. cm.. 

, . (i 7 ) 


U 

u 

(( 


(30) Cement left on tray = (5) X 


(17) 


(31) 

(32) 

(33) 

(34) 

(35) 

(36) 

(37) 

( 38 ) 

( 39 ) 

(40) 

(41) 


(17) 


Wt. water in set mortar = (10) 

- (29).; y 


(3 1 ). 

Specific gravity cement. 

“ “ aggregate. .. • 

{ ? 2 ) 

Absolute volume water = 


tc 


ti 


a 


u 


cement = 


(28) 

(33) 


(28 X (35) 

. (34) 

aggregate = 


(28) X ( 36 ) 


(39). v -/ •:. 

Density = (38) + (39).. • • .. 

Remarks: Fine Material on Surface .. 


152 


i : 2 


CO 

M 

W 


Sand 


150.0 


267.0 


53-4 


287.7 


228.7 


59 -o 


14.2 


Soft 


6 5 °F. 


476.0 


325-8 


322.2 


! 3- 6 


• 295.4 


• 7 6 7-9 


767.9 


0.0 


■ 47 2 •4 


• 472-5 


. 1 


ro. 1 5 a.m. 

, 

210.0 


2 hrs. 


209.5 


J 0.8 

) 




O . 7 


) 7 


• 58.2 


) 147-9 


. 266.3 


3.11 


2.71 


.278 


.227 


.469 


• 974 


. 696 


3 cc. 



Note: Weights are in grams; volumes in cubic centimeters. 































































140 


A TREATISE ON CONCRETE. 


The materials are carefully weighed, and enough water added,—the quan¬ 
tity varying with the fineness of the sand,—to produce a mortar softer than 
standard consistency which will scarcely hold its shape in the mixing pan. 
An examination of the various items in the table will show the purpose of 
each, the object being to correct, ior all losses and obtain a resulting volume 
corresponding to that of the mortar after setting. The figures following 
many of the items refer to the numbers of the other items, the fraction 
following item (29), for example, representing the water of the mix which 
adheres to the tray and tools. The weight of the water in this mortar which 
adheres is found from the proportion,—Mix adhering: total fine mortar = 
water in mix adhering : total water. Expressed in item numbers this 
becomes 

Item (17) 

Item (20) = ————-X Item (10). The cement and 

Items (5) + (7) + (10) 

aggregate left on tray, items (30) and (31), are similarly computed, and 
from these the weight of each of the materials in the set mortar is found. 
The absolute volumes, items (37) to (39), are then readily computed and the 
density determined. 

Volumetric Tests of Concrete. For volumetric or density tests of con¬ 
crete, molds at least 8 inches in diameter are necessary, but the process 
throughout is similar to that already described for the volumetric tests of 
mortar and a similar blank form may be readily made for records. 

The density tests as made at Jerome Park Reservoir are fully described 
in the paper by Messrs. Fuller and Thompson already referred tof and 
results of the tests are there given. 

Feret’s Formula for Strength. For studying the relation of absolute 
volumes to strength, let 

P — compressive strength of the mortar. 

K = a constant which differs for different cements and at different ages of 
the same mortar. 
c = absolute volume of cement. 

5 = absolute volume of sand. 
w — absolute volume of water voids. 
v = absolute volume of air voids. 

The value of determining the density of mortars is made evident by the 
following law of Mr. Feret:* 

“For any series of plastic mortars made with the same binding material 

♦Bulletin de la Societe d’Encouragement pour lTndustrie Nationale, 1897, Vol. TI, p. 1604. 

fSee also Chapter XI of this Treatise. 



STRENGTH IN KG. PER SQ. CM. 


STRENGTH OF CEMENT MORTARS 141 

and inert sands, the resistance to compression after the same length of set. 

under identical conditions, is solely a function of the ratio —--01 

c w + v 

1 _[~7) ’ whatever be the nature and size of the sand and the pro¬ 

portions of the elements, — cement, inert sand and water, — of which each 
is composed.” 

It follows from this law, as Mr. Feret says, that the strength of any 



Fig. 49. — Derivation of Feret’s Formula for Strength. (See p. 142.) 
(Bulletin de la Societe d’Encouragement pour l’Industrie Nationale— 1897.) 


mortar increases with the absolute volume of the cement (c) in a unit 
volume of fresh mortar, and also with the density (c + s), whatever may 
be the relative volumes filled with water and air. 

















142 


A TREATISE ON CONCRETE 


From very numerous experiments such as those tabulated on page 136 
Mr. Feret evolves the approximate formula 

p=;c(_l_Y (I) 

By suitably changing the value of K the formula may be adapted to either 
the English or the metric system of measurement. 

As a proof of this formula Mr. Feret plots on a diagram, shown in Fig. 

49, values of from column (12) in the table on pages 136 and 137 

for abscissas, and the average compressive strengths of the various mortars, 
from column (22), for ordinates. Since, in formula (1), K is equal to P 
divided by the square of the quantity in brackets, the value of K is the 
tangent of the straight line passing through the points. In Fig. 49 

K = 1965, if the strength is in kg. per sq. cm. 
or 

K = 28 000, if the strength is in lb. per sq. in. 

This particular value is applicable only to the cement used by Mr. 
Feret in his experiments and to specimens at the age of five months, but 
the principles involved are of general application. 

The most practical application of this formula is in the determination 
of the relative compressive strengths of various mortars made from the 
same cement, with sand in differing proportions and of different com¬ 
positions. Mr. Feret calls attention also to its possible use in laboratory 
experiments and specifications. A cement, for example, may be required 
to furnish, when mixed with any sand, a definite value of K , since the 
value of K is independent of the choice of the sand and of the composition 
of the mortar. 

Experiments by the authors tend to show that the formula does not 
apply strictly to specimens of different consistency, but that the general 
law of the increase of strength with the density is applicable except in ex¬ 
treme cases. The formula is inapplicable to tensile tests, although here, 
too, the general principle appears to hold good. 

This subject as related to concrete is discussed on pages 355 to 362 

GRANULOMETRIC COMPOSITION OF SAND 

Feret’s Three-Screen Method of Analyzing Sand. 

The determination of the physical characteristics of the sand, which, 
mixed with a cement, will produce the densest mortar, has been the object 




STRENGTH OF CEMENT MORTARS 


i43 


of a large number of experiments by Mr. Feret, which are recorded in 
Annales des Fonts et Chaussees, 1892. In America Messrs. William B. 
b uller and Sanford E. Thompson have extended the researches, by a different 
method, to the investigation of the properties of concrete. The mechanical 
analysis of sand and stone is discussed in Chapter XI, and the results of 
earlier experiments are tabulated on page 376. 

Mr. Feret, in studying any sand, separates it by screening into three sizes. 
He then recombines these three sizes in varying proportions, so as to obtain 
results which are applicable to any natural or artificially mixed sand. He 
distinguishes sand from gravel as consisting of grains which will pass 
through a screen having circular holes of 5 millimeters diameter (0.20 
in.). The three sizes of sand he then calls G, M, and F, representing, 
respectively, the large (gros), medium ( moyens ), and fine (fins) particles as 
defined by sifting through metallic sieves with circular holes, or wire cloth 
of definite mesh, as follows: 

Large grains, G, passing circular holes 5 mm. (0.20 in.) diameter. 

Retained by circular holes 2 mm. (0.079 in.) “ 

Medium grains, M, passing circular holes 2 mm. (0.079 i n -) “ 

Retained by circular holes 0.5 mm. (0.020 in.) “ 

Fine grains, F, passing circular holes 0.5 mm. (0.020 in.) “ 

These sizes, Mr. Feret states, are nearly equivalent to sand screened 
through sieves of wire cloth as follows: 

Large grains, G, passing screen of 4 meshes per sq. cm. ( s meshes per linear inch.) 

Retained on “ 36 “ “ (15 “ “ “ ) 

Medium grains, M, passing “ 36 “ “ (15 “ “ “ ) 

Retained on a “ 324 “ “ (46 “ “ “ ) 

Fine grains, F, passing “ 324 “ “ (46 “ “ ) 

Sometimes, for experimental purposes, he divides each of the sands, G, M, 
and F, into three intermediate sizes. 

The granulometric composition of any sand is represented by its relative 
proportions, expressed either in weights or absolute volumes, of G, M, and 
F. For example, a sand containing by weight 50% of the largest grains, 
30% of the medium, and 20% of the fine grains, has a granulometric 
composition of g = 0.50, m = 0.30, f = 0.20. 

The granulometric composition of a sand which has been mechanically 
analyzed, and plotted on a diagram similar to that shown on page 194, may 
be ascertained readily by drawing three ordinates corresponding respec¬ 
tively to screens of 5, 15, and 46 meshes per linear inch, and determining 
by the length or the difference in length of these ordinates the proportions 
which pass and which are retained by the screens of these three meshes. 
These three proportions or percentages represent the granulometric com- 


144 


A TREATISE ON CONCRETE 


position. An illustration of-this method of transforming mechanical analy¬ 
sis to granulometric composition is shown in Fig. 57 on page 151. 

Feret’s Triangles. To simplify the tabulation of results, and arrange 
them so that they may be understood at a glance, Mr. Feret has used a 
graphical arrangement which is exceedingly ingenious. In nearly all 
his writings we find little triangles with the apexes labeled G, M, and F. 
Curves or contours in these triangles, representing the various properties 
of the sands or mortars, are based on a system of three instead of two 


M 



Fig. 50.—Feret’s Three-Screen Method of Analyzing Sand. {See p. 144 ) 


co-ordinates, that is, each curve is the loci of points measured from 3 axes 
placed at angles of 6o° with each other. A full discussion of the theory of 
this is given in his paper “ Sur la Compacite des Mortiers Hydrauliques ” 
in Annales des Ponts et Chaussees, 1892, II, but the principles may be un¬ 
derstood by reference to Fig. 50. The apexes of the triangle are labeled 
G, M, and F, corresponding to the three sizes of sand described on page 143. 
The granulometric composition of any sand is plotted as a single point in 
this triangle. The proportion of each of the three sizes in the sand is rep¬ 
resented by its perpendicular distance from the side opposite each apex. 












STRENGTH OF CEMENT MORTARS 


i45 


For example, exactly at the apex G, the granulometric composition is 
g = 1.00, m = o, f = o. A sand represented by the point “A” in the 
triangle has for its granulometric composition, g = 0.48, m = 0.35, f = 
0.17. Sand, B , whose point is on the line G M is a mixture of G and M 
with no fine particles. It can be readily proved by geometry that if the 
altitude of the triangle is 1.00, the sum of the three perpendicular distances 
from any given point in the triangle to the three sides equals 1.00. Also, 
that any combination of G, M, and F is contained in the triangle or else on 
one of its sides. To use Mr. Feret’s language, “any sand will be repre¬ 
sented by a point in the triangle and by one alone, and, reciprocally, one 
granulometric composition of sand, and only one, will correspond to a given 
point on the interior or sides of the triangle.” If the altitude of the triangle 


M 



Fig. 51. —Absolute Volumes of Sand per 
Unit Volume of Sand not Shaken. 
(See p. 147.) 


M 



Fig. 52. —Absolute Volumes of Sand per 
Unit Volume of Sand Shaken to Re¬ 
fusal. (See p. 147.) 


is considered 1.00, any point, A, in the triangle is readily plotted by locating 
it at perpendicular distances from each of the three sides corresponding to 
each component of its granulometric composition. For example, suppose 
that the granulometric composition of a sand, A, is g = 0.48, m = 0.35, 
f = 0.17. As the apex G represents a sand containing only coarse grains, 
and the line opposite to it, M F, all sands containing no coarse grains, the 
locus of a sand containing coarse grains (g = 0.48) will lie somewhere upon 
a line parallel to M F and at a distance 0.48 from M F. By similar reason¬ 
ing it will also lie on a line parallel to G F and at a distance 0.35 from it. 
The intersection of these two lines is the locus of the sand A, and it will 
be seen that this intersection is at a perpendicular distance of 0.17 from the 
line M G (the side opposite F), which checks the plotting, since f = 0.17. 

For comparing a special property of different sands, or of mortars com- 
















146 


A TREATISE ON CONCRETE 


posed of different sands, each sand employed in the tests is plotted and 
labeled with its value, — which may be in units of strength, weight, or 
volume, — and “contour lines” are sketched in by the eye, as one would 
draw contours from elevations on a topographical drawing. 

Any point on the same contour line represents a sand made up of the 


M 



Fig. 53. —Absolute Volumes of Solid Ma¬ 
terials (c+s) per Unit Volume of 
Fresh Mortar in Proportions 1:3 (by 
Weight). (See p. 147.) 


M 



Fig. 55.—Compressive Strength in Pounds 
per Square Inch of Mortars with 
Various Mixtures of Sand, after One 
Year in Fresh Water. Proportions 
100 lb. Portland Cement to 3.2 cu. ft. 
Mixed Sand. (See p. 148.) 


M 



Fig. 54.—Compressive Strength in Pounds 
per Square Inch of 1:3 (by Weight) 
Mortars with Different Mixtures of 
Sand, after q Months in Air and 3 
Months in Sea Water. (See p. 148.) 


M 



Fig. 56. — Compressive Strength in Pounds 
per Square Inch of Mortars with 
Various Mixtures of Sand, after One 
Year in Air. Proportions 100 lb. 
Portland Cement to 3.2 cu. ft. Mixed 
Sand. (See p. 148.) 


different sizes, G, M, and F, in proportions corresponding to its perpen¬ 
dicular distances from the sides opposite each apex, but having the same 
strength, weight, volume, humidity, or whatever special function may be 
represented, as every other point on the same line. 































STRENGTH OF CEMENT MORTARS 


147 


Figs. 5 1 an d 5 2 , page 145, illustrate the use of the triangle for showing 
the volumes of sands composed of different sizes of grains. Any sand, 
for example, whose granulometric composition is represented by any point 
on the contour line labeled 0.575, i* 1 Fig. 51, has, when measured loose, 
°-575 °f its volume, or 57^%, of absolutely solid matter, or, taking the 
complement, 42 of voids. In Fig. 51 it will be seen that the greatest solid 
volume of loose sand is obtained by mixing G and F in proportions 60% G 
and 40% F by weight. The amount of solid matter in this mixture of 
maximum density is 0.61 of the unit volume; in other words, the sand con¬ 
tains 39% voids. By interpolating between the contour lines we may see 
that a sand consisting of equal parts of the three sizes, which would be 
represented by a point at the geometrical center of the triangle, has about 
0.597 solid matter, or 40.3% voids. In sands shaken to refusal, Fig. 52, 
the mixture of maximum density consists of sands G and F alone, in pro¬ 
portions about 55% G and 45% F, and the total solid matter, that is, the 
absolute volume of sand, in a unit volume of the shaken sand of maximum 
density, is 0.798, corresponding to 20.2% voids. 


EFFECT OF SIZE OF SAND UPON THE STRENGTH OF 

MORTAR 

As a matter of fact, the actual size of a sand, that is, the size of its grains, 
is subordinate, in its influence upon the strength and other qualities of a 
mortar, to the density of the mortar produced from it. One naturally 
would suppose that the densest sand, that is, the sand which contains, when 
dry, the fewest voids, when mixed with a given proportion of cement, would 
make, inevitably, the densest and therefore the strongest mortar. Such, 
however, is not necessarily the case, for the addition of both the cement 
and water change the mechanical composition. A mixture of fine sand 
and cement, for example, requires a larger percentage of water in gaging 
than a mixture of coarse sand and the same cement. The total volume of 
a mortar of plastic consistency is affected by the quantity of water used, 
as well as by the volumes of the dry materials. Hence, a mortar consisting 
of fine sand and cement will be less dense than one of coarse sand and the 
same cement, even though the fine and coarse sands, when weighed or 
measured dry, each contain the same proportions of solid matter and voids. 

Fine sand has more grains in a unit measure and therefore a greater 
number of points of contact of the grains. The water forms a film 
(see Fig. 63, p. 175,) and separates the grains by surface tension. 

The fact is graphically illustrated in Feret’s triangle, Fig. 53, page 146, 


1 4 8 A TREATISE ON CONCRETE 

in which the contour lines show the combined absolute volumes of the 
cement and sand in 1:3 mortar (proportioned by weight) made from sand 
of various compositions. It will be noticed that the point of maximum 
absolute volume, which is labeled 0.734, is much farther to the left than 
in Figs. 51 and 52, showing that for a mortar of maximum density, a sand 
is required containing more large particles, G, in proportion to the fine 
particles, F, than for maximum density with the same sand in its dry state. 

From such experiments Mr. Feret* derives the law that: 

The plastic mortars, which, per unit of volume, contain the greatest abso¬ 
lute volume of solid materials (c + s), are those in which there are no 
medium grains, and in which coarse grains are found in a proportion double 
to that of fine grains, cement included. 

Figs. 54, 55, and 56, page 146, show the strength in compression, con¬ 
verted to pounds per square inch, of mortars made from various mixtures 
of the three sizes of sand. 

Comparing these with Fig. 53 it will be seen that the curves of strength 
follow the same general direction as the curves of density. This is in con¬ 
formity with the general laws stated at the commencement of the chapter 
and with the principles upon which Feret’s formula (page 142) is based. 

There is one point which must be noticed when studying these and other 
similar triangles of Feret, namely, that his results, as shown by the curves 
on his triangles, apply exactly only to sands and cements, and not to mixtures 
of sand and coarse stone. In all the triangles, sands for maximum density 
are composed of a mixture of fine and coarse grains with no medium 
grains. It is shown on page 172 that a denser mixture can be obtained 
with stone and sand and cement, that is, v/ith three sizes of materials, than 
with sand and cement, and it is consequently probable that Feret could 
have obtained greater densities by making the size of G larger (that is, 
employing for G gravel or broken stone) and the size of F smaller, and 
that with this arrangement a portion of the medium grains would have 
been absolutely necessary to obtain the maximum density. In this con¬ 
nection, however, it must be remembered that Feret’s experiments were 
intended to cover, as far as possible, practical combinations of sizes of 
sand for mortar. It is noticeable, even with the sizes of sand which he 
uses, that the curves in Fig. 53 run sharply upward, and that mortars from 
mixtures of three sizes of sand are therefore very nearly as dense and 
strong as those made from two sizes. Furthermore, when the three sizes 

*Annales des Ponts et Chaussees, 1896, II, p. 182. 


STRENGTH OF CEMENT MORTARS 


149 


G, M, and F are mixed together, a graded mixture is formed in which 
there are particles ranging from 0.2 inch down to fine dust. 

Experiments indicate, as stated on page 206, that sand for concrete 
requires for best results more fine material than mortar sand. 

TESTS OF DENSITY AND STRENGTH OF MORTARS OF COARSE 

VS. FINE SAND 

The application of Mr. Feret’s tests is shown in the table on pages 136 
and 137, and to illustrate its practical use in comparing the quality of dif¬ 
ferent sands the following table is presented, giving the density and strength 
of three natural bank sands as tested in the laboratory of one of the authors.* 


Compressive Strength and Elementary Vdiametric Composition of 2-inch Cubes of 

Portland Cement and Bank Sand 

By Sanford E. Thompson 


Sand 


( 1 ) 


Coarse . . . 

Fine. 

Very Fine 


Propor¬ 

tions 

by 

Weight 


( 2 ) 


C 3 

C 


CO 

o <D 

V £ 

o.2 
a o 


2 . 6 
2 . 6 
2 . 6 


( 3 ) 


PERCENTAGES PASSING 
SAND SIEVES 


X" 

4 


Sieve 


(4) 


1 : 3 
1 : 3 
1 : 3 


100 

100 

100 


No. 8 No. 20 No. 50 


Sieve : Sieve 

I 


(5) I (6) 


Sieve 


No. 

200 

Sieve 


ELEMENTARY 

VOLUMES 


e 

£ 

o 


-3 

c 

cj 

Z/2 


CO 

0) 


c + s 


(t^)' 


O bo 

3)2 

-*-< co 


(7) 


(8) (9) | (10) j (11) | (12) 


<>? 
_, CO 1 

c4 g <u 

t 

< 


(13) 


84 62 

84 j 100 
84 


100 


28 

77 

92 


3 

6 

27 


0.171; o. 5 i 8 o. 689 
o. 1 ?4 o. 466; 0.620 
o. 149! o. 45 1 o. 600 


0.126 

0.083 

0.074 


7 1 5 
4 o 5 
330 


(14) 


3330 

2320 

2070 


PRACTICAL APPLICATIONS OF THE LAWS OF DENSITY 

It is probable that many who read this chapter will question the practical 
use of it all. Sand from the same bank usually varies largely in different 
places, and even when sands of a uniform character are to be obtained, it 
is considered impracticable to mix two or more sizes on account of the ex¬ 
pense involved. In other cases, only one quality of sand is obtainable, 
and consequently there is no opportunity for choice. 

In answer to such critics, we outline below several conditions under 
which the investigation of the physical properties of the sand is* not only 
interesting but essential from the standpoint either of quality or of maxi¬ 
mum economy. 

(a) The variation of the sand in different portions of the same bank 
may be utilized by requiring the contractor to mix two sizes without exact 

* From paper by Sanford E. Thompson on “Sand for Mortar and Concrete,” Bulletin No. 3 , 
Association American Portland Cement Manufacturers, 1906 . 































A TREATISE ON CONCRETE 


150 

measurement, so that the material as delivered shall contain not less than 
a certain percentage of sand coarse enough to be retained on a certain 
sieve. 

(b) If two sands are available, a study of their physical characteristics 
will determine which is better suited to the work in hand as the sand which 
produces the smallest volume of plastic mortar, when mixed with cement in 
the required proportions by dry weight, jurnishes the strongest and least 
permeable mortar. 

(c) A good sand brought from a distance at a high price may be more 
economical than a poor sand from a neighboring bank. 

(d) The relative value of crusher dust or of sand in a given locality may 
be determined by comparing their densities or the densities of mortars 
made from them. 

(e) Frequently, a mixture of a fine and coarse sand, or of sand and crusher 
dust, proportioned according to their relative granulometric compositions 
or analyses, may be shown to produce a better mortar than either material 
alone. 

(/) To produce impermeable mortar or concrete, it may be economical 
to screen a mixed gravelly sand into different sizes, and remix these in 
proportions which will produce a mortar of greater density. 

(g) The value of “sand cements” for use in mortar and concrete under 
certain conditions may be made evident. 

The use of mixed sand, as described in (a), was adopted by Mr. Thomas 
F. Richardson, Engineer, for the 1: 2 Natural cement mortar employed in 
the stone masonry of the Wachusett dam of the Massachusetts Metropolitan 
Water Works, after an exhaustive study of the comparative tensile strength 
and permeability of mortars made with different sands. He required 
the contractors to furnish sand so coarse that at least 50% would be 
retained on a sieve having 30 meshes per linear inch. The sand was 
excavated by scrapers, and the condition was readily complied with, 
whenever the sand in one section was shown by samples to be running too 
fine, by taking alternate scraper loads of coarse sand from another place 
in the bank. 

Mixed or graded sands are specially advantageous when concrete is made 
at a central plant such as a block manufactory. By using graded screen¬ 
ings, instead of the fine stone as it came from the crusher, and by slightly 
increasing the size of the coarse aggregate, Mr. Thompson obtained a 
strength two and one-half times as great with the same proportions of 
cement and, on the other hand, maintained equal strength with 40% less 
cement. 


STRENGTH OF CEMENT MORTARS 


151 

Comparative Tests of Different Sands. One of the most important 
applications of the laws of density is in the comparison of different sands. 
Void determinations of sand are valueless because of variations in moist¬ 
ure and compactness, but if equal dry weights of each of the sands to be 
compared are mixed with the same cement in the proportions required 
on the work, and then gaged to plastic consistency as described on page 
138a, the best sand, provided it does not contain vegetable loam or other 
impurities to affect it chemically, is that which produces the smallest volume 
of mortar. 



IN — ..... . 

000000 z 

o o Z Z Z z z z 


o 

> 

Q> 

CO 


Fig. 57.—Conversion of Mechanical Analysis to 
Granulometric Composition. {See. p. 151.) 


CONVERSION OF MECHANICAL ANALYSIS TO 
GRANULOMETRIC COMPOSITION 

As an illustration of methods of contrasting two different sands and of 
making practical use of Feret’s researches, we may compare tests made by 
Mr. R. L. Humphrey* in connection with the construction of the Pennsyl¬ 
vania Avenue Subway, Philadelphia. He found the tensile strength at the 
age of one year, of 1: 3 mortar made with sand screened from gravel, to be 
about 50% stronger than that made with sand dredged from the Dela¬ 
ware River. The mechanical analysesf of the two sands are plotted by 

^Transactions American Society of Civil Engineers, Vol. XLVIII, p. 558. 
fMechanical Analysis Curves are described in Chapter XI, page 190. 
























































































I 5 2 


A TREATISE ON CONCRETE 


the authors in Fig. 57, page 151, from tables presented by Mr. Humpnrey. 

To transform these mechanical analysis curves to Feret’s granulometric 
composition, we may draw on the diagram, ordinates corresponding to the 
sizesof sieves used by him, namely, No. 5,No. 15,and No. 46. (Seep. 143.) 
From inspection of the curve it is evident that the granulometric composition 
of the gravel sand is g = 0.56, m = 0.35, f = 0.09, and of the river sand is 
g = 0.00, m = 0.89, f = 0.11. Plotting these granulometric compositions 
as C and D on Feret’s triangle, Fig. 55, and interpolating between contours, 
we find the relative compressive strengths of mortars made from the two 
sands to be, after one year in fresh water, about as 1775 is to 2550, or as 
1: 1.44, while Mr. Humphrey’s ratio of tensile strength for the two mortars 
at the age of one year is as 304 is to 470, or as 1: 1.53. These ratios are 
remarkably similar -when the differences in conditions are considered. 

Numerous tests have been made in America* in proof of the general law 
that coarse sands are stronger than fine. Many experimenters have 
seemed to reach the result that coarse sand is stronger than mixed sand. 
In certain cases this is undoubtedly true, because of mixing the different 
sizes in wrong proportions, or because the mortar of coarse sand contains 
so large a proportion of cement that the voids are completely filled and the 
addition of fine sand decreases, instead of increasing, the density. Mortar, 
for example, as rich as 1 : 2 ( i.e ., one part cement to two parts sand) of 
coarse sand is as strong as, and often stronger than, mortar of similar propor¬ 
tions made of almost any mixed sands, but with leaner mortars, a small 
admixture of from 10% to 25% of fine sand improves it. Natural sand, 
which in appearance is very coarse, almost invariably has a small percentage 
of very fine particles which, with the fine grains of cement, may assist, in 
the leaner mixture, in producing a dense mortar. The mechanical analysis 
curves of sand shown in Fig. 72, on page 200, are an illustration of the fine 
matter contained in all bank sands. 

EFFECT OF QUANTITY OF WATER UPON THE STRENGTH 

OF MORTARS 

Fine sands require in gaging a larger percentage of water than coarse 
sands, in order to produce a mortar of the same consistency. This, as 
discussed on page 147, exerts an indirect influence upon the strength. 

The influence of different percentages of water upon the same cement 
and aggregate is largely physical, although a deficiency may affect the 

*E. S. Wheeler in Report Chief of Engineers, U. S. A., 1895, P* 3 OI 3 > A. S. Cooper in Journal 
Franklin Institute, Vol. CXL, p. 326, Ira O. Baker in Journal Western Society of Engineers, Vol. 
b p- 7 3 


STRENGTH OF CEMENT MORTARS 


i53 

permanent strength of a mortar, while an excess may for reasons given on 
page 271 injure the cement by dissolving a portion of it. 

The effect of different proportions of water upon the ultimate strength 
(as suggested on p. 142) depends chiefly upon the density of the resulting 
mortar; the consistency which produces with a given weight of the same 
materials, the smallest volume, after setting, of Portland cement paste or 
mortar, gives the highest strength. Dry mixed mortars usually test higher 
than wet, — especially at short periods, as they set and harden more rap¬ 
idly, — because they can be more densely compacted, but more uniform 
results in practice as well as in experiment, can be attained with plastic 
mixtures. 

Tests by Mr. E. S. Earned,* a portion of which are shown in the table on 
page 154, illustrate the practical effect of different proportions of water upon 
the strength of neat cement pastes at various periods. It is noticeable that 
although the Natural cement mixed very wet finally attains a high strength, 
its very low strength up to 28 days shows the inadvisability of mixing 
Natural cement with an excess of water. 


SAND VS. BROKEN STONE SCREENINGS 

The relative strength of mortars made from sand and from screenings of 
broken stone or crusher dust has occasioned much discussion and dis¬ 
pute. It is probably dependent chiefly upon the relative density of the 
different mortars. Usually, a mortar from screenings will show higher 
tes.ts, while occasionally mortar from sand will be superior, because of the 
difference in size or of the relative sizes of the particles or grains com¬ 
posing the two materials. 

In some cases the form of the grainf and the mineralogic composition^ 
may exert a certain influence, although tests show that these are usually 
of inferior importance to the mechanical or granulometric composition 
of the sand or screenings. It is possible that the fine dust or impalpable 
powder in certain stone may chemically react upon the cement. 

On the other hand, screenings from a soft stone like slate, shale or soft 
limestone, may contain so much dust as to produce a poor mortar or 
concrete, for the same reason that a very fine sand results in a weak mortar. 

♦Proceedings American Society for Testing Materials, Vol. Ill, I 9 ° 3 > P - 4 OI> 

fBaumaterialienkunde, V Jahrgang (1900), p. 21, and Annales des Ponts et Chaussees, 1892, 
II, p. 124. 

jMr. P. Alexandre found calcareous sands to give relatively high strength, and Mr. Feret 
obtained similar high results with marble. 


154 


A TREATISE ON CONCRETE 


Table Showing Strength of Cements Mixed Neat with Different 

Proportions of Water. 

By Edward S. Larned. {See p. 153.) 


Cement brand 

Water per cent 

Sieve test 
residue on 

Wire 

minutes 

Tensile strength 

0 

u-> 

6 

No. 100 

, 

No. 180 

Light 

Heavy 

C/3 

*-« 

3 

O 

o* 

7 days 

28 days 

3 months 

6 months 

12 months 



ri 3 














14 














15 

°- T 5 

5-4 

21.2 

12 

207 

37 1 

655 

875 

941 

720 

787 

Portland A. 


16 

m m 



29 

297 

3°3 

75 ° 

973 

1008 

7.35 

816 

•< 

18 

. . 

. . 


80 

3 55 

260 

649 

773 

83 1 

645 

748 



20 

. . 


. . 

142 

402 

233 

5 00 

69 3 

716 

621 

676 



22 

. . 

. . 

. . 

268 

47 3 

184 

546 

635 

658 

601 

589 



24 




3 2 7 

912 

167 

5.39 

649 

644 

629 

755 



13 

O.I 

7.0 

18.0 

13 

270 

366 

775 

859 

1067 

892 

832 



14 




18 

3°3 

404 

780 

891 

972 

852 

781 



r 5 

16 




22 

327 

363 

602 

725 

844 

806 

7 2 3 

Rortlancl rs. 


18 

. . 

. . 

. . 

15 

383 

308 

57 ° 

7 2 3 

785 

728 

724 



20 

. . 

. . 

. • 

56 

703 

225 

590 

718 

760 

674 

636 



22 

• • 

. . 

. . 

52 

833 

166 

554 

649 

7 31 

643 

604 



[24 




188 

918 

42 

5 10 

691 

695 

632 

574 



[2 3 

O.I 

4.6 

10.2 

13 

3 2 

212 

251 

252 

3 H 

275 

356 



24 














25 

• • 

. . 

. . 

18 

39 

i 8 5 

218 

215 

289 

300 

34 T 



27 

• • 

• • 

. . 

21 

42 

L 5 ° 

188 

220 

257 

272 

314 

Natural 


29 

. • 

. . 

. . 

20 

52 

128 

1 78 

202 

246 

248 

256 

(Lehigh Valley) 

- 

31 

. . 

. . 

. . 

21 

57 

112 

17 3 

199 

224 

259 

3°9 



33 

. • 

. • 

• . 

27 

8 5 

104 

172 

182 

267 

246 

290 



3 5 

• • 

• . 

. • 

3 8 

I3 7 

9 3 

121 

178 

260 

286 

319 



37 

• • 

• • 

. . 

3 4 

160 

8 5 

108 

168 

262 

306 

326 



139 




67 

233 

8 5 

119 

202 

252 

371 

400 

- 


f 2 3 

2 * 3 

12.4 

21.9 

22 

59 

158 

177 

271 

332 

284 

264 



24 

• • 

• • 

• • 


7 8 

125 

141 

264 

.342 

, 3°9 

310 



25 

• • 

• • 

• • 

3 5 

120 

15 ° 

164 

216 

308 

318 

321 



27 

• • 

• • 

• • 

49 

1 4.3 

117 

116 

194 

3 °5 

345 

272 

Natural 


29 

• • 

• • 

• • 

76 

166 

96 

i °5 

164 

272 

320 

267 

(Rosendale) 


31 

• • 

- - 

• • 

117 

212 

72 

72 

T 59 

270 

37 i 

225 



33 




ii 5 

23 5 

62 

7 1 

147 

277 

379 

244 



3 5 

• • 

• • 

. • 

127 

400 

50 

64 

112 

245 

318 

31 5 



37 

. • 

. • 

• • 

198 

828 

59 

62 

96 

• • 

284 

331 



[39 

• * 

- • 


260 

1057 

54 

5 6 

85 

• - 

355 

364 


Note. — Results shown are the averages of six briquettes made. 























































STRENGTH OF CEMENT MORTARS 


154a 

Such dusty screenings are also especially bad for granolithic surfacing for 
sidewalks, and must not be used. 

SHARPNESS OF SAND 

In the past all specifications have called for clean, 11 sharp ” sand in spite 
of the fact that in many parts of the country where sharp sand is not 
obtainable, sand with rounded grains is furnished and used with perfect 
satisfaction. 

Comparative laboratory tests under conditions as nearly as possible 
identical uphold the practice of using sand with rounded grains. They 
indicate, as may be inferred from the previous discussion in this chapter, 
that the chief difference in natural sands is due to the size of the grains, 
and while the. sharpness of grain may exert a certain influence it is of 
so much less importance than the size of the grain that the requirement 
of sharpness for sand should be omitted from concrete specifications. 

Referring to columns (n) and (22) in the table on page 136, and to 
Fig. 49, page 141, it is evident that the difference in strength of nearly all 
the mortars made with the various sands is explained by the differing 
percentages of cement and densities without reference to the character of 
the grains. The only noticeable exception is with the artificial sand, M', 
which consists of mixed sizes of crushed quartz. Mr. FeretJ believes that 
this exception may be due to chemical action produced by the large quan¬ 
tity (i its weight) of impalpable quartz. Sand N', also crushed quartz, 
but containing none of this fine powder, produces a mortar similar in 
strength to like mortars of natural sand having rounded grains. 

Other tests of Mr. Feret§ and comparative tests, in the United States, of 
mortar with crushed quartz and natural sands generally confirm the above 
conclusion. The variation in the shape of the grains of natural sands and 
crushed quartz is illustrated in Figs. 62, 64, and 65, page 175. 

EFFECT OF NATURAL IMPURITIES IN THE SAND UPON 
THE STRENGTH OF MORTAR 

A clause to the effect that a sand for mortar or concrete shall be “clean” 
is almost universally found in masonry specifications. The necessity for 
this requirement is often questioned by cement experimenters, because the 
results of tests of mortar to which percentages of loam or clay have been 
added, often give higher results than those of mortar made with cement and 
pure sand. 

^Bulletin de la Societe d’Encourage'ment pour llndustrie Nationale, 1897, Vol. II. 

§Annales des Ponts et Chaussees, 1892, II, p. 124. 


A TREATISE ON CONCRETE 


i54^ 

As a matter of fact, it is impossible to make a general statement either to 
the effect that natural impurities in sand are beneficial or that they are 
detrimental. In some cases fine material may be of actual benefit, while 
in others the contrary is true. 

The case is covered by three conditions: (1) the character of the impuri¬ 
ties; (2) the coarseness of the sand; (3) the richness of the mortar. 

Character of Impurities. If the fine material is of ordinary mineral 
composition, such as clay, the mortar is affected only mechanically, and the 
results depend upon the coarseness of the sand of which the fine material is 
a part and the richness of the mortar, as indicated in paragraphs which 
follow. One exception to this general rule is when the clay is in such con¬ 
dition as to “ball up” and stick together so as to remain in lumps in the 
finished concrete. On the other hand, a small percentage of .clay well dis¬ 
tributed may be valuable for making the concrete or mortar work smooth, 
and especially for increasing its water-tightness (see p. 343). 

Vegetable or Organic Impurities. When the impurities are of an 
organic nature, like vegetable loam, they frequently have been found to 
prevent the mortar or concrete from hardening or to retard the hardening 
for so long a period as to make the sands entirely unfit for use. A very 
minute quantity of vegetable matter may produce injury, so small a per¬ 
centage in fact that frequently a sand which has passed careful inspection 
fails in practice to set properly with any brand of cement; therefore a test 
is absolutely necessary for any sand which has a suspicion of organic matter. 

The following tests of 1 : 3 mortar made with sand satisfactory in appea:- 
ance, but which nevertheless caused the fall of a concrete building, are given 


Effect of Vegetable Impurities in Sand 
By Sanford E. Thompson, 1908. See p, 1546, 


Sand. 

Tensile strength 
of 1 : 3 mortar 
at 7 days. 

Lb. per sq. inch 

Tensile strength 
of 1 : 3 mortar 
at 28 days. 
Lb. per sq. inch. 

A*. 

A 

93 

Bt.... 

4 

43 

129 

i6 5 

B washed. 

II4 

Wt . 


Standard Ottawa. 

3°° 




* Poorest portion of bank; reddish and dark in appearance. 

I Average sand from bank which passed inspection. 

t A medium good sand from another bant similar to B ii“i appearance, mechanical analysis, and 
chemical composition except nearly free from vegetable impurity. 





















STRENGTH OF CEMENT MORTARS 


154 c 

in the following table. They are averaged from different series and for con¬ 
venience in comparison the results are all converted to the basis of standard 
sand mortar, considered as 200 pounds in 7 days and 300 pounds in 28 days. 
The mortars were stored in air to conform to the actual conditions. Com¬ 
parative tests on mortars from the same sands stored in moist air and in 
water corroborated the results. 

The cause of the failure was traced in the expert investigation, to vege¬ 
table impurities in the sand which had washed down into the bank from the 
soil above. The poorest sand, A, showed by mechanical analysis only 
4% by weight of fine material passing a No. 100 sieve and 1.61% silt by 
washing, but this silt was found to contain nearly 30% of vegetable matter 
corresponding however to only 0.5% in the total sand. The vegetable 
matter appeared to coat the grains of sand so as to prevent adhesion of the 
cement and also retarded the setting. 

Effect of Fine Material in Filling Voids. Lean mortars may be im¬ 
proved by small admixtures of pure clay or by substituting dirty for clean 
sand, provided it is free from vegetable matter, because the fine material 
increases the density. Rich mortars, on the other hand, do not require the 
addition of fine material, and it may be positively detrimental, because the 
cement furnishes all the fine material required for maximum density. This 
is illustrated in experiments by Mr. Griesenauer* in which an admixture of 
even 2 per cent of clay (based on the weight of the sand) slightly reduced the 
strength of 1 : 2 mortar, while 20% of clay, added to the 2 parts of sand, 
reduced the strength about 30%. In 1 : 3 mortar, on the other hand, the 
addition of 2% slightly increased the strength, and there was no appre¬ 
ciable injury up to 20% addition. 

In experiments by Mr. E. S. Wheelerj* clay reduced the strength of neat 
and 1 : 1 mortars, but improved leaner mixtures. 

In this connection, of course, it must be borne in mind that if the sand is 
composed largely of fine material, the strength of the mortar is com¬ 
paratively low, as indicated in preceding pages. 

EFFECT OF MICA IN THE SAND UPON THE STRENGTH OF 

MORTAR 

The effect of mica in screenings from stone of a micaceous nature has 
been the subject of considerable controversy. Tests by Mr. FeretJ in 
France indicated that the presence of 2% of mica has but slight influence 
upon the tensile strength of mortar, but a greater one upon its compressive 

* Engineering News, April 28, 1904, p. 413. 

f Report Chief of Engineers, U. S. A., 1895, P- 3 °° 4 ’ anc * ^96, p. 2827. 

t Bulletin de la Societe d’Encouragement pour l’Industrie Nationale, 1897, Vol. II. 


A TREATISE ON CONCRETE 


154 d 

strength. More recent tests by Mr. W. N. Willis* in 1907 on mortars 
made with standard Ottawa sand into which mica was introduced are 
illustrated in Fig. 57a. He found that the presence of mica increased the 
voids and decreased the strength. The sand used in tests, loosely shaken, 
contained 37% voids, but as mica was added, the voids increased rapidly 
until with 20% mica the voids were 67% with a corresponding decrease in 
weight, and three times the amount of water was required for mixing. 

It is thus evident that the reduction in strength was largely due to the 
decrease in density and not entirely caused by the slippery character of the 
grains. In crushed stone screenings it is probable that the effect of the 
same percentage of mica in the natural state would be less marked. 

7 DAYS 28 DAYS 3 MOS. 

300 
280 
260 
240 
220 
200 
180 
160 
140 
120 
100 
80 
60 
40 
20 

" 7 DAYS 28 DAYS 3 MOS ° 

AGE OF MORTAR 

Fig. 57a.—Effect of the Addition of Mica upon 1 : 3 Mortar of Standard Sand. 

B y W. N. Willis. (See p. i54d.) 

Black mica, which has a different crystalline form, is not injurious to 
inortar. 

EFFECT OF LIME UPON THE STRENGTH OF MORTAR 

As a principal constituent of mortar in masonry construction, lime is 
inferior to cement in durability and strength. However, not only because 
of its relative cheapness, but also because a small addition of slaked or 
hydrated lime may increase the density of the mortar and cause it to work 
easier under the trowel, a limited quantity often can be used to advantage 
in mortar which is to be subjected to high loading. 



* Cement Age, Mar. 1907, p. 172. 

































































STRENGTH OF CEMENT MORTARS 


I 55 


For concrete, lime has been suggested, as mentioned in Chapter XIX, on 
Water-tightness, as a suitable ingredient to fill the voids and thus render it 
more impermeable. 

Although lime mixed with neat cement is apt to decrease its strength, in 
combination with sand for cement mortars, a small admixture of lime may 
add to the strength of the mortar. The questions as to whether lime is 
beneficial, and as to the amount which can be used, are determined by the 
character of the cement, the coarseness of the sand, and the proportions in 
which the two are mixed. The effect of lime in cement mortar or concrete 
is chiefly mechanical. In a porous mortar or concrete a small quantity of 
it assists in filling the voids, and if it is thoroughly slaked so as to contain 
no quicklime, its expansion need not be feared. 

Since even a neat cement paste has 35% to 45% water plus air voids, the 
inference might be drawn that the addition of lime would increase its 
density, and thus that the lime would be valuable even in very rich mortars. 
However, it seems to be practically impossible, except under high pressure, 
to replace the water which occupies the voids in neat cement paste with 
lime or any other fine powder. But it is evident that a lean mortar, such 
as a 1: 4, or even a 1: 3, should be improved by the addition of lime, and 
that this is true is illustrated in the following tests by Mr. E. S. Wheeler.* 
In these experiments the addition of 10% of lime — based on the weight 
of the cement — increases the strength of 1: 3 mortar, and as shown by 
item (3) in the table, a 1: 3J mortar with 10% of lime is stronger than a 
1:3 mortar with no lime. Items (4) and (5) illustrate the reduction in 


Effect of Lime Paste upon the Strength of Portland Cement Mortar. 
By E. S. Wheeler. (See p. 155.) 



Proportions 

cement 

Proportions 

cement 

Cement 

Limef 

Sand 

Average 

Tensile Strength. 

Item 

plus lime 
to sand 
by weight 

parts 

to sand 
by weight 

parts 

grams 

grams 

grams 

at 28 dys. 

lb. per 
sq. in. 

at 3 mos 

lb. per 
sq. in. 

(0 

1: 3 

i: 3 

200 

O 

600 

201 

236 

(2) 

1 : 2f 

i: 3 

200 

20 

600 

242 

265 

(3) 

1: 3 

i: 3 i 

180 

20 

600 

238 

264 

(4) 

1: 3 

1:4 

15 ° 

5 ° 

600 

168 

171 

(5) 

1: 3 

1: 6 

100 

100 

600 

57 

70 


♦Report Chief of Engineers, U. S. A., 1896, p. 2823. 

fThe weight of the lime paste was 2.7 times the weights in this column. 























A TREATISE ON CONCRETE 


156 

strength when the lime becomes more nearly a principal ingredient. Each 
yalue is an average of five briquettes** 

With another brand of cement and sand of different coarseness the 
relative quantity of lime to produce similar results will differ, but the 
general principle will still hold. In determining the amount of lime to 
add without decreasing the strength of a certain mortar, tests should be 
made with the materials to be employed* 

In scientific experiments by Mr. Feret* the maximum strength of 1:4 
mortar of Portland cement and sand from Saint Malof was reached 
with an addition of 4% or 5% by weight of hydrated lime powder. As 
the mortar became richer, the lime had less effect, until at proportions 
1:2, the addition of lime reduced the density, and at proportions 1: i\ 
the strength was also lowered. 

A larger number of bricks can be laid in a given time with mortar con¬ 
taining lime than with a lean cement mortar because the lime fills the pores 
in the mortar so that it spreads more readily without crumbling and ad¬ 
heres better to the bricks in “ buttering ” them. 

Unslaked Lime. Unslaked lime mixed with cement either for mortar 
or concrete is liable to produce expansion in the masonry and it is therefore 
never permissible to use it under any circumstances. Builders recognize 
that lime, putty, or paste is much improved by standing for several days, 
or, better, for months, before being used, because all the small lumps are 
thus slaked. This thorough slaking is especially necessary when lime is 
to be used, even as a very small ingredient, in important concrete and 
masonry construction; an admixture of even 2% of ground quicklime may 
seriously reduce the strength of the mortar.{ 

Weight and Volume of Lime. In proportioning lime to cement, the 
method of measurement must be clearly stated. The volume of common 
lime or quicklime increases in slaking to about 2\ times its volume meas¬ 
ured loose in the lime cask, the exact increase varying with the chemical 
composition and the purity of the lime. The weight of lime paste is about 
2\ times the weight of the same lime before slaking. Hydrated lime 
powder also occupies more volume than quicklime from which it is made. 

GROUND TERRA-COTTA OR BRICK AS A SUBSTITUTE FOR SAND 

Experiments by Mr. E. S. Wheeler§ indicated that for a mortar of light 
weight terra-cotta may be ground and used instead of sand. Tests with 

*Chimie Appliquee, 1897, p. 481. 

fSee p. 137. 

jReport Chief of Engineers, U. S. A., 1895, p. 2999. 

§Report Chief of Engineers, XJ. S. A., 1896, p. 2866. 

**See tests by Dr. E. W. Lazell, Transactions American Society for Testing Materials, Vol. 
VIII, 1908, p. 418. 


STRENGTH OF CEMENT MORTARS 


i57* 


both Portland and Natural cement mixed with the ground terra-cotta in 
various proportions gave at the end of three months tensile strengths 
which are not appreciably different from the strengths obtained with 
standard crushed quartz. Red brick pulverized* may also be used for 
the same purpose with good results. 

EFFECT OF REGAGING MORTAR AND CONCRETE 

Engineers have frequently specified and insisted that concrete or mortar 
be used immediately, that is, within one hour or one-half hour after it is 
gaged. As opposed to this requirement, tests by various experimenters 
indicate with singular unanimity that, at least for Portland cements, it is 
unnecessary, and that Portland cement concrete or mortar may remain 
for at least two hours in the mortar bed without deterioration. In fact, 
the ultimate tensile and compressive strength appears to be thus increased. 

The results of such tests lead'to the following conclusions: 

(1) The tensile or compressive strength of Portland cement mortars or 

concretes is not lowered by standing two hours after mixing. 

(2) Continuous gaging increases the ultimate strength. 

(3) Regaging makes the cement slower setting. 

Because of the Slow Setting and Hardening it is Scarcely ever Advis¬ 
able in Practice to Permit the Regaging of Mortar or Concrete. 

With Natural cements, however, the results of experiments are somewhat 
contradictory. It is probable that some Natural cements are injured, and, 
therefore, if circumstances require delay in placing Natural cement mortar, 
the effect of such delay should be determined by tests upon the brand to be 
used. 

Mr. E. Candlot (see page 124) states that the adhesive quality of cement 
mortar is reduced by regaging. 

Extended tests to determine the effect of regaging neat cements and 
mortars have been made by Mr. P. Alexandref and Mr. E. Candlot! in 
France, by Mr. Henry Faija§ in England, by Mr. James E. Howard^ at 
the Watertown Arsenal, U. S. A., and by Mr. Thomas F. Richardson at 
the Wachusett Dam, Massachusetts. 

Mr. Richardson in the course of his experiments made a batch of 1: 2 
mortar from each cement, cut it into two portions and, leaving half of it in 

♦Report Chief of Engineers, U, S. A., 1896, p. 2830. 

JAnnales des Ponts et Chaussees, 1890, II, p. 340. 

!Candlot’s Ciments et Chaux Hydrauliques, 1898, p. 355. 

§Butler’s Portland Cement, 1899, p. 307. 

^[Tests of Metals, U. S. A., 1901, p. 497. 


• i S 8 A TREATISE ON CONCRETE 

the mortar box, had the other half worked continuously. At various 
periods ranging from seven minutes to two hours, samples were taken from 
each portion, and made into tensile briquettes. Several brands of Amer¬ 
ican and English Portland cements, both slow and quick-setting, and 
several brands of Natural cement having different periods of set, were 
tested. Referring to the results Mr. Richardson states:* 

For the quicker setting cements there was a considerable falling off in 
strength in the briquettes broken seven days after being mixed, and a 
somewhat less falling off for those broken twenty-eight days after mixing; 
but at the age of six months all the mortars which had been allowed to 
stand, or which were worked continuously for one and one-half and two 
hours, showed a considerable gain in tensile strength. 

A typical series of tests with Rosendale cement, which attained its 
initial set in forty minutes and its final set in ninety minutes, and coarse 
sand (passing a No. 8 and retained on a No. 30 sieve) is presented in the 
following table: 


Effect of Re gaging upon the Tensile Strength of 1: 2 Natural ( Rosendale) 

Cement Mortar. (See p. 158.) 

By Thomas F. Richardson. 


Age 

Periods of Sampling. 

Immediately 

After one hour 

After two hours 

lb. per sq. in. 

Worked 

lb. per sq. in. 

Not Worked 

lb. per sq. in. 

Worked 

lb. per sq. in. 

Not Worked 

lb. per sq. in. 

7 days. 

27 

2 3 

21 


15 

28 days. 

22 

34 

27 

32 

29 

3 months. 

120 

155 

141 

192 

150 

6 months. 

163 

223 

IQI 

225 

213 


As a result of his tests, Mr. Richardson allowed the contractor, when 
necessary, to use the mortar on the dam up to two hours after being mixed. 
This was often a great convenience because of the distance of the mortar¬ 
mixing machine from the dam. 

Mr. Howard at the Watertown Arsenal took samples of neat Portland 

*Personal correspondence. 























STRENGTH OF CEMENT MORTARS 


*59 


cement after longer periods of setting, in some cases up to one hundred and 
two hours. In general, his specimens showed at the age of one month no 
appreciable difference, whether they were taken when first gaged or at 
four, or in some cases eight, hours after gaging. The strerigth of specimens 
taken after longer periods of standing was found at the age of one month to 
be lower. Natural cements showed an immediate falling off, due to 
regaging, on the thirty days’ tests, but the tests were not extended beyond 
this age. 

The Setting of Regaged Mortars. The experiments of Mr. Candlot 
were made chiefly upon mortars which had attained their final set, as 
determined by the pressure of the thumb. These mortars, after regaging, 
set much more slowly than normally gaged mortars, and he states that the 
set occurred at approximately the same time with all cements. “Thus, 
whether a mortar originally sets in ten minutes or three hours, when 
regaged it requires, in either case, about eight to ten hours.” He concludes 
from this action that, in Portland cements, aluminate of lime, which plays 
an important part in the setting, has no action on the hardening. 

Consequently regaging should have little influence upon siliceous prod¬ 
ucts, while it would be expected to seriously affect aluminous cements. 
This is the effect in practice, for limes and Portland cements can be regaged 
without bad results, while the strength of Natural Vassy cement is con¬ 
siderably lowered by regaging.* 

Effect of Regaging upon Adhesion. Mr. Candlot* found that mortars 
which had set several hours before molding, although usually showing as 
great compressive or tensile strength as normal mortars, gave much lower 
strength in adhesion, the reduction in strength being often 50%. (See 
p. 124.) 

TESTS OF SAND FOR MORTAR AND CONCRETE 

Since it is frequently impossible even for the most expert engineer to 
determine positively whether or not sand is fit to use for mortar and concrete,! 
it should always be tested for important structures. The experience of 
one of the authors during the last few years in the investigation of failures 
of concrete structures leads to the conclusion that unless the sand is from a 
bank of known quality it is even more necessary to test the sand than 
to test the cement. 

The test recommended by the Joint Committee on Concrete and Rein¬ 
forced Concrete in 1909 is as follows: 

Mortars composed of one part Portland cement and three parts fine 

♦ Candlot’s Ciments et Chaux Hydrauliques, 1898, pp. 358 and 360. 

fSee p. 154b. 


iSga 


A TREATISE ON CONCRETE 


aggregate, by weight, when made into briquets should show a tensile strength 
of at least 70 per cent of the strength of 1 : 3 mortar of the same consistency 
made with the same cement and standard Ottawa sand. To avoid the 
removal of any coating on the grains which may affect the strength, bank 
sands should not be dried before being made into mortar but should con¬ 
tain natural moisture. The percentage of moisture may be determined 
upon a separate sample for correcting weight. From 10 to 40 per cent 
more water may be required in mixing bank or artificial sands than for 
standard Ottawa sand to produce the same consistency. 

Sieves for Testing Sand. Since the relative strength of sand mortars, 
which are free from organic or other impurities is governed by the sizes 
and relative sizes of the grains, mechanical analysis tests are recommended 
by the Reinforced Concrete Committee of the National Association of 
Cement Users, 1909, as frequently of great value in selecting a sand. 

The relative strength of mortars from different sands is largely af¬ 
fected by the size of the grains. A coarse sand gives a stronger mortar 
than a fine one, and generally a gradation of grains from fine to coarse is 
advantageous. If a sand is so fine that more than 10 per cent of the total 
dry weight passes a No. 100 sieve, that is, a sieve having 100 meshes to the 
linear inch, or if more than 35 per cent of the total dry weight passes a 
sieve having 50 meshes per linear inch, it should be rejected or used with 
a large excess of cement. 

For the purpose of comparing the quality of different sands a test 
of the mechanical analysis or granulometric composition is recommended, 
although this should not be substituted for the strength test. The per¬ 
centages of the total weight passing each sieve should be recorded. For 
this test the following sieves are recommended:* 

0.250 inch diameter holes, j* 

No. 8 mesh holes 0.0955 i nc h width No. 23 wire 

No. 20 “ “ 0.0335 “ “ No. 28 “ 

No. 50- “ “ o.oiio “ “ No. 35 “ 

No. 100 “ “ 0.0055 “ “ No. 40 “ 

The effect of mechanical analysis or granulometric composition upon 
the strength of mortar is illustrated in table, page 159b. By this table 
the relative strength of different sands may be approximately estimated. 

Washing Test for Organic Impurities. To determine the percentage 
of organic impurities, the silt can be removed from the sand by placing it in 
a large bottle and washing it with several waters. The wash water is 
evaporated, and the residue is screened through a No. 100 mesh sieve to 
remove coarse particles which do not affect the strength. The silt passing 

* Sheet brass perforated with round holes passes the material more quickly than square 
holes. Round holes corresponding to sieves No. 8, 20 and 50 respectively are approximately 
0.125, 0.020 inch diameter. 

f A No. 4 sieve, having 4 meshes per linear inch, passes approximately the same size grains, 
as a sieve with 0.25 diameter holes. 


STRENGTH OF CEMENT MORTARS 159^ 

this sieve is weighed to obtain the percentage in the original sand, and then 
ignited in a platinum crucible to determine, after driving off the water, the 
percentage of combustible organic matter. 

Although data on the subject is incomplete, tests by Mr. Thompson tend 
to indicate that if the silt in a sand has more than 10% organic matter, and 
at the same time if the organic matter amounts to over 0.1% of the total 
sand, the use of the sand may be dangerous.* 

Microscopical Examination of Sand. An examination of grains of dirty 
sand with a microscope will frequently show a crust of organic matter on 
the grains which is not readily brushed off. 

Chemical Composition of Sand. A sand found by chemical test to con¬ 
tain a large per cent, say, 95 per cent, of silica is apt to be of excellent 
quality for mortar. However, this is by no means a sure test or a neces¬ 
sary test, since sands are frequently found with as low as 75% of silica 
which make first-class mortar or concrete. 


Tests by New York Board of Water Supply of 1:3 Mortar Made With Sands 
of Different Mechanical Analysis. {See p. 159a) 


Percentages Passing Sieves. 

Tensile Test. 

Lb. per sq. in. 

Compression Test. 
Lb. per sq. in. 

No. 4 . 

No. 8. 

No. 50 . 

No. 100 . 

7 days. 

90 days. 

7 days. 

90 days. 

I OO 

70 

12 

5 

213 

613 

2690 

5640 

I OO 

86 

2 1 

6 

263 

412 

1915 

4660 

IOO 

99 

26 

2 

177 

3 2 5 

905 

2170 

IOO 

97 

28 

6 

1 7 8 

282 

1070 

1500 

IOO 

94 

44 

12 

139 

228 

9 °j 

113° 

IOO 

IOO 

5 2 

14 

122 

170 

2 75 

8lO 

IOO 

IOO 

94 

48 

80 

149 

33 ° 

49 ° 


EFFECT OF GAGING WITH SEA WATER 

Mr. Alexandref concludes from his own and other experiments which 
extend to a three-year period, that there is no essential difference in strength 
of mortars gaged with fresh and with sea water. Briquettes gaged with sea 
water, however, usually set very much slower than those gaged with fresh 
water. J 

Crushing tests made by the authors in 1909 on six 3-inch cubes of 1 : 2 : 4 
concrete 14 months old, three of which were gaged with sea-water and 
three with fresh water, gave a result which indicated no appreciable dif¬ 
ference between the two; the specimens gaged with sea-water averaging 
4070 lb. per sq. in. and the fresh water cubes 3870 lb. per sq. in. 

* See “Impurities in Sand for Concrete” by Sanford E. Thompson, Transactions American 
Society of Civil Engineers, 1909. 

-|-Annales des Ponts et Chaussees, 1890, II, p. 332,. 

tAlexandre and Feret in Commission des Methodes d’Essai des Materiaux de Construction, 
1895, Vol IV, p. hi- 

























i 6 o 


A TREATISE ON CONCRETE 


CHAPTER X 

VOIDS AND OTHER CHARACTERISTICS OF 
CONCRETE AGGREGATES 

In this chapter are given tables of the specific gravities and voids of 
different materials, and the method of determining them, also laws relating 
to the voids in concrete aggregates, and the effect of compacting such 
materials. 

Laws of Volumes and Voids. The most important of these general 
laws relating to volumes of different materials, and to their voids, may 
be stated as follows: 

(1) A mass of equal spheres, if symmetrically piled in the theoretically 
most compact manner, would have 26% voids whatever the size of the 
spheres, but by experiment it is found that it is practically impossible to 
get below 44% voids. (See p. 168.) 

(2) If a dry material having grains of uniform shape be separated by 
screens into grains of uniform dimensions, the separated sizes (except 
when finer than will pass a No. 74 screen) will contain approximately 
equal percentages of voids; in other words, a dry substance consisting of 
large particles, all of similar size and shape, will contain practically the 
same percentage of voids as a substance having grains of the same shape 
but of uniformly smaller size. (See p. 170.) 

(3) In any material the largest percentage of voids occurs with grains 
of uniform size, and the smallest percentage of voids with a mixture of 
sizes so graded that the voids of each size are filled with the largest par¬ 
ticles that will enter them. (See p. 171.) 

(4) An aggregate consisting of a mixture of coarse stones and sand has 
greater density — that is, contains a smaller percentage of voids — than 

. the sand alone. (See p. 172.) 

(5) By Fuller and Thompson’s experiments, perfect gradation of sizes 
of the aggregate appears to occur when the percentages of the mixed aggre¬ 
gate passing different sizes of sieves are defined by a curve which approaches 
a combination of an ellipse and straight line. (See Chap. XI, p. 201.) 

(6) Materials with round grains, such as gravel, contain fewer voids 
than materials with angular grains, such as broken stone, even though 


VOIDS AND OTHER CHARACTERISTICS 


161 


the particles in both may have passed through and been caught by the 
same screens. (See p. 174.) 

(7) The mixture of a small amount of water with dry sand increases 
its bulk. In the case of most bank sands the maximum volume — 
and hence the smallest amount of solid matter per unit of volume, 
that is, the largest percentage of absolute voids — being reached with 
from 5% to 8% of water. (See p. 176.) 


CLASSIFICATION OF BROKEN STONE* 

Rocks which are commonly employed for concrete or for road making 
are commercially classified as ( a ) traps, ( b ) granites, (< c ) limestones, (d) 
conglomerates, and ( e ) sandstones. 

The trade term “trap” includes dark green to black, heavy, close tex¬ 
tured, tough rocks of igneous origin, thus covering a variety of rock whose 
mineralogical names are diabase, norite, gabbro, etc. As shown in the 
table below, the traps usually range in specific gravity from 2.80 to 

3 -° 5 * 

Granites, commercially so called, include the lighter colored, less dense 
rock, such as not only true granite, but syenite, diorite, gneiss, mica schist, 
and several other groups. Their specific gravities range from about 2.65 
to 2.85, averaging close to 2.70. Although, as road metal, the traps are 
usually far superior to granites, for concrete there appears to be no great 
difference in the value of the two classes. The distinction, however, is 
worth keeping because a concrete stone is often purchased from road 
metal quarries. 

Limestones of normal type range in specific gravity from 2.47 to 2.76, 
averaging about 2.60, although the very soft stones, which are not suitable 
for high class concrete, may fall below 2.0. 

Conglomerate, or pudding stone as it is often termed, is essentially a 
very coarse grained sandstone, ranging in specific gravity from 2.50 to 
2.80. It makes a good concrete aggregate. 

Sandstones of compact texture, such as the Potsdam and Medina sand¬ 
stones, and the Hudson River bluestone, may run as high in specific 
gravity as 2.75, while the looser textured, more porous sandstones may 
fall as low as 2.10, a fair average being about 2.40. 

Shale and slate make poor concrete aggregates, because their crushing 
.and shearing strength is low. 

*The authors are indebted to Mr. Edwin C. Eckel for the material under this heading, which 
has been especially prepared by him for this Treatise. 


1(52 


A TREATISE ON CONCRETE 


Specific Gravity oj Stone from Different Localities. 
Compiled by Edwin C. Eckel. 


trap. 


GRANITE. 


Specific 


Locality. 

Gravity. 

Locality. 


Gravity. 

Massachusetts 


California 



Boston .. 

... 2.78 

Penrhyn. 


... 2.77 

Minnesota 


Rocklin. 


. .. 2.68 

Duluth. 

. . . 3.00 

Connecticut 



Duluth. 

... 2.80 

Greenwich. 

r 

. .. 2.84 

Taylors Falls. 

- - - 3 *°° 

New London. 


... 2.66 

New Jersey 


Georgia 



Jersey City Heights. 

- - - 3-°3 

Stone Mt. 


.. . . 2.69 

Little Falls. 

... 2.99 

Maine 



New York 


Hallo well. 



Staten Island. 


Maryland 





Port Deposit. 


. ... 2.72 



Massachusetts 





Quincy. 


. ... 2.70 



New Hampshire 





Keene. 


. . . . 2.66 



New York 





Ausable Forks ... 


__ 2.76 



Rhode Island 





Westerly. 


. . . . 2.67 



Vermont 



* 


Barre.. 


- 2.65 



Wisconsin 





Amberg. 


- 2.71 



Montello. 



limestone. 


SANDSTONE. 


> 

Specific 



Specific 

Locality. 

Gravity. 

Locality. 


Gravity 

Illinois 


Colorado 



Joliet. 

... 2.56 

Ft. Collins. 


- 2.43 

Lemont. 

... 2.51 

Trinidad.. 


- 2.34 

Quincy. 

... 2.57 

Connecticut 



Indiana 


Portland 1 . 



Bedford. 


Massachusetts 



Salem. 

... 2.51 

Longmeadow 1 ... 



Minnesota 


Minnesota 



Frontenac. 

... 2.63 

Fond du Lac .... 



Winona. 

. .. 2.67 

New Jersey 



New York 


Belleville 1 . 


. . . . 2.26 

Canajoharie. 

... 2.68 

New York 



(liens Falls. 

2.70 

Albion 2 . 


. . . . 2.60 

Kingston. 

... 2.69 

Medina 2 . 



Prospect. 

... 2.72 

Potsdam 3 . 



Sandy Hill. 


Oxford 4 . 



Williamsville. 

- 2.71 

Malden 5 . 


- 2.75 



Oswego. 


. . . . 2.42 

Soft Limestone 


Ohio 



France 


Berea 6 . 


. . . . 2.14 

Caen. 

- 1.84 

Cleveland. 





Massillon. 




! Brownstone. 
2 Medina sandstone. 
3 Potsdara sandstone. 


4 Bluestone. 

5 Hudson River Bluestone. 
6 Berea grit. 




















































VOIDS AND OTHER CHARACTERISTICS 163 

AVERAGE SPECIFIC GRAVITY OF SAND AND STONE 


The specific gravity of a substance is the ratio of the weight of a given 
volume to the weight of the same volume of distilled water at a tempera¬ 
ture of 4 0 Cent. (39 0 Fahr.). For ordinary tests of stone and sand, the 
water need not be distilled and may be at ordinary temperature. 

A knowledge of the specific gravity of the particles of the sand and 
stone is important to the engineer as a ready means of determining the 
percentages of voids. 

The uniformity in the specific gravity of different sands is very con 
venient for calculation. Different authorities who have tested large quan¬ 
tities of sand have reached almost identical conclusions as to the average 
specific gravity, and all state that it is practically a constant. Mr. Allen 
Hazen gives 2.65, Mr. William B. Fuller, 2.64, Mr. R. Feret in France 
states that “one may without appreciable error adopt an average specific 
gravity of 2.65 for siliceous sands/’* while Mr. E. Candlot gives limits of 
2.60 to 2.68 for sands which are not porous.f The specific gravity of 
calcareous sands averages about 2.69 by absolute determination, or about 
2.55 if measured by the total volume of the particles having their pores 
filled with air. 

Gravels also have quite uniform specific gravity. According to Mr. 
A. E. Schutte, who has tested gravel from more than forty localities in the 
United States and Canada, an average value is 2.66. 

The following table gives average values of various concrete aggregates. 
In every case, the specific gravity is the ratio of the weight of an abso¬ 
lutely solid unit volume of each material to the weight of a unit volume 
of water. Specific gravities of stone from various localities are given on 
page 162. 


Average Specific Gravity of Various Aggregates. (See p. 163.) 

Weight of a solid 
Specific cu. ft. of rock. 


Material. Gravity. lb. Authority. 

S an d. 2.65 165 Allen Hazen 

Gravel. 2.66 165 A. E. Schutte 

Conglomerate. 2.6 162 Robert Spurr Weston 

Granite. 2.7 168 Edwin C. Eckel 

Limestone. 2.6 162 Edwin C. Eckel 

Trap . 2.9 180 Edwin C. Eckel 

Slate . 2.7 168 Tod’s TablesJ 

Sandstone. 2.4 150 Edwin C. Eckel 


Cinders (bituminous) .... 1.5 95 The authors 

^Bulletin de la Societe d’Encouragement pour l’lndustrie Nationale, 1897? Vol. II, p. 159 1 * 
-j-Ciments et Chaux Hvdrauliques, 1898, p. 246. 

^Encyclopedia Britannica. 










164 


A TREATISE ON CONCRETE 


METHOD OF DETERMINING SPECIFIC GRAVITY 

The specific gravity of a sample of material is determined by dividing 
its weight by the weight of water which it displaces when immersed. 

The size of sample necessary for the accurate determination of a sand 
or stone of fairly uniform texture depends chiefly upon the delicacy of the 
apparatus employed. If scales reading to grams, and measures reading 
to cubic centimeters, are employed, a sample of 250 grams should give 
accurate results to two decimal places. With scales reading to J ounce, 
a sample of 4 lb. is necessary for similar accuracy. The water must be 
maintained at 68° Fahr. (20° Cent.). 

The sample should be taken by the method of quartering described on 
page 398. 

Before finding the specific gravity of siliceous sand, the sample should 
be dried in an oven at a temperature as high as 212 0 Fahr. (ioo° Cent.) 
until there is no further loss in weight. A porous stone, on the other hand, 
may be first moistened sufficiently to fill its pores, and then the surfaces 
of the particles dried by means of blotting paper. If this method is 
followed, the material should be .in a similar condition when its voids 
are determined by the method given on page 165. The absolute 
specific gravity of the porous stone may be afterward found by drying in 
an oven and correcting for the moisture lost. 

The apparent specific gravity of sand or stone may be determined 
with an apparatus consisting of scales reading to J ounce or to 5 grams, 
and a tall glass vessel with a reference mark, such as a cylinder or a 
pharmacist’s graduate. The method is as follows: 

Make a mark at any convenient place on the neck of the vessel; 

Fill the vessel with water at a temperature of 68° Fahr. (20° Cent.) up 
to this mark; 

Take a known weight in grams or ounces of the material; 

Pour material into vessel carefully, a few grains at a time, so that no 
bubbles of air are carried in with it; 

Pour out the clear water displaced by the material (leaving water in the 
vessel up to the level of the mark), and weigh the water poured out. 
Let 

S = Weight of material placed in vessel. 

W = Weight of water displaced. 

Then 

A 

Specific gravity of material = — (1) 



VOIDS AND OTHER CHARACTERISTICS 


i6 5 

It is essential that the weight of water displaced be weighed to within 
±2%. If the scales are not sufficiently sensitive, more material must 
be taken and a larger vessel used. With balances sensitive to i gr. or 
ik oz. the displacement of more than 3 ounces of water is necessary. 

METHOD OF DETERMINING VOIDS 

The voids in sand, gravel, and broken stone may be obtained directly 
from the tables on pages 166 and 167. Special determinations may be 
made as described below. 

The percentage of voids in sand or fine broken stone cannot be accu¬ 
rately obtained by the ordinary method of placing in a measure and pour¬ 
ing in water, because it is physically impossible to drive out all the air. 
There may be enough of this held to amount to 10% of the volume of the 
sand, and thus cause a corresponding error in the percentage of voids. 

The voids in coarse stone containing no particles under ^-inch 
diameter may be determined by placing in a box or pail of known 
volume and pouring in water, but if the specific gravity is known, the 
method described below is simpler and more accurate. 

The only apparatus required are scales of fair accuracy and an exact 
measure which contains not less than \ cu. ft. If a cubic foot measure is 
not available a 16-quart pail will answer the purpose, although com¬ 
pactness of the sand is less easily adjusted because of the small 
diameter. Such a pail holds slightly over \ cu. ft. and the exact measure 
is determined by weighing the pail, pouring in 31 lb. 2 oz. of water, and 
marking the level of the surface. The pail up to this mark contains 
\ cu. ft. of any material. 

The method of determining the voids is as follows: 

Weigh the measure; 

Fill the measure to the required level with the material in the state in 
which the percentage of voids is required, that is, loose, shaken, or 
packed; 

Weigh, and deduct the weight of the measure, calling the net weight of a 
cubic foot of the material, S; 

If the material consists of, or contains, sand or fine stone, correct for 
moisture by taking an exact weight, — about 10 lb., — drying in an 
oven at a temperature of at least 212 0 Fahr. (ioo° Cent.) until there 
is no further loss in weight, and after calculating the percentage of 
moisture in terms of the weight of the original moist sand or stone, 
express the percentage as a decimal, p. 


A TREATISE ON CONCRETE 


166 


Select the weight of a cubic foot of absolutely solid rock* from the 
table on page 163, and call it R. 


Per cent of absolute voids = 



S — Sp\ 
R ) 


100 



The air voids are determined, if desired, 
moisture (its weight divided by the weight 


by deducting the volume of 
of one cubic foot of water) 


Percentages of Voids Corresponding to Different Weights per Cubic Foot of Sand, 
Gravel, and Broken Stone Containing Various Percentages 
0} Moisture. (See p. 168.) 


■J +7 






<U K© 

St 

^+7 






<D kO 

. ** 






Is 







IS 

<L> bC 

PERCENTAGES OF ABSOLUTE VOIDS IN 

> 

bjO 

w. 3 

2 S 

S bO 

PERCENTAGES OF ABSOLUTE VOIDS IN 

^ be 


MATERIAL CONTAINING MOISTURES 


O 

u 

MATERIAL CONTAINING MOISTURES 


eight of < 
of sand c 


BY WEIGHT.i 


3 cn O 
Z> <^ > 

'S> U ^ 

"o 0 >• 

U-* O 
0_- 
Tj 

rC ci 
b C & 

'Z'Z 


BY 

WEIGHT. J 


c £ 

2 SG 

•§ t r 

0 0 

•5I uXi 

£ 

0% 

2% 

4 % 

6% 

8% 

S 

$ 

0% 

2% 

4 % 

6% 

8% 


% 

% 

% 

% 

% 

% 


% 

% 

% 

% 

% 

% 

70 

57-6 

5 8 -4 

59-3 

60.I 

61.0 

I.I 

98 

40.6 

41.8 

43 -° 

44.2 

45-3 

1.6 

75 

54-5 

55-4 

5 6 -4 

57-3 

58.2 

1.2 

99 

40.0 

41.2 

42.4 

43 - 6 

44.8 

1.6 

80 

81 

5 i -5 

5°-9 

5 2 -5 

5*-9 

53-4 

5 2 -9 

54-4 

53-9 

55-4 

54-8 

1-3 

i -3 

100 

101 

102 

39*4 

38.8 

38.2 

40.6 

40.0 

39-4 

41.8 
41.2 
40.7 

43 -° 

42.5 

41.9 

44.2 

43-7 

43 - 1 

1.6 

1.6 

1.6 

CO 00 OC 

5°-3 
49-7 
49. 1 

5 i -3 

5°-7 

5 0 - 1 

5 2 -3 

5 i -7 

5 1 * 1 

53-3 

5 2 -7 

5 2 - 2 

54-3 

53-7 

53 - 2 

i -3 

i -3 

1.4 

10 3 

104 

10 5 

37-6 

37 -o 

364 

38.8 

38.2 

37-6 

40.1 

39-5 

38.9 

4 i -3 

40.8 

40.2 

42.5 

42.0 

41.4 

1.6 

i -7 

i -7 

00 00 00 
O\0n 

48.5 

47-9 

47-3 

49-5 

48.9 

48.3 

5°.6 

50.0 

49.4 

5!-6 

5 1 * 0 

5°-4 

52.6 

5 2 -° 

5 i -5 

1.4 

1.4 

1.4 

106 

107 

108 

35-8 

35-2 

34-6 

37 -° 

3 6 -4 

35-9 

38-3 

37-7 

37-2 

39-6 

39 -° 

38.5 

40.9 

40-3 

39*7 

i -7 

i -7 

i -7 

88 

46.7 

47-7 

48.8 

49.9 

5°-9 

1.4 

iog 

110 

33-9 

33-3 

35-3 

34-7 

36.6 

36.0 

37-9 

37-3 

39-2 

38-7 


89 

90 

46.1 

45-5 

47. 1 

46.5 

48.2 

47.6 

49-3 

48.7 

5°-4 

49.8 

1.4 

1.4 

!-7 

1.8 

9 i 

44.8 

45-9 

47 -° 

48.2 

49 - 2 

i -5 

ii 5 

3°-3 

3 r -7 

33 - 1 

34-5 

35-9 

1.8 

92 

44.2 

45-4 

46.5 

47.6 

48.7 

i -5 

120 

2 7-3 

28.7 

30.2 

3 i -6 

33 - 1 

i.g 

93 

43-6 

44.8 

45-9 

47 -° 

48.1 

i -5 

I2 5 

24.2 

25.8 

2 7-3 

28.8 

3°-3 

2.0 

94 

43 -o 

44.2 

45-3 

46.5 

47.6 

i -5 

130 

21.2 

22.8 

24.4 

2 5-9 

27.5 

2.1 

95 

42.4 

43 - 6 

44-7 

45-9 

47.0 

1.5 

18.2 

19.8 


96 

41.8 

43 -° 

44.1 

45-3 

46.4 

i -5 

i 35 

21.4 

23.1 

24.7 

2.2 

97 

41.2 

42.4 

43 - 6 

44-7 

45-9 

1.6 

140 

15.2 

16.8 

18.5 

20.2 

21.9 

2.2 


*The weight per cubic foot of a solid is the specific gravity of the rock multiplied by the weight of a 
cubic foot of water. 

tAlso applicable to broken stones such as granite, conglomerate, and limestone, whose specific gravity 
averages from 2.6 to 2.7. Table is based on specific gravity of 2.65, 

JThe per cent, of absolute voids given in the columns include the space occupied by both the air and 
the moisture. To determine the per cent, of air space, multiply the figure in the last column, opposite 
the weight of sand under consideration, by the per cent, of moisture by weight, and deduct result from the 
per cent, already found. 































VOIDS AND OTHER CHARACTERISTICS 167 


in a unit volume of the sand or stone, from the total voids. Expressed 
in percentages with notation same as above, 

Sp 

Per cent, of air voids = Per cent, of absolute voids-— 100 (4) 

62.3 

Example. — Given a sand whose loose weight per cubic foot is found 
to be 92 lb. and its moisture 3% by weight. Find the percentage of voids 
in the loose sand. 

Solution by formula. — Since from the example S = Q2 and p = 0.03, 
and, from table on page 163, R = 165, 


f 

Percentage of absolute voids = 



92 — 0.03 (92)' 
165 


100 


= 45 - 9 % 

This percentage includes the space occupied by the moisture. The net 
percentage of voids occupied by air alone is the difference between the 
absolute voids and the percentage of moisture by volume. Moisture is 

2.76 

92 x 0.03 = 2.76 lb., or —— = 0.044 cu. ft., corresponding to 4.4% voids 

62.3 

by volume, hence air voids are 45.9% — 4-4% = 41.5%. 


Percentages 0} Voids Corresponding to Different Weights per Cubic Foot of Dry 
Broken Stone of Various Specific Gravities. (See p. 168.) 


Weight PERCENTAGES OF ABSOLUTE VOIDS CORRESPONDING TO 


01 SPECIFIC GRAVITIES OF STONE OF 

one cu. ft. of 


dry broken 
stone. 

2.4* 

2 -5 

2.6f 

2-7t 

2.8 

2 - 9 § 

. 

% 

% 

% 

% 

% 

% 

70 

53-2 

55 -° 

56.8 

584 

59-9 

61.3 

75 

49.8 

51.8 

537 

554 

57 -° 

58.5 

80 

46.5 

48.6 

50.6 

524 

54-1 

557 

85 

43-2 

45-4 

47-5 

49-5 

5 i -3 

53 -° 

90 

39-8 

42.2 

44-5 

46.5 

484 

50.2 

95 

3 6 -5 

39 

41.4 

43*5 

45-5 

474 

100 

33 - 1 

35-8 

38.3 

40.6 

42.7 

447 

105 

29.8 

32.6 

35-2 

37-6 

39-8 

41.9 

no 

26.4 

29.4 

32.1 

34-6 

36.9 

39 -i 

US 

23.1 

26.2 

29.0 

3 1 - 6 

34-1 

3 6 4 

120 

19.8 

23.0 

25-9 

28.7 

3 1 - 2 

33-6 

125 

16.4 

19.8 

22.8 

257 

28.3 

30.8 

130 

1 3 - 1 

16.6 

19.8 

22.7 

25-5 

28.1 

135 

97 

13-3 

16.7 

197 

22.6 

25-3 

140 

6.4 

10.1 

13.6 

16.8 

19.7 

22.5 


Note. —Average specific gravity of bituminous coal cinders may be taken as 1.5. 
♦Sandstone. JGranite and slates, 

fLimestone and conglomerates. §Trap. 



















A TREATISE ON CONCRETE 


168 

Solution by table (p. 166.) — Opposite 92 lb. per cu. ft., interpolating 
between 2% and 4% moisture, is 46.0% of absolute voids. From last 
column 3% by weight corresponds to 3% x 1.5 = 4-5% by volume. 
46.0% — 4.5% = 41-5% air voids - 

Tables of Voids. From the tables on pages 166 and 167, the voids 
in sand, gravel, and broken stone may thus be determined simply by 
weighing the material and finding the percentage of moisture contained in 
it, as above described. Since the percentage of moisture by volume is 
always greater than its percentage by weight, and the two are not pro¬ 
portional to each other, the final column is inserted in the first table 
for convenience in calculating the moisture by volume. 

VOIDS AND DENSITY OF MIXTURES OF DIFFERENT 

SIZED MATERIALS 

The term density as applied to mortar is defined on page 135. Similarly, 
in a dry material, such as a concrete aggregate, it is represented by the 
total volume of the solid particles entering into a unit volume of the aggre¬ 
gate. In dry materials the density is the complement of the voids, since a 
material which has, say, 40% voids will have a density of 0.60; but density 
is a more correct term to use than voids because it is applicable to con¬ 
cretes and mortars in which connection the term voids is somewhat 
ambiguous. The example on page 138a illustrates the method of de¬ 
termining the density of a concrete or mortar. 

The densities of dry aggregates of uniform specific gravity, or of mixtures 
in uniform proportions of materials with different specific gravities, are in 
direct proportion to their weights. For example, the densities of different 
dry sands may be compared by weight; or the densities of different mix¬ 
tures of sand and broken trap in proportions, say, 2 parts sand to 4 parts 
trap may be compared by weight; but the density of sand and the density 
of trap screenings cannot be compared by weights unless the differing 
specific gravities are taken into account. 

In the following discussion of the laws formulated on page 160, both the 
terms density and voids are used in relation to the dry materials. 

Voids in Masses of Similar Sized Particles. (1) The fact that the 
percentage of voids in a mass of equal spheres symmetrically piled in the 
theoretically most compact manner is independent of the actual diameter 
is simply a geometrical proposition, evident without demonstration by in¬ 
spection of Fig. 58. 

In actual experiment it has been found that while the percentage of 
voids is uniform regardless of the size of the spheres, it is impossible to 


VOIDS AND OTHER CHARACTERISTICS 


169 


pour spheres into a measure so that they will arrange themselves sym¬ 
metrically, and the rather astonishing result has been reached by Mr. 
Fuller (see p. 185) that 44% is the smallest percentage of voids which can 
be obtained with equal perfect spheres, no matter what may be their 
actual diameters or the size of the receptacle. 

The following simple demonstration,* which is of theoretical interest, 
proves that the percentage of voids in a mass of equal spheres symmetri¬ 
cally piled in the most compact manner is 26%, and that the radii (and 
consequently the diameters) of the two next smaller spheres which can 



be inscribed between the larger ones are respectively 0.41 and 0.22 of 
the radius of the large spheres. 

The circles in Fig. 58 represent a horizontal plan of two layers of spheres. 
The centers A x A 2 B l form a regular tetrahedron. 

Let edge be 2. 

Altitude = difference between level of centers A, B, C, and level of 

centers D, E is — 's/fT 

3 

Let number of spheres in a layer be m, number of layers n. 

*For which the authors are indebted to Dr. Harry W. Tyler. 


A TREATISE ON CONCRETE 


170 

Volume of one sphere is —— 

3 

Volume of spheres in a layer, -— 

3 

Volume of all spheres, ^ m n 77 (approx.) = F 1 

3 

Cross-section of including space is 2 \ZN m (approx.) 

Volume of including space is 2 \/^ m X— \Tb n (approx.) 

3 

= 4 \Z~2 m n (approx.) = V 2 

Ratio — 1 = — 4 m n 77 _ _—T- = 0.74 (approx.) corresponding to 

V 2 3X4 w n V2 3 VT 

about 26% voids. 

Inscribed Spheres. 

1. Sphere inscribed between spheres A 1 A 2 and Dj! 

Distance from any vertex A t of tetrahedron to center is \ \T 6 

_ 2 2 

Radius of small sphere = 1 \/6 — 1 = 0.22 (approx.) or about —- G f 
the radius of the large spheres. 

2. Sphere inscribed between A 2 B x B 2 and D x D 2 E x : 

Distance from A- to E. is 2^/2" 

41 

Radius of small sphere = \/~2 — 1 = 0.41 (approx.) or about- of 

100 

the radius of the large spheres. 

(2) The proposition that if a dry material such as sand, pebbles, or 
irregular broken stone, having grains of fairly uniform shapes, be separated 
by screens into grains of uniform dimensions, the separated sizes will con¬ 
tain approximately equal percentages of voids, is not so self-evident, but 
experiment proves that in portions of the same material screened to 
uniform sizes the percentages of voids will be substantially alike until 
very fine sizes are reached, such as will pass a No. 74 sieve; below this 
degree of fineness the particles are entangled by air. The authors have 
found by experiments given in the following table, that different lots of 
broken stone from the same quarry, each screened to uniform size, will 
contain substantially the same percentages of voids, but that lots of stone 
from different quarries screened to the same size may differ because of 
the structure of the rock. Published records usually show slight 
variations in the weight per cubic foot of different sized broken stone, 
but it is noticeable that some authorities give the heaviest weight, 









VOIDS AND OTHER CHARACTERISTICS 


171 

which corresponds to the smallest percentage of voids, for the larger sizes, 
while others give the reverse. For example, Patton’s Civil Engineering 
gives the smallest percentage of voids in the coarsest broken stone, while 
Butler’s Portland Cement gives the smallest percentage in the finest 
stone. The variation in results is undoubtedly due to differences in 
methods of compacting and to the variations in the sizes of the stones of 
each lot. 

Experiments by Mr. Feret in France, and Mr. Thomas F. Richardson 
in the United States, show that the percentages of voids in absolutely dry 
sand which has been screened to uniform size are almost identical. Mr. Feret, 
experimenting by shoveling dry sand loosely into a 50 liter (1.8 cu. ft.) 
box, — a measure large enough to eliminate errors of placing, — found 
that fine (F) medium (M) and coarse (G) sands each contained about 50% 


Voids and Compression of Broken Trap and Gravel. (See p. 170.) 


Size of 
Stone 

Class of 
, Stone 

Crusher 

Size of 
Particles 

<D 

CJ 

0 

-*-* 

C/3 

<u 
c n 

O 

C 

•ession by light 
ning or shaking 

"O 

0 

s 

£ g 

2! 

”3 c 

' 

a 00 

•ession by heavy 
ramming 

n heavily rammed 
stone 






CD 

rs 

d £ 

£ § 


a 

£ 

C/3 

r2 







u 

> 

O 

> 






% 

% 

% 

% 

% 


No. 2 

No. 3 

Nos. 2,3, 4 

HardTrap 

Rotary 

2Y to 1" 

1" to i" 

2Y to dust* 

54-5 

54-5 

45 -o 

14-3 

14-5 

46.9 

35-7 

19.2 

20.5 

20.8 

43-7 

42.8 

30.6 


No. 2 

No. 3 

Soft Trap 

Jaw 

U 

2" to f" 

¥ to f" 

51.2 

51-2 

11.9 
14-3 

44.6 

43 - T 

17.8 

23-9 

40.6 

35-0 

(Variation is due to trap 
/ breaking under rammer 


Gravel 


2 y to r 

36.5 

I 2 - 5 t 

27.4 

ii-5t 

28.2 



Loose stone is as thrown by a laborer into a measuring box or barrel. 
Material rammed in 6-inch layers. 


voids, while mixing the sizes, which are defined on page 142, in the best 
proportions reduced the voids to 34%. 

Densest Mixture of Sand and Stone. (3) The fact that the densest 
mixture occurs with particles of different sizes is so evident as to require 
no proof, and this being recognized, it follows that the least density 
and hence the largest percentage of voids occurs when the grains are 
all of the same size. The converse of this proposition, that the smallest 
percentage of voids occurs in a mixture graded so that the voids of 
each size are filled with the largest particles which will enter them, is 

*Mixed in proportions 44.4% No. 2, 33.3% No. 3, and 22.2% No. 4 (dust). 

"(Another gravel tested, compressed, 8.5% on shaking, and 11.2% on hard ramming. 





























172 


A TREATISE-ON CONCRETE 


illustrated in Figs. 59, 60, and 61, and is important in its application to 
the selection of materials for concrete. 

(4) The fact that an aggregate consisting of a mixture of stones and 
sand has greater density, that is, contains fewer voids than the sand alone, 




Fig. 60. — Large Stones with Voids filled with small Stones and Sand. (See p. 172.) 

is illustrated by comparison of Figs. 59 and 61. The voids of the large 
stone in Fig. 59 are filled with sand, while the voids in the same large 
stone in Fig. 61 are filled with mixed sand and stone, and the mass of the 
mixture is evidently denser, that is, it contains more solid material. This 





























VOIDS AND OTHER CHARACTERISTICS 


*73 

law relates directly to the difference between mortar and concrete. The 
substitution of stones for small masses of sand reduces the voids and con¬ 
sequently the quantity of cement required. Extending the principle to 
the fixing of proportions of sand and stone, it is evident that for maximum 



Fig. 6i. — Large Stones, with Voids filled with medium sized Stones surrounded by 
smaller Stones and Sand so as to give Graded Mixture. ( See p. 172.) 


economy and equal strength there should be used the largest possible 
quantity of stone in proportion to the sand, the strength of concrete being 
often actually increased simply by substituting more stone for a portion 
of the sand. In the following table this is illustrated by tests selected 
from Mr. Fuller’s 6-inch beam experiments, which are given in full on 
page 376. 


Relation of Strength of Concrete to Relative Proportions of Sand 

and Stone. (See p. 173.) 


Proportions by weight of 
cement to total 
aggregate. 

1 : 6 
i: 6 

1: 6 
1: 6 
1: 6 


Proportions by weight of 
cement to sand and 
broken stone. 

i:i:5 

1:2:4 

i:3:3 

1:4:2 

1:6:0 


Modulus of Rupture 
lb. per sq. in. 

5°4 

439 

355 

210 

93 


The total amount of aggregate in each case is the same, namely, one part 
cement to 6 parts sand and stone, but the strength varies with the relative 
proportions of each, from 93 lb. to 504 lb. 

(5) The discussion of Fuller’s experiments on the relation of the best 













A TREATISE ON CONCRETE 


174 

practical mixture of sizes to a parabolic curve is given in Chapter XI, 
page 201. 

Effect of Shape of Grain. (6) The fact that round grains, such as 
gravel, contain fewer voids than material with angular grains, such as 
broken stone, even if the particles in both are the same size, is proved 
from experiments in America and France. Mr. Allen Hazen states* that 
round grained water-worn sands have from 2% to 5% less voids than 
corresponding sharp grains of sand. Mr. Feretf also has studied the 
effect of the shape of the grain upon the density of sand, using in each 
case an artificial mixture of three sizes, with the following results: 


Effect of Character of Sand Grains upon the Volume of the Sand. (See p , 174.) 

By R. Feret. 


Nature of Sand 

Shape of Grains 

Actual solid volume per 
liter of sand 

Not shaken, Shaken to 
liter refusal, liter 

Quartzite crushed in jaw crusher. 

Laminated 

°-5 2 5 0.654 

Crushed shells. 

Flat 

0.557 0-682 

Ground quartzite. 

Angular 

0.579 0.726 

Natural granitic sand . 

Rounded 

0.651 0.744 


The voids in each case are the complements of the figures given. 

The conclusion to be drawn is that the real volume increases (and 
therefore the voids decrease) as the sand approaches the round form. 

When experimenting upon gravels and broken stone Mr. Feret J sepa¬ 
rated each into three sizes which he called respectively: 

G (coarse) passing holes of 6 cm. (2.36 in.) diameter and retained by 
holes of 4 cm. (1.57 in.) diameter; 

M (medium) passing holes of 4 cm. (1.57 in.) diameter and retained 
by holes of 2 cm. (0.79 in.) diameter; 

F (fine) passing holes of 2 cm. (0.79 in.) diameter and retained by holes 
of 1 cm. (0.39 in.) diameter. 

Each size of broken stone loosely measured gave about 52% voids, and 
each size of gravel about 40% voids. The voids in the broken stone were 
reduced to 47%, the lowest result obtainable, by mixing G and F in about 

♦Twenty-fourth Annual Report, Massachusetts State Board of Health, 1892. 
fAnnales des Ponts et Chaussees, 1892, II, p. 22. 

1 'Annales des Ponts et Chaussees, 1892, II, p. 153. 
















VOIDS AND OTHER CHARACTERISTICS 


I 75 


equal parts with no M, and in the gravel to 34% with about 3! parts of 
G to one part of F. These figures are of course directly applicable only 



Fig. 62. — Standard Ottawa Sand, dry.* Fig. 63. — Standard Ottawa Sand with 
No. 20 to No. 30 Sieves. (See p. 175.) 6% moisture.* No. 20 to No. 30 Sieves. 

(See p. 175.) 



Fig. 64. —Natural Bank Sand.* No. 20 Fig. 65. — Crushed Quartz* No. 20 to 
to No. 30 Sieves. (See p. 175) No. 30 Sieves. (See p. 175.) 

to the special materials which he studied, and do not apply to gravel or 
stone containing sand or dust. 

Photographs of Sand. Photographs of three types of sand are shown 
in Figs. 62 to 65. Figures 62 and 63 are photographs of the Ottawa, 

*Each sand has passed a No. 20 and been retained on a No. 30 sieve. Magnified 10} 
diameters. 





A TREATISE ON CONCRETE 


176 

Illinois, bank sand screened to the size selected for the standard sand 
by the Committee of the American Society of Civil Engineers. They 
* illustrate the effect of moisture upon the arrangement of the sand grains, 
which is more fully described below. Fig. 64 is an ordinary bank sand 
from Eastern Massachusetts which has passed through and been re¬ 
tained by the same screens as the Ottawa sand. Fig. 65 is a sample 
of crushed quartz sand, formerly the standard in the United States. 
The sands are all reduced by the same number of diameters. The 
Ottawa sand, Figs. 62 and 63, is apparently of finer grain than either 
the bank sand or the crushed quartz, but close inspection will show that 
its grains, very uniform in size, are of about the same diameter as the 
smallest grains in the other sands. In other words, all the grains cor¬ 
respond very closely to a No. 30 sieve, the lot of sand from which it 
was screened containing no larger particles. 

Effect of Moisture on Sand and Screenings. (7) Moist sand occupies more 
space and weighs less per cubic foot than dry sand. This is directly con¬ 
trary to what one would naturally suppose. Indeed, it is almost incredible 
that the addition of water can reduce the weight of any material. The 
statement is readily proved, however, by shoveling a small quantity of 
natural sand as it comes from the bank with, say, 3% or 4% of moisture into 
a measure and drying it. The sand will settle, leaving the surface much 
below the level of the top of the measure. The explanation of this apparent 
anomaly lies in the fact that a film of water coats each particle of sand and 
separates it by surface tension from the grains surrounding it. This is 
illustrated in Figs. 62 and 63, page 175, the grains of the moist sand 
being separated from each other by the film of water. Fine sand, having 
a larger number of grains, and consequently more surface area, is more 
increased in bulk by the addition of water than coarse sand. The 
volume of coarse broken stone and gravel is but slightly, if at all, 
changed by moisture, while small broken stone composed largelv of 
particles of less than ^-inch diameter is affected like sand. 

If a small quantity of water is poured into a vessel containing dry sand, 
the bulk is not increased because of the inertia of the particles, but if the 
sand after moistening is dumped out and then turned back into the vessel 
with a shovel or trowel, its bulk will be increased. On the same principle, 
a sand bank does not swell in bulk during a shower, but the effect of the 
moisture is shown in the excavated material as soon as it is loosened with 
the shovel, and therefore its loose measurement for concrete or mortal 
is effected. 


VOIDS AND OTHER CHARACTERISTICS 


1 7 7 



46 


44 


42 


40 3 
> 

38 “ 

CO 

Q 

O 
> 


36 


The diagram in Fig. 66, plotted by Mr. Fuller* from experiments 
upon a single sample of natural sand mixed by weight with varying per¬ 
centages of water, illustrates the effects of moisture upon the actual percent¬ 
ages of voids in sands loose and tamped. The volumes produced by varying 
degrees of compacting are located between the two curves. It is noticeable 
that both the loose and tamped sand increase in volume with the addition 
of water and reach a maximum with about 6% of water, then decrease, and 
finally, when saturated, return to slightly less than their original dry 
bulk. The same sand, it is seen, may contain from 27% to 44% of absolute 
voids, according to the percentage of water and the degree of compacting. 

The percentage of water by 
weight which will give the 
greatest bulk, — corresponding, 
of course, to the largest per- 
‘ centage of absolute voids, — 
varies with different sands from 
5% to 8%. 

The actual variation on dif¬ 
ferent days in the percentage 
of moisture in a natural bank 
sand was found by the authors, 
in a series of experiments, to 
range from i\% t° 5J% of the 
total weight, or from 2^% to 
7i% °f the bulk of the moist 
sand. The sand, screened 
from a gravel bank in Eastern 
Massachusetts, ranged in 
coarseness from very fine to 
that which would pass a f-inch 
mesh screen. The moist sample was taken from the pile the day after a 
shower, and weighed 84^ lb. per cubic foot, while the dryer sample, taken 
after a period of dry weather, weighed 107 lb. per cubic foot. 

A sample of very fine sand which had been standing in a pile through 
the same shower contained g\% of moisture by weight, corresponding to 
13% by volume. Ordinary gravel, on the other hand, from which the 
sand had been screened, was found after a heavy rain to contain only 1.8% 
of moisture by weight, this being apparently the maximum quantity which 
it would hold. 

^Engineering Neivs, July 3 b I 9° 2 > P* 81 . 


< 

z 


30 < 

h- 

O 
< 


28 


26 


24 


PERCENTAGE, (BY WEIGHT) OF WATER TO SAND WHEN DRY 

Fig. 66. — Percentage of Absolute Voids in a 
Natural Bank Sand containing Varying Per¬ 
centages of Moisture. (See p. 177.) 






















































i 7 8 


A TREATISE ON CONCRETE 


The maker of concrete is especially interested in the influence of moisture 
upon the bulk of sand and upon its voids (i) because of its effect upon the 
actual measurement of sand used in construction work, and (2) because 
of its effect upon his experimental determinations of proportions. 

' Rather incomplete experiments of the authors tend to show that the 
actual effect of moisture upon the volume of sand used in concrete and 
mortar may often be less than would naturally be inferred from the various 
experiments cited, and depends largely upon the processes of handling the 
sand. For example, fairly dry sand (3% moisture) shoveled by laborers 
from the pile into the regular sand-measuring box weighed 454 lb., while 
after a rain, the sand (with 5% moisture) shoveled from the pile into the 
same box weighed 464 lb., that is, the moist sand was slightly heavier than 
the dry. Further handling reversed these relations, for on weighing these 
two sands in a half cubic foot measure, the moist sand, as we should ex¬ 
pect, was lighter than the dry. ' 

The explanation of this apparent discrepancy is undoubtedly due to the 
fact that as the rain which affected the moisture occurred after the sand 
had been excavated and piled near the mixing platform, its bulk, as 
suggested on page 176, was not affected. The laborers handling the 
moist sand took large shovelfuls and the arrangement of the grains was 
not greatly disturbed. If the sand had been excavated after the rain, 
the handling with shovels and dumping from the cart probably would 
have rearranged the grains so that the moist sand would have weighed 
less than the dry in the large measure as well as in the small box. 

Mr. Feret* calls attention to the fact that mortars of nominally the same 
proportions are richer in winter than in summer because of the greater 
amount of moisture in the sand, which, by increasing its bulk, reduces the 
absolute volume of the grains in a unit of measure. On the other hand, 
mortars are leaner in dry than in damp weather because the sand has 
greater density when dry. 

In the experimental study of sand for determining the proportions of 
cement to be used, the effect of moisture is exceedingly important. 
The voids in absolutely dry sand are certainly no criterion of its qualities 
for mortar, while a moist sand will give entirely different results on differ¬ 
ent days. The best that can be done, if the study can be pursued no 
further than void determination, is to select conditions as near as possible 
to the average, and after determining the voids, considered as air alone and 
also as space occupied by the air and moisture, to use the results as a basis 
for judgment, bearing in mind that the volume of paste made from 100 lb, 

*Annales des Fonts et Chaussees, 1892, IT, p. 26. 


VOIDS AND OTHER CHARACTERISTICS 


179 


of neat Portland cement, while varying largely with different brands, 
averages about 0.86 cubic feet, and that the volume of the additional water 
required for the sand (see pages 146 and 221) actually occupies space in 
the resulting mortar. 

The most important conclusion to be drawn from the extreme variation 
in the same sand under different conditions is the impossibility of attaining 
results by the usual void experiments upon sand alone, which will be of 
accurate value in the consideration of mortar and concrete, and the prac¬ 
tical necessity of employing methods such as are described by the authors 
in Chapter IX, page 138, or by Mr. Fuller in Chapter XI. 

In the preceding paragraphs we have referred chiefly to the variation 

in the condition of the same sand. 
The importance of studying mortars 
rather than the sand alone is still 
further emphasized by the varying 
effect of moisture upon sands of dif¬ 
ferent sizes. This is brought out very 
clearly in Mr. Feret’s paper.* In 
studying the normal consistency of 
mortars he finds that not only every 
cement but also every sand has a 
definite percentage of water necessary 
to bring it to what may be called 
normal consistency. This he illus¬ 
trates in the triangle shown in Fig. 67 
(constructed as described on page 
143), giving the “proportions of water (by weight) required for ground 
quartz sands of all granulometric composition.” It is evident from the 
diagram that coarse sands,f G, require 3% by weight of water, medium 
sands, M, 9%, and fine sands, F, 23%, while mixtures of the three sizes 
require intermediate percentages. 

Compacting of Broken Stone and Gravel. Since concrete is usually 
compacted by ramming or lubrication of semi-liquid mortar, the 
density or the percentage of voids in compacted material is an important 
function. The statement has been made frequently that the aggregate 
compacts more when rammed in concrete than when rammed dry or merely 
moistened with water, because the mortar acts as a lubricant. Experi¬ 
ments by the authors indicate that broken stone under the same ram- 

♦Annales des Ponts et Chaussees, 1892, II. 

+The sizes of screens defining coarse, medium, and fine sands are given on page 142. 


M 



Fig. 67. — Percentages of Water Re¬ 
quired to Gage Ground Quartz Sand 
of all Granulometric Compositions. 
{See p. 179.) 








A TREATISE ON CONCRETE 


[80 

ming will compress on the average i% more when it is moistened than 
when dry, and that an amount of mortar sufficient to lubricate without 
filling the voids produces no further reduction in volume. For example, 
a volume of broken stone mixed with 20% of mortar and rammed in 
6-inch layers produced a volume exactly equal to that of the rammed 
broken stone which had been merely moistened. 

Further experiments, partially outlined in the table on page 171, upon 
gravel and also upon varying sizes and mixtures of trap rock from two 
quarries, the one producing a soft and the other an exceedingly hard stone, 
lead to the conclusion that with stones of the same general structure, the 
percentage of reduction in volume by similar ramming in 6-inch layers is 
quite uniform, irrespective of the actual sizes of the particles, their 
relative sizes, the percentage of voids, and, within certain limits, the 
degree of hardness. On the other hand, the method of ramming the 
same stone will very largely affect the amount of compacting. Broken 
stone of the nature of trap, whether hard or soft, was found to compact 
when spread in 6-inch layers about 14% either under light ramming or 
shaking the measure, and about 21% under heavy ramming. In actual 
concrete work this large reduction of volume is of course seldom reached, 
because imperfect mixing and the necessary coating of the particles require 
a larger percentage of mortar than will just fill the voids of the rammed 
stone, and the bulk of concrete is usually greater than that of the original 
stone. 

Screened gravel spread in 6-inch layers and unconfined, compacted about 
12% under either light or heavy ramming. 

These percentages of compacting are based upon the loose meas¬ 
urement of the material as thrown by a laborer into a barrel or box 
measure. Rehandling a material like broken stone as it comes from the 
crusher tends to mix particles of unequal size and therefore to compact it 
very slightly. In one case a screened stone fresh from the crusher 
compacted 1% when rehandled once, and an additional 1% when re¬ 
handled the second time. 

It is interesting to note that the method of shoveling broken stone into 
a measure has but slight effect upon its shrinkage; for example, a lot of 
stone thrown with force into an inclined barrel occupied a space scarcely 
appreciably less than when very carefully and lightly placed. On the 
other hand, dropping from a considerable height does affect the volume, 
for Mr. Desmond Fitzgerald* states that broken stone dropped 12 feet into 
a car shrank to a volume 7% less than when it was measured in a box, 

♦Transactions American Society of Civil Engineers, Vol. XXXI, p. 303. 


VOIDS AND OTHER CHARACTERISTICS 181 

Sand, unlike stone, is largely affected by the manner of shoveling and the 
size of the receptacle. 

Compacting of Sand. The degree of compacting of sand is largely 
dependent upon the percentage of moisture which it contains. The dry 
sand shown in diagram in Fig. 66, page 177, when thoroughly tamped 
compacted from 34% to 27% voids or 9.6% in volume,* the sand with 6% 
moisture from 44% to 31% voids or 18.8% in volume, and the saturated 
sand from 33% to 26^% voids or 8.8% in volume. 

Attention is called by Mr. Feret to the fact that the measurement of the 
weight of a given sand depends not only upon the quantity of moisture in 
it, but also upon the depth of the box which is used for the measure, the 
quantity of sand introduced at a time, — that is, the size of a shovelful, — 
the height from which it falls, the amount of shaking, if any, given to the 
box during filling, the amount of compacting given to the mass when leveling 
it off, and the smoothness of the surface left. As an illustration of the 
difference due to the method of placing in the measure, the authors found 
that a certain coarse sand shoveled into a pail about as a laborer would fill 
a measure weighed 88.9 lb. per cubic foot, while the same sand carefully 
poured into the pail weighed 83.3 lb. per cubic foot. 

DEFINING COARSENESS OF SAND BY ITS UNIFORMITY 

COEFFICIENT 

The size of a sand may be indicated by what is termed its uniformity 
coefficient. This gives an idea of the actual variation in the size of the 
particles, and thus affords a means for comparing sands in different locali¬ 
ties. A sand which is termed coarse in one section of the country is often 
considered fine in another. 

To find the uniformity coefficient of a sand, screen it into at least 
five sizes, determine the percentage by weight of each size, and plot 
the mechanical analysis curve as described on page 196, and illustrated 
in Fig. 72, page 200. Then divide the diameter of the particles repre¬ 
sented by the point at which the curve of the sand crosses the 60% 
horizontal line by the diameter of the particles where the curve crosses 
the 10% line. The quotient is the uniformity coefficient. 

As an illustration of the value of the uniformity coefficient (u. c.) for 
different sands, reference may be made to the three mechanical analysis 
curves in Fig. 72, page 200. The curve of the coarse sand crosses the 

0.34— 0.27 , 

*Ratio of compacting = —- = 0.090 

1.00—0.27 



182 


A TREATISE ON CONCRETE 


horizontal 60% line at the ordinate corresponding to a diameter of 
0.117 inch, and the 10% horizontal line at ordinate 0.023 inch. Its 
uniformity coefficient and similarly the uniformity coefficients of the 
other sands are as follows: 




Uniformity 

Coefficient 

Coarse sand 

0.117 

0.023 

5-1 

Medium sand 

0.038 

0.009 

4.2 

Fine sand 

0.018 

2.2 

0.008 


In general, it may be said that a sand with a uniformity coefficient 
above 4.5 is a good coarse sand for concrete work, and in comparing 
different natural sands the one having the highest uniformity coefficient 
may be considered the best. 

As in ordinary bank sands the size of the particles at the 10% line 
(which is termed the effective size,* e. s..) does not greatly vary, the 
diameter at the 60% line alone is a very good indication of the coarse¬ 
ness of the sand. A knowledge of the effective size and the uniformity 
coefficient of any sand enables one accustomed to mechanical analysis 
diagrams to form a picture of its character. 

Mr. Allen Hazen^ who first used these terms in the examination of 
filter sand, states with reference to the percentage of voids or “open 
space” in compacted sand corresponding to different coefficients: 

A rough estimate of the open space can be made from the uniformity 
coefficient. Sharp-grained materials having uniformity coefficients below 
2 have nearly 45 per cent, open space as ordinarily packed; and sands 
having coefficients below 3, as they occur in the banks or artificially 
settled in water, will usually have 40 per cent, open space. With more 
mixed materials the closeness of packing increases, until, with a uni¬ 
formity coefficient of 6 to 8, only 30 per cent, open space is obtained, 
and with extremely high coefficients almost no open space is left. 

For loose sand at least 10 should be added to these percentage 
values. 

* The effective size itself is of considerable value for comparison of sand for filters, but not 
for concrete. 

•j-Twenty-fourth Annual Report of State Board of Health of Massachusetts for 1892. 





PROPORTIONING CONCRETE 



CHAPTER XI 

PROPORTIONING CONCRETE 

By William B. Fuller* 

IMPORTANCE OF PROPER PROPORTIONING 

The proper proportioning of concrete materials increases the strength 
obtainable from any given amount of cement, and also the water-tightness. 
Conversely, it permits, for a given requirement of strength and water-tight¬ 
ness, a reduction in the amount of cement, thereby reducing the cost. 

Upon large or important structures it pays from an economic standpoint 
to make very thorough studies of the materials of the aggregates and their 
relative proportions. This fact has been seriously overlooked in the past, 
and thousands of dollars have sometimes been wasted on single jobs by 
neglecting laboratory studies or by errors in theory. Since cement is 
always the most expensive ingredient, the reduction of its quantity, which 
may very frequently be made by adjusting the proportions of the aggregate 
so as to use less cement and yet produce a concrete with the same density, 
strength and impermeability, is of the utmost importance. 

As an example of such saving, the ordinary mixture for water-tight con¬ 
crete is about 1:2: 4,which requires 1.57 barrels of cement per cubic yard 
of concrete. By carefully grading the materials by methods of mechanical 
analysis the writer has obtained water-tight work with a mixture of about 
1 : 3 : 7, thus using only 1.01 barrels of cement per cubic yard of concrete. 
This saving of 0.56 barrels is equivalent, with Portland cement at $1.60 
per barrel, to $0.89 per cubic yard of concrete. The added cost of labor 
for proportioning and mixing the concrete because of the use of five grades 
of aggregate instead of two was about $0.15 per cubic yard, thus effecting a 
net saving of $0.74 per cubic yard. On a piece of work involving, say, 
20 000 cubic yards of concrete such a saving would amount to $14 800.00, an 
amount well worth considerable study and effort on the part of those in 
responsible charge. 

Proper proportioning is also important for reinforced concrete so as to 
give the uniformity and homogeneity which cannot be obtained without 
careful attention to the proportions and grading of the aggregates. 

* The authors are indebted to Mr. Fuller for the material for this chapter. 


184 


A TREATISE ON CONCRETE 


METHODS OF PROPORTIONING 

It is recognized generally that for maximum strength a concrete should 
be as dense as possible, that is, that it should have the smallest practicable 
percentage of voids. The various methods of aiming toward this result 
have been outlined as follows:* 

(1) Arbitrary selection; one arbitrary rule being to use half as much 
sand as stone, as 1 : 2 : 4 or 1 : 3 : 6; another, to use a volume of stone 
equivalent to the cement plus twice the volume of the sand, such as 1 12:5 
or 1 : 3 : 7. 

(2) Determination of voids in the stone and in the sand, and propor¬ 
tioning of materials so that the volume of sand is equivalent to the volume 
of voids in the stone and the volume of cement slightly in excess of the voids 
in the sand. 

(3) Determination of the voids in the stone, and, after selecting the pro¬ 
portions of cement to sand by test or judgment, proportioning the mortar 
to the stone so that the volume of mortar will be slightly in excess of the 
voids in the stone. 

1 

(4) Mixing the sand and stone and providing such a proportion of cement 
that the paste will slightly more than fill the voids in the mixed aggregate. 

(5) Making trial mixtures of dry materials in different proportions to 
determine the mixture giving the smallest percentage of voids, and then 
adding an arbitrary percentage of cement, or else one based on the voids 
in the mixed aggregate. 

(6) Mixing the aggregate and cement according to a given mechanical 
analysis curve. 

(7) Making volumetric tests or trial mixtures of concrete with a given 
percentage of cement and different aggregates, and selecting the mixture 
producing the smallest volume of concrete; then varying the proportions 
thus found, by inspection of the concrete in the field. 

The most practical method known to the writer for accurately determin¬ 
ing the proportions of each material is by mechanical analysis of the aggre¬ 
gates, as described on page 211. 

Volumetric synthesis, or proportioning by trial mixtures (p. 210) is 
another method which is sometimes useful, and produces fairly scientific 
results. 

Since in many cases the proportions for a concrete must be selected more 
or less arbitrarily, after outlining the principles of proper proportioning, 
some of the less exact methods which are frequently used in practice will be 

* From “Proportioning Concrete,'’ by Sanford E. Thompson, Journal Association Engineering 
Societies. Vol. XXXVI, Apr. 1906, p. 18c 


PROPORTIONING CONCRETE 


185 

taken up before referring to the more scientific ones, and some of the causes 
for inaccuracies of these approximate methods discussed. 

PRINCIPLES OF PROPER PROPORTIONING 

The principles underlying the correct proportions of the materials of 
concrete are the same as those for mortar, namely, that the mass when 
compacted shall have the greatest possible density. In order, therefore, to 
obtain a knowledge of correct proportioning it will be best to first study the 
general conditions which are known to affect density. 

Perfect spheres of equal size piled in the most compact manner theoreti¬ 
cally possible leave but 26% voids. If the spaces between such a pile of 
equal-sized perfect spheres were filled with other perfect spheres of diameter 
just sufficient to touch the larger spheres, it would take spheres having 
relative diameters of 0.414 and 0.222 of the larger spheres, and the voids 
in the total included mass would be reduced to 20%. Using in this same 
manner smaller and smaller perfect spheres, it is conceivable that the 
voids could be reduced to so low a per cent of the total mass and to a size 
so small as to be only in a capillary form, and thus prevent the passage of 
water. This is assuming that every particle is placed exactly in its assigned 
place, but it is inconceivable that such an arrangement should take place 
under practical conditions, and in fact numerous trials by tbe writer with 
large masses of equal-sized marbles have demonstrated that they cannot be 
poured or tamped into a vessel so as to give less than 44% voids. 

If equal quantities of spheres of, say, three sizes are mixed together, the 
per cent of voids in the total mass immediately increases, becoming about 
65%, due probably to the smallest spheres getting between and forcing 
apart the largest. If, however, the containing vessel is continually shaken 
and the spheres stirred around, the smallest spheres will gradually all 
gravitate to the bottom and the largest to the top and the amount of voids 
in the total mass will again approach 44%. If a large number of different 
sized spheres are used, employing an increasingly large number of the 
smaller sizes so that each larger size may be said to be wholly surrounded 
by the next smaller size, the voids remain the same, no matter what the 
shaking, and will in some cases reach as low as 27%. 

With ordinary stones and sands the same law holds as with perfect 
spheres except that they do not compact as closely, and the percentage 
of voids under comparable conditions is larger, varying with the degree of 
roughness and other features of the stones and sands used for the ex¬ 
periments. 

When dry cement is added to a dry aggregate of stone and sand it acts 


A TREATISE ON CONCRETE 


186 

in the same manner as fine sand, and for obtaining the greatest density 
with dry cement, the cement must replace an equivalent amount of fine sand. 

The theory of a concrete mixture is well stated by Mr. Feret* as follows: 

The problem of making the best concrete is thus reduced to the selec¬ 
tion of a mixture of materials whose granulometric compositionf corre¬ 
sponds to the maximum of density, since when this composition is known 
absolute volumes of cement may be substituted for equal absolute volumes 
of fine sand and vice versa, so as to vary the strength as desired while the 
density remains the same. 

In other words, having mixed dry, inert materials in proportions neces¬ 
sary for greatest density, a portion of the grains of the very finest aggregate 
(that is, the finest particles of sand or dust) may be replaced by a corre¬ 
sponding quantity of cement to the extent required for the desired strength. 
This is not strictly true for concrete mixtures, because, when water is added 
to dry cement, the cement particles are separated from each other by the 
surface tension of the film of water, and it is no longer possible to obtain 
as dense a mixture as is theoretically possible with the dry mixture. 

The density of concrete therefore has been found to depend upon the 
varying degree of roughness of the stone and sand, the relative sizes of the 
diameters of the stone, sand and cement, and the amount of water used. 

The fineness of the cement particles and the amount of water to be used 
are determined by questions discussed elsewhere, and we have to deal here 
only with the proportioning of the sand and stone. 

DETERMINATION OF THE PROPORTION OF CEMENT 

The most difficult question to decide with accuracy in proportioning is 
the proportion of cement to use. This is to a considerable extent a matter 
of mature judgment, depending upon the nature of the construction, the 
degree of strength required within a certain limit of time, the required 
watertightness, the character of the aggregates, and many other matters 
which must be considered in direct connection with the work to be done 
and the available materials. An engineer experienced in concrete con¬ 
struction and tests can estimate approximately the strength of concrete 
made with certain materials, and select the proportions accordingly. The 
surest plan after selecting and grading the aggregates is to make up speci¬ 
mens of concrete and test its crushing strength, but this is usually impracti¬ 
cable for lack of time. The next best plan is to have the tensile strength 
determined of mortar made from the sand to be used and by comparing 


*Chimie Appliquee 1897, p. 523. 
■{•Proportioning of sizes. 


PROPORTIONING CONCRETE 


187 


this with the strength of the mortar of standard sand an idea can be formed 
of the proportion of cement to select. If a sand is fine, a richer mortar 
must be used, frequently instead of a 1 : 2 selecting a 1 : i| or even 1:1, 
and the amount of coarse aggregate also reduced to accord with this. 

An experimental plan which has been followed to determine the minimum 
quantity of cement which will produce a concrete practically free from air 
voids is to mix the aggregates in the correct proportions as described in the 
pages which follow, compact them by ramming or hard shaking, and then 
determine their voids by weighing and correcting for specific gravity.* The 
sand should be in the natural state of moisture found in the interior of the 
bank, not because this is the condition in which it will be mixed in the con¬ 
crete, but because it may be assumed in the natural state to contain a 
quantity of moisture varying with its fineness. If gravel is used it may be 
taken in the same way, while coarse broken stone should be dry, and dry 
broken stone screenings may be mixed with about 4% of water by weight. 
Correction must be made for this moisture after weighing the mixed material, 
so that the voids calculated will be simply air voids. 

In determining the quantity of cement to fill these air voids it may be 
assumed without appreciable error that 100 lb. of cement will make 1.0 
cu. ft. of neat paste. This is a larger volume than would result with ordi¬ 
nary plastic paste, but makes a slight allowance for the additional moisture 
required for the sand and stone. To the quantity of cement thus deter¬ 
mined 10% may be added, i. e., 10% of the cement, not of the total mix¬ 
ture, to provide for imperfect mixing. 

PROPORTIONING BY ARBITRARY SELECTION OF VOLUMES 

The common custom of specifying arbitrarily the proportions of cement, 
sand and stone in parts by volume, while convenient in construction, causes 
wide discrepancies in results because of different methods of measuring the 
materials. A concrete called a 1 : 2 : 4 mixture by one man may not con¬ 
tain any more cement than a concrete termed a 1 : 3 : 6 mixture by another, f 

Notwithstanding this, if the units of measurement and the methods of 
measuring are stated definitely, arbitrary selection of proportions may give 
good results in practice, although necessitating a larger quantity of cement 
with consequently a greater net cost than more scientific proportioning 
would require. 

The percentage of volume of sand required for ordinary gravel or broken 

♦See page 165. 

-j-These variations aie discussed more fully by the authors on page 218. 


A TREATISE ON CONCRETE 


188 

stone from which the finest material has been screened may be taken between 
the limits of 40% and 60% with an average, which is suitable under many 
conditions, of 50%. If the cement is taken as additional, which is not 
strictly correct, this ratio corresponds to proportions 1 : 1^ : 3, 1:2:4, 
1 : 2\ : 5, and 1:3:6, which are suggested by the authors in Chapter II 
as standard mixtures for the use of those who are inexperienced in concrete 
work. 

In cases where the coarse material contains a good many small particles, 
as does crusher run, broken stone or graded gravel, or the sand is so fine 
as to flow readily into the voids of the stone, the proportion of sand should 
be slightly less than half the volume of stone. Since the cement also increases 
the bulk of mortar and hence assists to fill the voids in the stone, it is sug¬ 
gested that with such aggregates the volume of the stone be made equal to 
the cement plus twice the volume of the sand. This would give propor¬ 
tions 1 : 1^ : 4, 1:2:5, 1 : 2\ : 6, and 1 : 3 : 7 for these special conditions. 

Proportions adopted by various authorities and tabulated on page 212 
may serve as a guide to arbitrary selection. 

It is a good plan on work which will not warrant special tests and for 
which there is no choice of aggregates, to use at first twice as much stone or 
gravel as sand and then vary the relative proportions of the sand to the 
stone as the work progresses, governing this by the way the concrete works 
into place. Too much sand will be indicated by the harsh working of the 
concrete, while if there is too little sand, stone pockets are apt to occur on 
the surface of the concrete, and it will be difficult to fill the voids of the 
stone. 

Screened vs. Unscreened Gravel or Broken Stone. Unscreened gravel 
is often used alone for the aggregate, but there is scarcely any case where 
the cost of screening and re-mixing the materials will not be less than the 
saving in the cement by using screened aggregates. The quantity of sand 
in different parts of the same gravel bank always varies greatly and the run 
of the bank rarely contains sufficient coarse stone to make a dense concrete. 
If, as is sometimes the case, the quantity of material coarser than J inch is 
about the same as that which passes a ^-inch sieve, then, if used without 
screening the same quantity of total aggregate must be ysed as would 
otherwise be specified for the coarse aggregate; that is, instead of 1:2:4 
proportions, the unscreened gravel would require 1 : 4. 

Broken stone as it runs from the crusher will contain considerable dust, 
and may sometimes be used economically by simply adding sand without 
screening. However, there is apt to be a separation of the coarse particles 
from the fine as they roll down the pile so that less homogeneous propor- 


PROPORTIONING CONCRETE 


189 


tions can be attained. Consequently the writer is in favor of separating 
the aggregate into as many parts as is consistent with economy for the work 
in hand. Even on small work he believes it preferable to screen out the 
sand or dust and re-mix it in the specified proportions. 

PROPORTIONING BY VOID DETERMINATION 

The determination of proportions by finding the volume of water which 
may be poured into the voids of a unit volume of stone and selecting a 
volume of sand equal to this volume of water is one which gives no better 
results in practice than arbitrary selection of the proportions, as described 
in the preceding paragraphs, and varying the relative proportions of sand 
to stone when placing. The determination of the proportion of cement to 
sand by void measurement is still more misleading; in fact, for reasons dis¬ 
cussed below, it is so inaccurate that no consideration will here be given 
to it. 

The theory of proportioning by voids is that if the stone or gravel contains, 
say, 40 per cent voids as measured by the contained volume of water, the 
required volume of sand is theoretically 40% of the volume of the stone, 
and supposing the ratio of cement to sand to be as 1 : 2, the relation of parts 
of sand to parts of the coarse aggregate would be as 2 : 5, thus making the 
proportions 1:2:5. Because of the inaccuracy of this method of proced¬ 
ure, as discussed below, it is necessary in most cases, even although the 
cement and water will still further increase the bulk, to take a volume 
of sand, say 5% to 10% in excess of the voids; that is, for gravel with 
40% voids to use 45% to 50% of its volume of sand, thus making the 
proportions 1 : 2 : 4J. If the coarse material is screened broken stone of 
large size, say ij or 2-inch, the volume of sand may be taken equal to the 
volume of voids instead of in excess of them, because the particles of sand 
will all be small enough to fit into the voids of the stone without appre¬ 
ciably increasing its bulk. Such stone usually has about 45% to 50% 
voids, so that we should have proportions 1 : 2 : 4J or 1 : 2 : 4, the same 
as for the gravel concrete. 

The irregular distribution of the materials by imperfect mixing may 
usually be disregarded, because the volume of gaged mortar is always in 
excess of the volume of sand from which it is made. 

Care must be exercised in any case to guard against a larger excess of 
sand than is absolutely necessary, because the voids in a concrete are 
lessened by using stone in place of sand. Take, for instance, sand having 
45% voids and stone having 40% voids. With the sand just filling the 
voids of the stone it is easily calculated that the resultant mass has 18% 


190 


A TREATISE ON CONCRETE 


voids; but supposing an excess of 10% of sand, there would be 10% of the 
material having 45% voids, which means there would be 2.5% more voids 
in the resultant mass.* 

Authorities differ as to whether the stone should be loose or shaken 
when determining the voids. Loose measurement is generally considered 
preferable because it corresponds more nearly to the final volume of the 
concrete, and more sand is always necessary than will just fill the voids of 
rammed stone, since the sand and cement separate the stones and prevent 
their lying close together in concrete. In determining, however, the quan¬ 
tity of cement required for the mixture of aggregates the materials should be 
compacted as described on page 211. 

The chief inaccuracy of this method of basing the proportions of the 
finer materials of a concrete mixture upon the water contents of the voids 
in the larger is due to the difference in compactness of the materials under 
varied methods of handling, and to the fact that the actual volume of 
voids in a coarse material may not and usually does not correspond to 
the quantity of sand required to fill the voids, and that therefore the com¬ 
mon method of proportioning by basing the volume of sand or of mortar 
upon the volume of water which can be poured into the broken stone leads 
to false conclusions. The reasons for this inaccuracy are chiefly because 
the grains of sand thrust apart the particles of stone, and because with 
most aggregates a portion of the particles of sand or fine screenings are 
too coarse to enter the voids of the coarsest material. 

Even in a mass of stones of uniform size many of the separate voids are 
much smaller than the particles. If we have, then, a mass of gravel rang¬ 
ing from fine to coarse or a mass of crusher-run broken stone, even with 
the finest sand or the dust screened out of them, the individual voids are 
many of them so small that a large number of the particles of natural 
bank sand will not fit into them, but will get between the stones and in¬ 
crease the bulk of the mass. On account of this increase in bulk, even 
with thorough mixing more sand is required than the actual volume of the 
voids in the coarse material. The separation of the particles of stone by 
the sand is illustrated in the mixture shown in Fig. 2, page 15. 

To illustrate this important principle, an extreme example may be cited. 
Suppose that we have a mixture in equal parts of i-inch stone and |-inch 
stone. By the usual method of reasoning employed in proportioning 
concrete, if the i-inch stone has 50% voids, we should require a volume 
of J-inch, equal to 50% of the volume of the i-inch stone, in order to fill 

* See discussion by the writer in Transactions American Society of Civil Engineers, Vol. XLII, 
o. 142. 


PROPORTIONING CONCRETE 


191 

the voids in the latter. The absurdity of this is apparent, because the two 
stones are so near a size that the smaller cannot fit into the voids of the 
latter, and the bulk of the mixture is inappreciably less than the sum of 
the separate volumes, that is, the mixture still has nearly 50% voids. The 
principle is just as true, although the total effect is less, if we consider it 
with reference to the finer particles of the gravel or the crusher-run broken 
stone and the sand or fine screenings which are to be introduced to fill 
the voids. The sizes of many of the particles of the latter are so 
nearly equal to the sizes of the smallest particles of the coarse material 
that they increase the total bulk instead of reducing the voids. They also 
get between the surfaces of the stone particles and prevent the stones touch¬ 
ing each other. 

We might conclude from the above that the best concrete can be made 
with a coarse stone of uniform size and a sand whose particles are all 
small enough to fit into its voids; in fact, this is the conclusion reached by 
the advocates of broken stone of uniform size in preference to crusher-run 
stone. 

Our experiments indicate that while this may be true in theory, in prac¬ 
tice in making concrete the graded materials give about the same density 
and work rather smoother in handling and placing. 

The point, however, which is to be emphasized is the inaccuracy of 
determining the exact volume of sand or mortar by simply measuring the 
water contents of the voids in the coarse aggregate. 

The selection of the proportion of cement by determination of the water 
contents of the voids in sand is even more inaccurate than the propor¬ 
tioning of sand to stone by void measurement. The varying effect of 
moisture on the sand so influences the volume of the voids that their deter¬ 
mination is chiefly important as an aid to the judgment; and as a matter 
of fact, although in practice the quantity of cement is supposed to depend 
upon the volume of voids in the sand, it is customary to select a definite 
relation of cement to sand varying according to the character of the con¬ 
struction from 1 : 1 to 1 : 3, recognizing, however, that fine sand—and fine 
sands in an ordinary state of moisture will almost always have the distin¬ 
guishing characteristic of a lighter weight per cubic foot than coarse sands 
and a consequently larger percentage of voids—requires more cement 
for equivalent strength. 

As already stated, if the work is too small to warrant a thorough study 
of the materials by mechanical analysis or volumetric synthesis, or some 
other scientific method, it is evident from the above discussion that it is 
nearly as accurate to determine the proportions by arbitrary selection (sec 
p. 186) as by a study of voids. 


192 


A TREATISE ON CONCRETE 


RAFTER’S METHOD OF PROPORTIONING 

Mr. George W. Rafter* has called attention to the method of propor¬ 
tioning the mortar as a percentage of the volume of the stone slightly 
shaken, the relation of cement to sand having been determined by the 
required strength of concrete. 

Quoting from specifications for the Genesee Dam, the concrete is pro¬ 
portioned as follows: 

In forming concrete such a proportion of mortar of the specified com¬ 
position will be used as may be found necessary by trial to a little more 
than fill the voids in the aggregate. Tests of the voids will be made from 
time to time under the direction of the engineer, and instructions given 
as to the per cent of mortar of the specified composition to be used. For 
the information of the contractor, in the way of computing the cost of 
concrete of the quality herein required, it may be stated that ordinarily 
the per cent of mortar will be about 33 per cent of the measured volume 
of the aggregate. In case of the use of a certain proportion of gravel in 
the aggregate, the proportion of mortar may be reduced to somewhat less 
than 30 per cent. 

* 

This method of proportioning is more accurate than the usual procedure, 
because there is less apt to be an excess of mortar. It does not, however, 
take account of the fact that with a coarse aggregate of varying sized 
particles some of the grains of sand are too large to fit into the voids of the 
stone, and that therefore the coarse and fine aggregates must be studied 
together. 

An examination of the analysis of the sand used by Mr. Rafter indicates 
that to its fineness was due the small proportion of mortar to stone which 
he was able to use. Ninety-two per cent of the sand passed a No. 30 
sieve, so that the grains were small enough to enter the voids of the stone 
without appreciably increasing the bulk of the concrete. 


FRENCH METHOD OF PROPORTIONING 

In France, proportions are ordinarily stated in terms of the volume of 
mortar to the volume of stone, and the mortar is described by the number 
of kilograms of Portland cement to 1 cubic meter or liter of sand. 

The following table gives the nominal proportions in English measure 
based on a volume of 3.8 cubic feet corresponding to similar French pro¬ 
portions based on kilograms of cement to a cubic meter of sand. 

*“On the Theory of Concrete'’ Transactions American Society Civil Engineers, Vol. XLII 

p. 104. 


PROPORTIONING CONCRETE 


*93 


American Equivalents of French Proportions. {See p. 999.) 


French meas¬ 
ure, kilograms 
cement per 
cubic meter 
of sand. 

American’meas- 
ure, cement to 
sand by 
volume.* 

Pounds of 
cement per 
cubic foot 
of sand. 

French meas¬ 
ure, kilograms 
cement per 
cubic foot 
of sand. 

American meas¬ 
ure, cement to 
sand by 
volume.* 

Pounds of 
cement per 
cubic foot 
of sand. 

200 

• 

1 : 8.0 

12.5 

700 

1 

; 2-3 

43-7 

3 ° 0 

1 : 5 • 3 

18.7 

800 

1 

2 . O 

5 ° • 0 

400 

1 14.0 

25.0 

IOOO 

1 

i. 6 

62.5 

5 °° 

1:3.2 

3 1 -3 

1200 

1 

i -3 

75 

600 

1 : 2 . 7 

37-5 

1600 

1 

I . O 

100.0 


*Proportions based on standard weight of cement, i. e., 100 pounds per cubic foot 


Concrete in France is frequently designated with respect to the ratio 
of mortar to stone; for example, one volume of mortar to two volumes of 
stone, the mortar then being designated as indicated in the above table. 
To express the parts more definitely, the basis is sometimes a cubic 
meter of sand; for example, 650 kilograms cement to one cubic meter 
sand to 1.8 cubic meter stone, this corresponding substantially to pro¬ 
portions 1 : 2-j- : 4^ by volume, as ordinarily used in America. 

MECHANICAL ANALYSIS 

Mechanical analysis consists in separating the particles or grains of a 
sample of any material, — such as broken stone, gravel, sand or cement, — 
into the various sizes of which it is composed, so that the material may be 
represented by a curve (see Fig. 70, p. 198) each of whose ordinates is the 
percentage of the weight of the total sample which passes a sieve having 
holes of a diameter represented by the distance of this ordinate from the 
origin in the diagram. 

The objects of mechanical analysis curves as applied to concrete aggre¬ 
gates are (1) to show graphically the sizes and relative sizes of the particles; 
(2) to indicate what sized particles are needed to make the aggregate more 
nearly perfect and so enable the engineer to improve it bv the addition or 
substitution of another material; and (3) to afford means for determining 
best proportions of different aggregates. 

To determine the relative sizes of the particles or grains of which a given 

*Chimie Appliquee, 1897, p. 523. 

•{■Proportioning of sizes. 






















194 


A TREATISE ON CONCRETE 


sample of stone or sand is composed, the different sizes are separated from 
each other by screening the material through successive sieves of increasing 
fineness. After sieving, the residue on each sieve is carefully weighed, and 
beginning with that which has passed the finest sieve, the weights are suc¬ 
cessively added, so that each sum will represent the total weight of the 
particles which have passed through a certain sieve. ’The sums thus 
obtained are expressed as percentages of the total weight of the sample and 
plotted upon a diagram with diameters of the particles as abscissas and 
percentages as ordinates. 

The method of plotting and the uses of the curves thus obtained are 
more fully described in the pages which follow. 

Sieves and Other Apparatus. Fig. 68 illustrates a convenient 
outfit for such a mechanical analysis as above described, consisting 
of a set of sieves, an apparatus for shaking the sieves, and scales for 
weighing. A standard size of sieve is 8 inches in diameter and 2\ 
inches high. Sieves with openings exceeding o.io inches are preferably 
made of spun hard brass with circular openings drilled to the exact 
dimensions required. Sieves with openings of o.io inch and less are 
preferably of woven brass wire set into a hard brass frame. Woven brass 
sieves are made for many purposes, and are sold by numbers which ap¬ 
proximately coincide with the number of meshes to the linear inch. As 
the actual diameter of the hole varies with the gage of wire used bv 
different manufacturers, every set of sieves must be separately calibrated 

An approximate idea of the diameters of holes which may be expected 
in commercial sizes of sieves is presented in the following table, which is 
sufficiently exact to serve as a guide to the purchase of the sieves: 


Commercial No. 

Diameter of 

Commercial No. 

Diameter of 

of sieve. 

hole in inches. 

of sieve 

hole in inches. 

IO 

°°73 

60 

0.009 

15 

0.047 

74 

0.0078 

16 

0.042 

100 

0.0045 

18 

0.037 

140 

0.003625 

20 

0.034 

15 ° 

0.00325 

3 ° 

0.022 

170 

0.0031 

35 

0.017 

180 

0.00306 

40 

0.015 

190 

0.0028 

5 ° 

0.011 

200 

0.00275 


For separating particles smaller than those passing through a No. 200 
sieve, recourse must be had to processes of elutrition which have been de¬ 
veloped to great precision by soil analysis chemists.* 

*See page 85. 




PROPORTIONING CONCRETE 


195 



Fig. 68. — Mechanical Analysis Sieves and Shaker. (See p. 194 ) 
























A TREATISE ON CONCRETE 


196 

In selecting the right series of sieves to purchase, first decide on the 
limiting diameters, say, from 3.00 inches to No. 200 = 0.00275 inches. 
Then decide on the total number of sieves, say, twenty. Look up the 
logarithm of 3.00 and of 0.00275 and by proportion find eighteen other 
logarithms between these having equal differences between each. Look 
for the number corresponding and take the nearest commercial sieve giving 
this diameter. The diameters of holes exceeding 0.10 inch can be made 
as required. A convenient set of twenty sieves, — ten for stone, which give 
the diameter of the holes in inches, and ten for sand, giving the commercial 
number (see p. 194), — is as follows:* 


Stone Sieves 

Sand Sieves 

inches. 

Commercial No. 

3 -°° 

IO 

2.25 

15 

I - 5 ° 

20 

1.00 

30 

0.67 

40 

0-45 

60 

0.30 

74 

0.20 

100 

0.15 

150 

0.10 

200 


After the sieves are obtained it is necessary that they should be very 
carefully calibrated to ascertain the average diameter of the mesh. This 
should be done by averaging the diameters of the openings measured in two 
positions at right angles to each other, as the meshes of commercial 
sieving are not exactly square. Sieves having meshes exceeding 0.10 
inch are most conveniently calibrated by ordinary outside calipers; those 
having meshes of less diameter, by a micrometer microscope. 

When many analyses are to be made, it is convenient to have a printed 
cross section form, such as is shown in Fig. 69, p. 197, with appropriate 
spaces for filling in the number of the analysis, description of the ma¬ 
terial, location of the work, and other facts relating to the material. 

Plotting Analysis Curves. For those who are unfamiliar with me¬ 
chanical analysis a detailed explanation of the method of locating the 
curve is here given. The method can best be understood by referring 
to the diagrams of typical materials which are also of practical inter¬ 
est as illustrating the curves which may be expected in special cases. 

Fig. 70, p. 198, represents a typical mechanical analysis of crusher-run mi¬ 
caceous quartz stone which has been run through a J-inch revolving screen so 
as to separate particles finer than J inch, that is the dust, for use with sand. 

For a sample of stone, which may be taken by the method of quartering 

* A still smaller set for ordinary use is suggested on page 159a. 


SIZE OF SEPARATION OF SAND SIEVES IN INCHES 


197 



SIZE OF SEPARATION OF STONE SIEVES IN MILLIMETERS 

Fig. 6 g. — Blank Form for Mechanical Analysis Diagram. (See p. ig 6 .) 












































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































198 


A TREATISE ON CONCRETE 


described on page 280, 1 000 grams is a convenient quantity for 8-inch 
diameter sieves 21 inches in depth, and also permits of easy reduction from 
weights to percentages. To obtain the analysis shown in Fig. 70, the 
sample of stone is placed in the upper (coarsest) sieve of the nest of stone 
sieves given on page 190, and after 1 000 shakes the nest is taken apart, and 
the quantity caught on each sieve is weighed. The results obtained in the 



Fig 70. — Typical Mechanical Analysis of Crusher-Run Micaceous 

Quartz Stone. (See p. 198.) 


particular case under consideration are illustrated in the following table, 
which shows the method of finding the percentages: 


Results of Screening Samples of Stone of Fig. 70. 


Size sieve 


Retained in 
each sieve* 

Amount finer than 
each sieve 

Percentage 
than each : 

inches. 


grams. 

grams. 

% 

O.IO 


8 

0 


0.15 


II 

8 

I 

0.20 


8 

19 

2 

0.30 


72 

27 

3 

0-45 


1 2 3 

99 

10 

0.67 


2 35 

222 

22 

1.00 


344 

457 

46 

1.50 


199 

801 

80 


Total, 1000 

*In practise this column is not required, the weights in the next column being obtained directly 
by placing each successive residue on the scale pan with that already weighed. 


The various percentages are plotted on the diagram and the curve drawn 
through the points. The vertical distance from the bottom of the diagram 




















































































































PROPORTIONING CONCRETE 


*99 


to the curve, that is, the ordinate at any point, represents the percentage 
of the material which passed through a single sieve having holes of the 
diameter represented by this particular ordinate. Since the percentage of 
material passing any sieve is always the complement of the percentage of 
grains coarser than that sieve, the vertical distances from the top of the 
diagram down to the curve represents the percentages which would be 
retained upon each sieve if employed alone. For example, taking 1.25, 
62%, the distance from the bottom of the diagram, represents the percentage 
of material finer than i|- inch diameter, and 38%, the distance down from 
the top of diagram, represents the percentage coarser than 1^ inch. 

Fig. 71 represents a typical analysis of crushed trap rock which has been 



DIAMETERS OF STONE IN INCHES 


Fig. 71. — Typical Mechanical Analysis of Crushed Trap Rock Separated into Three 
Sizes by Revolving Screens having 3, i|, f and J inch perforations. (See p. 199.) 

separated into stone of three sizes and dust, by a revolving screen 2 feet 
6 inches in diameter and 12 feet long set on a slope of 1 foot 9 inches. This 
was made up of four sections having respectively 3, 1^, | and J inch per¬ 
forations. The curves not only show the sizes of trap rock which ordinarily 
pass through crusher screens of given diameter of hole, but also illustrate 
how inefficient the screening process may be. For example, if the sizes of 
the particles had corresponded exactly to the diameters of the holes and 
the screening had been more perfectly done, we should have had curves 
whose general direction and location is shown by the dotted lines No. 
2 V No. 3 j, and No. 4 V that is, for example, No. 3, since it represents 
stone which passes a ij inch screen and which is retained on a f inch screen, 
should occupy a position between the ordinates representing 1.50 and 
























































































































200 


A TREATISE ON CONCRETE 


0.75 diameters. If the stone had rumbled longer in the screen because 
of flatter slope or screen sections of greater length, the curves would have 
approached more nearly to these dotted lines. 

Typical curves of a fine, a medium well graded, and a coarse sand are 
shown in Fig. 72. For convenience in plotting, the horizontal scale is ten 



DIAMETERS OF SAND IN INCHES 


Fig. 72. — Typical Mechanical Analyses of Fine, Medium, Well Graded 

and Coarse Sands. (See p. 200.) 

times greater than that of Figs. 70 and 71, the diagram showing diameters 
ranging from o to 0.200 inches diameter. The “granulometric composi¬ 
tion” of these sands may be determined if desired by reference to page 149. 

The mechanical analysis of crusher dust is apt to vary between the curves 
of fine sand and medium sand which are shown in Fig. 72. 

STUDIES OF THE DENSITY OF CONCRETE 

In the year 1901 the writer, through the permission and assistance of 
Mr. E. LeB. Gardiner, Vice-President, and Mr. J. Waldo Smith, Chief 
Engineer, of the East Jersey Water Company, was enabled to make an 
extended series of experiments on the comparative strengths of different 
proportions of concrete aggregate. Many mixtures of different propor¬ 
tions w r ere made up into beams, their curves of mechanical analyses drawn 
as explained above,, and the strength of the beams determined by breaking 
tests.* 

These tests indicated that the strength of concrete varies with the per¬ 
centage of cement contained in a unit volume of the set concrete, also with 


* The results of these tests are presented in the table on pages 376 and 377. 




















































































































PROPORTIONING CONCRETE 


201 


the density of the specimen. With the same percentage of cement, the 
densest mixture, irrespective of the relative proportions of the sand and 
stone, was in general the strongest. These tests further indicated that for 
the materials used there was a certain mixture of sizes of grains of the 
aggregate which, with a given percentage by weight of cement to the total 
aggregate, gave the highest breaking strength. In practice also it was 
found that the concrete made with this mixture worked most smoothly in 
placing. 

These tests led to a still more extended series by the writer and Mr. 
Sanford E. Thompson at Jerome Park Reservoir, New York, in 1903 and 
1904, under the authorization of the Aqueduct Commission of the city of 
New York, Mr. J. Waldo Smith, Chief Engineer. 

The method of procedure and the results of the tests are given in full in 
a paper on “The Laws of Proportioning Concrete,” by William B. Fuller 
and Sanford E. Thompson, Transactions American Society Civil Engineers, 
Vol. LIX, p. 67, 1907. The experiments were begun with a series of tests 
on the density of different mixtures of aggregate and cement to determine 
the laws of proportioning for maximum density for different materials, 
and these density experiments were followed by the manufacture of con¬ 
crete specimens in the attempt to determine the relation between the laws 
of strength and the laws of density. 

The mechanical analysis diagram furnished a ready means of studying 
the effect of various sized particles on the density of concrete. For this 
purpose crusher-run stone and bank gravel were screened into twenty-one 
sizes ranging from 3 inches down to that passing a No. 100 sieve, having 
meshes 0.0027 inch in diameter. These sized materials were then re-com- 
bined in a predetermined mechanical analysis curve by weighing out the 
necessary quantities of each size. 

This material was next thoroughly mixed with a given weight of cement 
and the whole amount wet and mixed and tamped into a strong cylinder in 
which its volume could be measured. This batch was then thrown away 
and another batch made up according to another mechanical analysis curve 
and its volume recorded. In this way over 400 different mechanical analysis 
curves were tested as to volume for the purpose of determining the ideal 
curve corresponding to the densest concrete mixture. 

Both broken stone and gravel were used in the tests, and to reduce the 
number of variables, most of the experiments were made upon the same 
proportions, using 10 per cent by weight of cement to the total dry materials, 
corresponding to proportions 1 : 9 by weight. 

In all of the tests instead of following the more usual plan of testing the 


202 


A TREATISE ON CONCRETE 


aggregate separately, every experiment was performed with a mixture of 
the aggregate and cement gaged with the water necessary to produce the 
proper consistency. The water was found necessary both in theory and 
practice. The cement and water actually occupy space in the mass, since 
many of the voids are too small for the grains of cement to fit into them 
without expanding the volume and the water also occupies actual bulk in 
the concrete. Besides this, a concrete mixed up with water is easier and 
smoother to handle than a mixture of dry materials alone which tend to 
separate when being placed. 

Curve of Maximum Density. The Little Falls tests made by the writer 
indicated that the curve at greatest density was substantially a parabola. 
The Jerome Park tests based on a larger number of experiments define the 
curve still more accurately as a combination of an ellipse and a straight line.* 

One of the most interesting developments was that a curve of substan¬ 
tially the same form would fit different materials whatever the maximum 
size of the stone. The J-inch stone, for example, required but very slight 
change in curve equation from the 2j-inch stone. 

The maximum density curve then was found to consist of a combination 
of an ellipsef and a straight line, the ellipse being first constructed with its 


* Mr. Fuller’s method of proportioning the materials so that their mixture will form a smooth, 
clearly defined curve appears, on its face, to conflict with Mr. Feret’s conclusion (see p. 147) that the 
best mixture of sand and cement for mortar is made up of coarse 4nd fine grains only, with no inter¬ 
mediate grains. For sand mortars, Mr. Feret’s methods are undoubtedly more exact than Mr. 
Fuller’s, but for a concrete mixture the conditions are different, and, as we have stated on page 172, 
more than two sizes of materials are theoretically necessary for obtaining the densest mixture. In 
practice, too, all classes of materials are more or less varied, and experiments show that the particles 
will best fit into each other if the sizes are graded. The best proof of the practical efficiency 
of Mr. Fuller’s method lies in the fact that he has employed it day after day for determining the 
proportions of the aggregate for concrete used in constructing thin, water-tight walls. The pro¬ 
portions used by him for such work are about 1 : 3 : 7, whereas for water-tight construction where 
the materials are not scientifically graded 1:2:4 mixtures are commonly used. 

The method is exact and scientific and not “rule-of-thumb.’’ The nature of the materials and 
their variation from hour to hour makes great refinement unnecessary, so that an accuracy of, say, 
2% or 3% in the percentages are all that is necessary in practice. Although further tests may show 
that for other materials the form of the curve vanes from that indicated by Mr. Fuller, the 
general method of analyzing materials and combining the curves is undoubtedly applicable what¬ 
ever the form of the curve, so that Mr. Fuller’s general principles and methods still hold. 

f In practice ellipses may be most readily plotted graphically by the Trammelpoint method as 
follows: 

Plot the major and minor axes on the diagram. The major or horizontal axis in all cases is on a 
line 7% above the base. The minor or vertical axis is at a distance, a, to the right of the vertical 
zero ordinate of the diagram. Lay a strip of paper or a thin straight-edge upon the major or hori¬ 
zontal axis, and mark upon it two points to represent the length of the semi-major axis, calling one 
of these points—the point on the zero ordinate— 0, ind the other point A. Mark off on the strip 
or straight-edge, in the same direction from 0, the length of the semi-minor axis, calling this point 
B. Now, swing the strip of paper or straight-edge little by little so that the outline of the curve may 
be marked off by the point 0, while the points A and B are kept at all times upon the axes b and a 
respectively. The straight lines to continue the curves are drawn as tangents to them, or may be 
readily plotted from the data on the following page. 


PROPORTIONING CONCRETE 


203 


major axis coinciding with 7 per cent line of percentages, and the equation 

72 

of the ellipse, using the zero coordinates of the diagram, being (y — 7) 2 = — 

a 3 

(2ax — x 2 ). One of the ideal curves is illustrated in Fig. 73, page 207, 
showing the general form which it takes. 

In practice it was necessary to raise the curve somewhat higher, that is, 
to use more sand than the very careful laboratory tests would indicate as 
the ideal mix. 

The values of a and b for the different materials, including the cement 
for the Ideal Mix, based on the Jerome Park stone and Cowe Bay sand and 
gravel, which, as already stated, were fairly representative materials, are as 
follows: 


Data for Plotting Ellipses in Curves of Ideal Mix. 


Materials. 

Ideal Mix 

Axes of Ellipse. 


a 

b 

Crushed stone and sand .... 

0.04 + 0.16D 

28.5 + 1.3D 

Gravel and sand. 

0.04 +0. I6D 

26.4 +1.3D 

Crushed stone and screen- 



ings. 

0.03 5 +0.14D 

29.4+ 2.2D 


In this table, D = the maximum diameter of the stone, in inches. 


For the Practical Mix the values of b must be greater so as to give a 
higher curve with more of the finer material. A quick and sufficiently 
accurate method of drawing the curves for the practical mix is to draw a 
straight line from the point where the largest diameter stone reaches the 
100% line to the point on the vertical ordinate at zero diameter given in 
Column (1) in the following table. 


Data for Plotting Curves of Practical Mix. 


Materials. 

Intersection of 
tangent with vertical 
at zero diameter 

(1) 

Height of 
tangent point 

(2) 

Axes of Ellipse. 

a 

( 3 ) 

6 + 7 
( 4 ) 

Crushed stone and sand. 

28.5 

35-7 

0.1 50D 

37-4 

Gravel and sand. 

26.0 

33-4 

O. I 64D 

35-6 

Crushed stone and screen- 
ings. 

29,0 

36. 1 

0.147D 

37 - 8 






























204 


A TREATISE ON CONCRETE 


Then mark the tangent point on this line where it is intersected by 
the vertical ordinate for one-tenth the maximum diameter stone. This 
mark should check with the values given in column (2) of above table. 
Then plot the location of minor axis of the ellipse from the values of 
a and b + 7, given in columns (3) and (4) in the above table. This point, 
together with the tangent point and the point at + 7 on the vertical ordi¬ 
nate at zero diameter where the curve begins, gives three points on the 
ellipse, which is usually sufficient for drawing the curve with the aid of 
an irregular curve. If more points are wanted, they may be plotted 
graphically by the trammel point method as given in the note on 
page 202. 


RELATION OF DENSITY TO STRENGTH 

Having determined the maximum density curve as just explained, it was 
important to know if the greatest strength coincided with the greatest 
density, and for this purpose a large number of beams, six inches square 
and six feet long, were made up and tested for transverse and crushing 
strength, for permeability and modulus of elasticity. Some beams were 
made using the proportions determined by the maximum density curve and 
other beams according to higher and lower curves to note if there were any 
decrease in these properties as the maximum density curve was departed 
from. The full result^ of the tests are given in the paper referred to,* 
but in general it may be said that a departure from the maximum density 
curve represented a reduction in all these properties except that when the 
curve was modified so as to use a uniform size of coarse stone instead of 
the graded stone it gave practically the same results as the graded. Any 
curving above the straight line in the coarse material decreased the density, 
and also the strength, indicating that the coarse aggregate should not have 
an excess of medium particles. 

LAWS OF PROPORTIONING 

From these experiments, laws of proportioning and also laws relating to 
strength and permeability which are outlined in full in the paper by Messrs. 
Fuller and Thompson* were evolved. 

Those relating specifically to strength are given on page 390 and those 
relating definitely to permeability on page 349, and reference should be 
made to these for complete conclusions. The laws relating especially to 
the grading of the aggregates are as follows: 


♦See footnote p. 201 


PROPORTIONING CONCRETE 


205 


i-—Aggregates in which particles have been specially graded in sizes 
so as to give, when water and cement are added, an artificial mixture of 
greatest density, produce concrete of higher strength than mixtures of 
cement and natural materials in similar proportions. The average improve¬ 
ment in strength by artificial grading under the conditions of the tests was 
about 14 per cent. Comparing the tests of strength of concrete having 
different percentages of cement, it is found that for similar strength the best 
artificially graded aggregate would require about 12% less cement than like 
mixtures of natural materials. 

2. —The strength and density of concrete is affected but slightly, if at all, 
by decreasing the quantity of the medium size stone of the aggregate and 
increasing the quantity of the coarsest stone. An excess of stone of medium 
size, on the other hand, appreciably decreases the density and strength of 
the concrete. 

3. —The strength and density of concrete is affected by the variation in 
the diameter of the particles of sand more than by variation in the diameters 
of the stone particles. 

4. —An excess of fine or of medium sand decreases the density and also 
the strength of the concrete, as will also a deficiency of fine grains of sand 
in a lean concrete. 

5. —The substitution of cement for fine sand does not affect the density of 
the mixture, but increases the strength, although in a slightly smaller ratio 
than the increase in the ratio of cement. 

6. —It follows from the foregoing conclusions that the correct propor¬ 
tioning of concrete for strength consists in finding, with any percentage of 
cement, a concrete mixture of maximum density, and increasing or decreas¬ 
ing the cement by substituting it for the fine particles in the sand or vice 
versa.* 

7. —In ordinary proportioning with a given sand and stone and a given 
percentage of cement, the densest and strongest mixture is attained when the 
volume of the mixture of sand, cement and water is so small as just to fill 
the voids in the stone. In other words, in practical construction, use as 
small a proportion of sand and as large a proportion of stone as is possible 
without producing visible voids in the concrete. 

8. —The best mixture of cement and aggregate has a mechanical analysis 
curvef resembling a parabola, which is a combination of a curve approach¬ 
ing an ellipse for the sand portion and a tangent straight line for the stone 


* Thisveryimportantlawrequiresfurthertests for confirmation,outside of thelimits of the present 
tests. 

. t For definition of mechanical analysis, see page 193. 


206 


A TREATISE ON CONCRETE 


portion. The ellipse runs to a diameter of one-tenth of the diameter of the 
maximum size of stone, and the stone from this point is uniformly graded. 

9. —The ideal mechanical, analysis curve, i.e., the best curve, is slightly 
different for different materials. Cowe Bay sand and gravel, for example, 
pack closer than Jerome Park stone and screenings, and therefore require 
less of the size of grain which the authors designate as sand. 

10. —The form of the best analysis curve for any given material is nearly 
the same for all sizes of stone, that is, the curve for -Tinch, i-irfch, and 21- 
inch maximum stone may be described by an equation with the maximum 
diameter as the only variable. In other words, suppose a diagram in which 
the left ordinate is zero, and the extreme right ordinate corresponds to 2J- 
inch stone, with the best curve for this stone drawn upon it. If, now, on 
this diagram the vertical scale remains the same, but the horizontal scale 
is increased two and a quarter times, so that the diameter of i-inch stone 
corresponds to the extreme right-hand ordinate, the best curve for the 1- 
inch stone will be very nearly the one already drawn for the 2j-inch stone. 
The chief difference between the two is that the larger size stone requires 
a slightly higher curve in the fine sand portion. 

11. —It follows from this last conclusion that from a scientific standpoint 
the term sand is a relative one. With 2j-inch stone, the best sand would 
range in size from o to 0.22 inch diameter, while the best sand for ^-inch 
stone would range in size from o to 0.05 inch diameter. 

APPLICATION OF MECHANICAL ANALYSIS DIAGRAMS TO PRO¬ 
PORTIONING 

The mechanical analysis diagram offers a very exact method of determin¬ 
ing the proper proportions of any materials for concrete by sieving each of 
the materials, plotting their analyses and combining these curves so that the 
result is as near as possible similar to the maximum density curve. 

Plot on the diagram the maximum density curve for the given materials 
to be used; if the equation for this material is not known use the practical 
equation previously given. Make a mechanical analysis of all of the 
materials which it is desired to mix together in the right proportions and 
plot the result of each analysis on the diagram on which the maximum den¬ 
sity curve has been plotted. 

The aim is to find a new curve representing the mixture of the materials, 
but which will conform as nearly as possible to the curve of maximum 
density. The proportions of different materials required to produce this 
curve will show the relative quantity of each which must be used in pro¬ 
portioning. The theory of the combination and complete discussion of the 


V 


I 

PROPORTIONING CONCRETE 207 

methods to be employed with different forms of curves are treated in 
Appendix IV. 

A less exact method, but one which is convenient in practice, is by inspec¬ 
tion and trial of different percentages. To illustrate this trial plan, the 
method of forming a curve of a mixture of several materials in stated pro¬ 
portions such as 1 12:4 will be given, then the curve for the mixture of the 
same materials which corresponds nearest to the curve of maximum density, 
and finally the application will be made to material like run of the bank 
gravel which may be separated into two or three parts. 

In reading this discussion it must be borne in mind that the same prin¬ 
ciples will apply to mixtures of several aggregates, although for simplicity 
the principal part of the discussion refers to two aggregates. The same 



Fig. 73.—Curves of Fine and Coarse Crushed Stone and Mixtures, (p.207) 

approximate plan may be used for the larger number of aggregates or the 
more exact method in the Appendix may be adopted. 

Plotting Curve of Mix in Studying Proportions. In Fig. 73 we have 
f-inch Shawangunk grit as one aggregate and the same material rolled to 
J-inch maximum size as the other, giving the mechanical analysis curves 
shown in the diagram.* 

In this diagram a curve of cement is also plotted so that the 1:2:4 
curve represents the combination of the three materials. The curve marked 
1:2:4 then represents the analysis of the mixture of cement, screenings 

* This diagram and the ones which follow are made up from materials used in subsequent studies 
by the New York Board of Water Supply, and referred to in the Discussion by Mr. James L. Davis, 
Transactions American Society Civil Engineers, Vol. LIX, p. 144. 






























































208 


A TREATISE ON CONCRETE 


and stone in these proportions. This curve is made up by plotting various 
points and connecting these by a smooth curve. To find the point, for 
example, where the curve cuts the ordinate corresponding to the No. 20 
sieve, the sums of the percentages of the individual materials at this same 
ordinate are taken in the proportion which they bear to the concrete mixture. 
All of the cement is finer than the No. 20 sieve, and since the cement is one 
part of the seven parts in the mixture, one-seventh of 100 per cent repre¬ 
sents the percentage of cement in the mixture at the given ordinate. Simi¬ 
larly, since there are two parts of sand in the seven parts, the sand percent¬ 
age at the No. 20 ordinate, 61 per cent, is multiplied by two-sevenths, and 
the stone percentage, 6 per cent, by four-sevenths, thus giving as the point 
on the No. 20 sieve ordinate in the combined curve: 

1 X 100 percent = 14.3 per cent for cement 

f X 61 percent = 17 .4 per cent for sand 

7 X 6 per cent = 3.4 per cent for stone 

/ _ _ 

Total. 35.1 per cent for the point in the curve. 

The other points in the curves are found in a similar manner. 

Curve of Mix to Best Fit the Maximum Density Curve. Take the same 
two aggregates plotted in Fig. 73, but in this case disregard the cement or 
rather consider it a part of the sand. (Frequently the cement must be con¬ 
sidered in the trial mixtures in order to study the part of the curve repre¬ 
senting the fine material to see that the percentages of the finest particles are 
satisfactory). The slide rule is convenient for this proportioning. 

Averaging the f-inch stone by a straight line, we see that it crosses the 
0.15 line at about 9%; we note also that the ^-inch sand crosses the same 
line at 98% and the maximum density curve crosses the line at 43%, that 
is, along this line it is 34% from the f-inch stone to the maximum density 
curve and 55% to the |-inch sand. The percentages to be used to obtain a 
43 % mixture would be an inverse ratio of these two numbers to their total, 
that is, |-J = 38% of fine material and -ff = 62% of the coarse material. 
With the slide rule take these percentages of each curve, add together and 
plot a new curve, and see if it conforms reasonably with the maximum den¬ 
sity curve. If it does not, make another trial of percentages, the plot of 
the curve indicating by inspection the new percentages. 

It must be remembered that the fine portion of the curve includes also the 
cement, so having decided on the amount of cement to use, say the equiva¬ 
lent of a 1 : 7 mix, which has 12^% of cement, the actual proportions 
would be 1 2\ parts cement to 38 — 12^ = 25-0- parts fine aggregate to 62 parts 
coarse aggregate, or translated into the usual nomenclature, 1:2.04 : 4.95, 
or practically 1 : 2 : 5, showing that the ordinary mixture with this particu- 




PROPORTIONING CONCRETE 


209 


lar material is the best. Supposing, however, the equivalent of a richer 
mixture, say 1 : 2 : 4, is wanted. This would contain 1:6 = i4j% cement 
and the proportions would be 

M? : 23^ : 62, 

or 


or practically 


1 : 1.62 : 4.27, 


1 : 1 § : 4 i, 

showing that for richer mixtures less fine materials is desirable. 







































































































































210 


A TREATISE ON CONCRETE 


Run of Bank Gravel. Gravel as it is found in the natural bank almost 
always contains too much fine material. In many cases screening this into 
two sizes produces a good curve which fits very closely to the curve of 
maximum density.* 

Other gravels, especially where the sand is greatly in excess, require two 
screenings for the best result. Fig. 74 represents a common run of such 
gravel, showing that screening into two sizes will not permit a mixture fitting 
very near to the maximum density curve. The figure also shows how far 
away the original analysis of the run of the bank is from the ideal curve. 
In Fig. 75 the same sand is shown screened into three sizes, and illustrates 
the improvement that can be obtained in this case by the extra screening, 
the effect of which is to leave out some of the medium size particles which 
are too large to fill the voids of the coarse stones, and therefore decrease the 
density and the strength of the mixture. 

VOLUMETRIC SYNTHESIS OR PROPORTIONING BY TRIAL 

MIXTURES 

The density tests at Jerome Park and the relation there found of the 
strength to the density indicate a method of proportioning by trial mixtures, 
which in fact compared the density of the same materials mixed in different 
proportions or different materials mixed in similar proportions. 

Having determined the particular sand and stone which are to be used on 
any piece of work, a simple and accurate way of determining proportions 
is by actual trial batches of fresh material. For this it is only necessary to 
have good scales and a strong and rigid cylinder, say, a piece of 10-inch 
wrought-iron pipe capped at one end. Carefully weigh out and mix 
together on a piece of sheet steel or other non-absorbent material all the 
ingredients, having the consistency the same as is intended to be used in 
the work. Place these in the pipe, carefully tamping all the time, and note 
the height to which the pipe is filled. Weigh the pipe before filling and 
after being filled, thus checking weight of material mixed. Throw this 
material away before it has time to set, and clean the pipe. Make up another 
batch, using the same weights of cement and water and the same total 
weight of sand and stone, but have the ratio of weights of the sand and 
stone slightly different from the first. Note whether, after placing, the 
height in the cylinder is less or more than was the height of the first batch, 
and this will be a guide to further similar mixes, until a proportion is found 
which gives the least height in the cylinder, and at the same time works 

*An illustration of this is given by Mr. James L. Davis, in Transactions American Society of 
Civil Engineers, Vol. LIX, p. 145. 


PROPORTIONING CONCRETE 


211 


well while mixing and looks well in the cylinder, all the stones being covered 
with mortar. This method, if carefully followed, will give very accurate 
results, but of course does not indicate, as does mechanical analysis, what 
other changes can be made in the physical sizes of the sand and stones so 
as to get the best available composition. 

Mr. A. E. Schutte, in studying the proportions of materials for bitumi¬ 
nous macadam pavement for the Warren Brothers Company, has very 
effectively developed the method of volumetric synthesis with dry materials.. 
His experiments included various classes and sizes of stone, sand, and 
screenings ranging from 3 inches diameter down to that which passes a No. 
200 sieve. He found that the best method for compacting dry materials, 
such as sand, gravel or broken stone, is to place them in a vessel the shape 
of a truncated cone, with the largest diameter at the bottom. The cone is 
filled with the coarsest material and taken by a laborer, who compacts it 
by repeatedly striking the cone against the ground, keeping the measure 
full by adding new material of the same kind. When it ceases to settle, the 
contents is emptied and mixed with a portion of a finer material, replaced 
in the measure and compacted as before. By repeated trials the exact size 
and maximum volume of successive finer materials, which may be added 
without appreciably increasing the bulk of the coarsest after thoroughly 
compacting, are determined. Mr. Schutte has found that for different 
shapes of particles the proportions of each size must be varied, but having 
determined the required percentages for a certain stone, that is, for a stone 
from a certain quarry, the proportions of the sizes from day to day need be 
varied but little. 

Practical Proportioning During Progress of the Work. The above 
methods of mechanical analysis and volumetric synthesis are methods to 
be used in the office or laboratory in determining the relative values of all 
the aggregates available for the work. When the work is begun, however, 
and the same general character of aggregate is used day by day, it is only 
necessary to see that the material does not change or, if it does, simply to 
readjust the relation between the fine and coarse aggregate. To do this 
by the mechanical analysis method, it is only necessary to have a nest of 
about six 8-inch sieves: say, stone sieves with 1 inch, J-inch and J-inch 
diameter holes and sand sieves No. 8, 20, 50 and 100, together with a cover 
and pan. The shaking can be done by hand, and the sievings beginning 
with the finest emptied into a long glass tube. If a standard sample has 
been previously put in the tube in the same way and the points of division 
between the different sievings marked on a paper pasted on the outside 
of the tube, the difference between the standard and the sample under test 
can be quickly seen and modifications made in the mix accordingly. 


212 

Proportions in Actual Structures. 


Compiled by Taylor and Thompson. 



</} 

i.l 

Cement 

380 lbs. 

T 3 

C 

c 

0 . 
c/ 5 >£ 

tmes based 
nominal or 

tual meas¬ 

ement. 



Structure. 

11 

ro 

d _; 

8 a 
8° 

<D ^ 

O u 

O 

Authority. 

Reference. 


P* 

"pxi 

S-a 

►-) 

►-1 

3 C U >. 

00<43 





Oh 



> 



New Brooklyn Bridge Piers . . . 


I 

8.5 

195 

nominal 

Asst. Engineer 


Boston El. Ry. Column Foundations 

1 :2£:s* 

I 

9-5 

19.1 

nominal 

G- A. Kimball 

Jour. A. E. S. 





June ’03, p. 353 

N. Y C. & H R. R. R. 







Assn, of Ry. Supts. 

Footings.. 

1:4:7$+ 

I 

13.9 

26.2 

actual 

W. J. Wilgus 

Abutments. 

1:3:6+ 

I 

122 

237 

actual 


1900, p. 207 

Facing Old Masonry .... 

1:2:4 

I 

7.0 

14.0 

actual 



Coping and Bridge Seats . . . 

1 :i :2 

I 

3-5 

7 -i 

actual 



C. M. & S. P Ry. 






W. A. Rogers 

Assn, of Ry. Supts. 

Piers and Abutments .... 

1:2:5 

I 

7-8 

21.4 

actual 

Culverts and Foundations . . 

1:3:7$ 

I 

10.5 

28.5 

actual 


1900, p. 228 

Or R. R. & Nav. Co. 






W. H. Kennedy 

Assn of Ry- Supts. 

Abutments, Piers and Culverts . 

1 =3 :.5 

I 

11.0 

18.3 

nominal 

Foundations and Light Buildings 

?i: 3 $ :6 
\i: 4:7 

I 

I 

12.8 

14.7 

22.0 

25-7 

nominal 

nominal 


1900, p. 182 

C. & E. I. R. R. 


I 

9-3 

26 7 

actual 

A. S. Markley 

Assn, of Ry. Supts. 
1900, p. 245 

Northern Pacific Rv- 






E. H. McHenry 

Foundations. 


I 

I 1.2 

20.2 

actual 

Assn, of Ry. Supts 

Abutments and Piers .... 

1:3:5 

I 

I 1.2 

20.2 

actual 


1900, p. 235 

C., B. & Q. R. R. 

1:3:6 

I 

12.5 

22.5 

actual 

Fred Eilers 

Lewis Kingman 

Assn, of Ry. Supts. 

1900, p. 231 

Assn, of Ry. Supts. 

Mexican Central Ry. 


I 

13-5 

27.0 

nominal 







N.Y.R.T Com. 

1900, p. 212 

N. Y. Subway 






Spec. 1900, p. 83 

Roofs and Sidewalls 








not over 18 in. thick . . . 

1:2:4 

I 

7.2 

14.4 

nominal 



Sidewalls or Tunnel Arches . . 
Wet Foundations 

i:2$:5 

I 

9.0 

18.0 

nominal 



not over 24 in. thick . . . 

1:2:4 

I 

7 2 

14.4 

nominal 



Wet Foundations 







exceeding 24 in. thick . . 

1 : 2$ : 5 

I 

9 ° 

18.0 

nominal 



Boston Subway. 


I 

8-3 

13.2 

nominal 

H. A. Carson 


* 

Harvard University Stadium . . . 

1:3:6 







Maine Fortifications 







Report Chief of 

Leveling for Foundations . . . 

1:5:1° 

I 

18.2 

36.5 

nominal 

S. W.Roessler 

Walls and Masses 






Engrs. U. S. A. 

not exposed to fire .... 

1:4:8 

I 

14.6 

29.2 



1901, p. 911 

Walls and Masses 








exposed to fire. 


I 

II.O, 

22.0 

nominal 



Masses for greater imperviousness 

1:3:5 

I 

11.0 

18.3 

nominal 



Little Falls 






W. B. Fuller 


Mass Concrete . 

1:3:7 

I 

11.4 

26 6 

nominal 



Tanks, Buildings, etc., .... 

1:2:4 

I 

7.6 

15-2 




Duluth Ship Canal Piers .... 


I 

j 1.8 

23.8 

nominal 

C. Coleman 

Cement, Sept., ’oo, 

Boonton, N. J., Dam. 


I 

10.5 

23.8 


W. B. Fuller 

p. 144 

Genesee Dam. . . 

f 33 % 

\mortar 

I 

11.4 

36.8 

nominal 

Geo. W. Rafter 


Buffalo Breakwater. 


I 

5 

3 °ll 

nominal 

Emile Low 

Trans. A. S. C. E. 







Vol. L 1 I. p. 102 

Pennsylvania Tunnel. 


I 

9 - 6 ±H 

I 9 - 3 ±H 

nomina 

Specifications 

Eng. News. Oct. 






nomina 


15 . ’° 3 . P- 337 

East Boston Tunnel. 


I 

7-7 

12.4 

tl. A. Carson 

Specifications, 1900 


* Mixture varied with loading from 1:1:3 to 1:3:6. t 25% of the mass is rubble. 

J Boulders added- § 55% of the mass is rubble- 

II15 cu. ft. gravel and 15 cu- ft. broken stone Actual volumes of aggregates, 25% higher. 

If The specifications give proportions in volumes shaken, hence 10% has been added to convert them to loose 
measurement. 




















































PROPORTIONING CONCRETE 213, 214,* 215* 

The test by volumetric synthesis is one easily made in a modified way in 
the field and with care gives good results. Procure a galvanized tin pail 
and a spring balance graduated to half pounds; take a representative sample 
of concrete, being careful that it contains no more stones or mortar than 
the regular concrete; tamp it into the pail until level full and weigh. Any 
variation from the standard weight will show a change in the character of 
material, and this change can usually be detected and corrected by observ¬ 
ing th.e materials arid mixing. If not, then mechanical analysis methods 
will have to be used. 

PROPORTIONS OF CONCRETE IN PRACTICE 

► 

The proportion of cement to the aggregate depends upon the nature of 
the construction and the required degree of strength or water-tightness as 
well as upon the character of the inert materials. Strength and imper¬ 
meability are discussed in Chapters XX and XIX respectively, but the 
table which follows, compiled by the authors, giving the proportions 
adopted upon important structures, may in some cases be useful as an 
arbitrary guide. Actual measurement, that is, measurement of propor¬ 
tions as actually used, almost invariably shows leaner mixtures than the 
nominal proportions called for. This is largely due to the heaping of the 
measuring boxes in practise. 

In general, as both strength and imperviousness increase with the pro¬ 
portion of cement to aggregate, relatively rich mixtures are necessary for 
loaded columns and beams in building construction, for thin walls subjected 
to water pressure, and for foundations laid under water. 


* Pages 214 and 215 are omitted in this Edition. 


2 l6 


A TREATISE ON CONCRETE 


CHAPTER XII 

TABLES OF QUANTITIES OF MATERIALS FOR 
CONCRETE AND MORTAR 

This chapter presents tables, curves, and formulas (pp. 221 to 235), by 
which the volumes of materials required for a known volume of concrete 
may be estimated, and emphasizes the importance of distinctly stating 
the proportions (p. 217). 

The volume of concrete, even when made from materials in the same 
proportions, varies largely with the character of the materials and the 
methods of placing it. A mixed aggregate like gravel contains fewer voids 
and with the same proportions by volume of the same cement and sand 
produces a larger quantity of concrete than a screened broken stone. The 
fineness of the sand also largely affects the volume of the concrete and 
mortar, a fine sand requiring more water, and therefore producing a larger 
volume of mortar than coarse sand in the same proportions by volume. 
If the sand is dry, a slightly larger bulk of mortar is produced than with 
the same sand when containing a larger percentage of moisture, because 
the latter is less compact (see p. 176). Some cements require more water 
in gaging than others, and produce a larger amount of paste, which in¬ 
creases the volume of the concrete or mortar. The method of mixing and 
placing the concrete also affects the resulting volume, since an imperfectly 
mixed or poorly compacted mass contains voids which increase the volume. 
An excess of water in mixing affects the resulting volume of the set concrete 
or mortar to a slight extent, although most of the surplus water is expelled 
during setting. 

It is possible to provide for all these variations, except those relating 
to improper mixing and placing, in rational formulas from which 
the resulting volumes may be accurately estimated if the characteristics 
of all the materials are known. For most practical purposes, however, 
average values, such as are presented in the tables and curves, are 
sufficiently accurate for estimating quantities. These average values are 
based upon a large number of tests in the United States, France, and 
Germany. 

The theory of a concrete mixture is discussed, and formulas for volumes 
and quantities are given on pages 220 to 227 preceding the tables. 


217 


QUANTITIES OF MATERIALS 

EXPRESSING THE PROPORTIONS 

In framing concrete specifications, the proportions of the constituents 
should be stated so distinctly that there can be no misunderstanding be¬ 
tween the engineer and the contractor as to the quantities which will be 
required for the work. The quantity of cement should invariably be 
regulated by its weight; if the proportions are stated by volume a 
definite weight or number of packages of cement must be assumed to 
the unit volume. For reasons discussed in Chapter XI, it is also more 
accurate and scientific to measure the aggregates by weight than by volume, 
and since with a properly constructed plant using materials of several 
sizes, the cost need be no more than volume measure, the authors be¬ 
lieve this will eventually become common practice in the case of impor¬ 
tant construction. 

With our present system of weights and measures, it is advisable either 
to specify the number of cubic feet (or pounds) of sand and gravel, stone, 
or mixed material to a definite weight of cement, or else to stipulate a 
definite weight of cement to a cubic yard of concrete tamped in place, 
with an aggregate of clearly described material proportioned as the en¬ 
gineer may direct. 

In stating the proportions for both mortar and concrete, it is now custom¬ 
ary in the United States to separate the materials by colons, the first 
figure always representing the cement, followed by the aggregates in the 
order of the size of their grains. For example, 1:3:6 means 1 part cement 
(the unit of measurement should be stated), 3 parts sand, and 6 parts 
coarse material; or 1: 8 means 1 part cement (of defined weight) to 8 parts 
of graded aggregate. Mortar in proportion 1: 2 signifies one part cement 
to two parts sand by either weight or volume as specified. 

In France, proportions are stated as one or more volumes of mortar to a 
definite number of volumes of stone, — “un volume de mortier pour deux 
volumes de cailloux.” 

Unit for Proportioning. If the proportions must be stated in parts, it 
is recommended that the weight of cement be assumed as 100 lb. per cubic 
foot, and the corresponding volume of a barrel as 3.8 cu. ft. By this 
system of units, proportions 1:3:6 would represent 100 lb. cement to 3 
cu. ft. of sand to 6 cu. ft. of gravel or stone; or, 1 bbl. cement ( i.e ., 4 
bags or 376 lb.) to 11.4 cu. ft. sand to 22.8 cu. ft. gravel or stone. 

The authors offer these recommendations after correspondence or per¬ 
sonal interview with some fifty authorities* (members of the American 


*See Preface. 


2 l8 


A TREATISE ON CONCRETE 


Society of Civil Engineers) on concrete construction, representing all sec¬ 
tions of the United States. 

With reference to the unit which should be selected for the volume of a 
cement barrel (corresponding to 376 lb. Portland cement) the opinions 
were varied, but nearly every authority advocated specifying a definite 
weight of cement instead of measuring it loosely by volume. The units 
which met with the most favor were 3.5, 3.6, 3.8 and 4.0 cu. ft. The 
advocates of the first two values based their figures upon the measured 
volume of a cement barrel, while those selecting the last two did so on the 
presumption that the unit is an arbitrary one in any case, and 100 lb. per 
cubic foot, or 95 lb. per cubic foot (the latter equivalent to 1 cu. ft. to the 
bag), is convenient for calculation. An approximate average of all the 
figures suggested was 3.8 cu. ft. to the barrel, corresponding to 100 lb. per 
cubic foot, the advocates of this value being, among others, Messrs. Charles 
E. Fowler, William B. Fuller, Peter C. Hains, Allen Hazen, Rudolph 
Hering, George A. Kimball, Leonard Metcalf, J. Waldo Smith, and 
J. H. Wallace. Accordingly, in cases where it is advisable to specify 
the proportions by parts, the authors have adopted this unit as their 
standard. 

When stating the proportions by volume, too much stress cannot be laid 
upon the necessity for the adoption of a standard unit, such as a barrel of 
3.8 cu. ft. or the equivalent assumption that a cubic foot of cement weighs 
100 lb., and upon distinctly specifying this standard, as otherwise an 
unscrupulous contractor may adopt for his unit the volume of cement 
very loosely measured, and thus produce too lean a concrete. Moreover, 
without a standard there is no means of comparing the concrete in different 
structures or the results of different experiments. It is even inaccurate to 
state that proportions shall be based on packed or on loose measurement 
of cement, for either of these terms is very elastic. The authors have 
personally known engineers to place the volume of a barrel of packed 
cement all the way from 3.1 to 3.8 cu. ft., corresponding to a variation in 
weight of from 123 to 100 lb. per cubic foot, while loose measurement, on 
the other hand, is variously fixed at from 3.8 to 4.5* cu. ft. to the barrel, 
or 100 to 84^- lb. per cubic foot. The extreme actual variation is therefore 
from 3.1 to 4.5 cu. ft. per barrel, or 123 to 84$ lb. per cubic foot. Propor¬ 
tions 1:3:6 in the first case would require 1 bbl. or 376 lb. cement to 9.3 
cu. ft. of sand and 18.6 cu. ft. of gravel; in the last case, proportions 1:3:6 
would stand for 1 bbl. or 376 lb. cement to 13.5 cu. ft. of sand and 27 cu. ft. 

*This value is given by one engineer in Proceedings Association of Railway Superintendents 
of Bridges and Buildings, 1900, p. 212. 


QUANTITIES OF MATERIALS 


219 


of gravel. In other words, concrete mixed 1:3:6 by one man may be 
called 1: 4J: by another.* 

It may be contended that this variation is of little moment provided the 
unit is distinctly stated. The fact is, however, that it is customary in 
discussing a piece of work to give the proportions of materials without 
stating the unit selected, and many records giving tests of strength of 
concrete do not even specify the units used in proportioning the ingredients. 
It is especially confusing also, to a contractor who is not very careful in 


Tests of Capacity of Portland Cement Barrels and Weight of Contents. 

(Tabulated by the authors from measurements of Boston Transit Commission, 

1896, Howard A. Carson, Chief Engineer.) (See p. 219.) 


-O 

D 



u 

13 


s 

1 

C/3 

Volume of 

Net weight 






O O 


a 

O 

d 

c 

C/3 

E 

(D 

U 

cement per 

of cement 

Weight per cubic foot 

D 

w b c 

rr 03 


D 

E-r 

0 

N 


O *73 

CU 

D 


barrel 

per barrel 





c 3 

>- 

Brand 

ht bet\ 
heads 

.2 u 

^ S 3 

CJ 22 



*d 











D 

t % 

ge hoi 
area 

c c 

O 

O X 
(3 > 
•2_0 

0.0 

*d 


* 

q 

Before 

dumping 

After 

dumping 

*d 


q 


O 

X 

O m 
. D 

0 *-• 
£ 


.£? 

’o 

E 

2 0 

O 

> 

< 

d 

u 

o 

> 

< 

0. ^ 

CJ 

c/J CD 

<D 

u* 

Q* 

<D 

E 

0 

0 

> 

D 

M 

u 

d 

CU 

Loose 

CJ 

M 

n 

X 

in 

D 

D 

a 

cu 

D 

tf> 

O 

O 

D 

a 

A 

in 

Sifted 

*D 



ft. 

ft. 

sq.ft. 

cu.ft. 

ft. 

cu.ft. 

cu. 

ft. 

cu. 

ft. 

cu. ft. 

lb. 

lb. 

lb. 

lb. 

ib. 

lb. 

ib. 

5 

A 

2.12 

1-437 

1.622 

3-446 

0.17 

0-235 

3.21 

3-75 

3-432 

377-4 

376.9 

117.5 

100.5 

109.4 

00.6 

21.X 

6 

B 

2.19 

1.430 

1.605 

3-495 

0.12 

0.171 

3-35 

4.17 


381.0 


113.8 

91.4 



29.0 

3 

C 

2.07 

1.412 

i- 57 i 

3-249 

0.07 

0.096 

3-15 

4-05 


387.0 


112.8 

94.2 



22.7 

5 

D 

2.01 

1.407 

1-554 

3-123 

0.07 

0.093 

3-°3 

3-99 

3-522 

373-2 

37 i -4 

123.2 

93-2 

105.5 


25.6 

6 

E 

2.08 

W 

4 ^ 

O 

Go 

1.546 

3.219 

0.04 

0.059 

3.16 

4.19 


374-2 


118.4 

89.2 



24-3 

I 

F 

2.13 

1.38 

1.496 

3-t86 

0.03 

0.039 

3 -i 5 

4.27 

3-695 

378.0 

378.0 

120.1 

88.5 

102.3 


22.0 

5 

G 

2.01 

1.46 

1.662 

3-327 

0.10 

00 

M 

6 

3.21 

4.06 

3-598 

370.7 

370.2 

H 5-7 

91.4 

102.9 

80.3 

23-3 

Final 










377-4 

374 -it 




85 - 4 + 

24.0 

Averages 

2.oq 

1.42 

1-579 

3.292 

0.09 

0.120 

3-i8 

4.07 

3 - 562 t 

118.8 

92.6 

105.1+ 


Note. —A and B are American Cements; C. D E and F are German Cements; G is a Danish Cement; 


Paper weighs about 1 lb. • 

*Box rocked over bar. 

fPartial averages, to be compared only with like brands. 

reading specifications, to find that, say, 25% or 30% more cement than he 
had figured is required to a cubic yard of concrete. When considering 
this question, the authors were surprised to find that the sidewalk and 
paving specifications of fifteen of the largest cities in the United States 
failed to state the proportions by definite weight or volume, but gave the 
quantities simply in “parts,” a few of them adding that the parts shall 
be “by measure” or “by exact measure.” 

Weight of Cement. Experiments by Mr. Howard A. Carson, for 
Boston Transit Commission, upon 31 barrels of Portland cement of 

♦For further data, see letter of Sanford E. Thompson to Engineering News, Nov. 12, 1903, p. 434. 























































220 


A TREATISE ON CONCRETE 


American and foreign brands, furnish an interesting illustration of the 
difference in weight of the same cement in different stages of compact¬ 
ness. The results,* a summary of which is presented in the table on 
page 219, show a variation from 86 to 118 lb. in the average weights of 
the same cement, according as it was weighed sifted, or packed in a 
barrel, while the actual weight of one brand, the average of 5 barrels, 
was as high as 123 lb. per cubic foot as it came from Germany packed 
in a barrel. 

From the experiments just described, the ratios of volume and weight 
of the same cements in different degrees of compactness are calculated by 
the authors as follows: 

Ratio of volume of packed cement to capacity of barrel between heads 0.97 


Ratio of volume packed to volume loose. 0.78 

Ratio of volume packed to volume shaken. 0.88 

Ratio of volume loose to volume shaken. 1.13 

Ratio of weight packed to weight loose. 1.28 

Ratio of weight packed to weight shaken. 1.13 

Ratio of weight packed to weight sifted. 1.37 


From the table it is evident that the selection of the volume of a barrel 
is arbitrary. The adopted volume of 3.8 cu. ft. is convenient for calcula¬ 
tion because it assumes a cubic foot of cement to weigh approximately 
100 lb. 

THEORY OF A CONCRETE MIXTURE 

The discussion and the formulas which follow relate to plastic mortars 
and plastic or medium concrete. While a small amount of water in 
mixing may result, with heavy ramming, in a concrete or mortar of 
less than average volume, in practice the volume is more apt to be in¬ 
creased by lack of water because of the less perfect mixture and the 
visible voids. The volume of set concrete or mortar produced by a very 
wet mixture is approximately the same as that of a plastic mixture, 
because nearly all of the surplus water is thrown to the surface and 
expelled by the settling of the solid materials. This the authors have 
repeatedly proved by experiment. 

The frequently repeated assertion that a very wet mixture contains 
visible air voids because of the drying out of the water is incorrect. This 
may be proved by carefully pouring neat cement grout into a rectangular 
mold, one of whose sides is formed by a piece of glass. The surplus water 
is expelled, and the specimen after setting is dense and glassy with no 
visible voids. The large visible voids which sometimes occur in very wet 

^Tabulated by Sanford E. Thompson in Engineering News, Oct. 4, 1900, p. 229. 








QUANTITIES OF MATERIALS 


221 


concrete, similar in appearance to visible voids in dry concrete, are due 
to the grout running away from the stones, or to too violent agitation in 
placing. 

The volume of fresh concrete or mortar produced by any mixture of 
cement and aggregate or aggregates is equal to the sum of the volumes of 
the separate particles of the cement, the sand, and the other dry materials, 
the water contained in the aggregate and added in mixing, and the small 
volume of air entrained between the particles. The volume of set mor¬ 
tar or concrete is not appreciably different from its compacted volume 
when fresh or green, except in very wet mixtures, which expel a portion 
of the water. The volumes of the particles of dry materials are termed 
absolute volumes , and it is important to note the distinction between the 
absolute volumes and the apparent volumes determined by measuring 
the materials. Absolute volumes are discussed on pages 135 to 139. 

The fact that water actually occupies space in a mass of fresh concrete 
or mortar has been entirely ignored by many writers on the subject of 
concrete mixtures. As stated on page 216, the fineness of the sand and 
the moisture contained in it affect the volume of the resulting concrete 
or mortar. Mr. Feret has proved by experiments (cited on page 179) 
that fine sands require more water for gaging than coarse. This extra 
volume of water produces a mortar of less density and consequently less 
strength; even stones such as are found in gravel or coarse broken stone 
require a very small percentage of water. 

FORMULAS FOR QUANTITIES OF MATERIALS AND VOLUMES 

A concrete is therefore made up of solid grains of cement plus water 
required for the cement, plus solid grains of sand plus water required for 
the sand, plus solid stone particles plus water required for the stone, plus 
air voids. The last term, the air voids , represents the voids entrained 
by the sand, which may be considered as a function or percentage of the 
sand, and the voids due to imperfect mixing of the concrete materials, 
which may be considered a function or percentage of the stone. Accord¬ 
ingly the volume of a concrete mixture may be expressed as a rational 
formula, which is applicable to all concrete and mortar mixtures in which 
the voids of the coarse stone are filled with mortar. The formula (1) 
which follows is presented to illustrate the theory, but because of the 
variation in the coefficient with different sands and different proportions, 
formula (2), page 222, and formulas (3) to (8), which are based on a"\er- 
age conditions, are suggested for practical use as sufficiently accurate 
for most purposes. 


222 


A TREATISE ON CONCRETE 
Let 

c = absolute volume* of cement. 

5 = absolute volume* of sand. 
g = absolute volume* of stone. 

m = ratio of the absolute volume of the water plus air voids of the 
cement, to the absolute volume of cement. 
n = ratio of the absolute volume of the water coating the grains of 
sand plus the air entrained in gaging it, to the absolute volume of sand. 
p = ratio of the absolute volume of the water coating the stone particles 
plus the air voids due to imperfect mixing, to the absolute volume 
of stone. 

W = volume of concrete produced. 

In other words, these ratios, m, n, and p , represent the sum of the vol¬ 
umes occupied by the water required for the material in mixing plus the 
air, in terms of the respective volumes of cement, sand, and stone. 

Then 

W=c + me+ s+ ns+ g+pg 

or 

W --=.(1 + m) c + (i + n) s + (i 4 - p) g (i) 

The coefficient n is really composed of two variables, one depending 
upon the coarseness of the sand, and the other upon the ratio of cement to 
sand, since a lean mortar contains more air voids. It is possible to ex¬ 
press this coefficient as a more complex term with this ratio as a factor, 
but by what appears to be a peculiar coincidence, experiments show that 
for ordinary bank sand the variation in voids caused by different propor¬ 
tions may be provided for by taking the cement and sand together; in 
other words, for different proportions of the same cement and sand, the 
sum of the water and the air voids in the mortar is approximately a con¬ 
stant. Where there is no sand, or where the stone and sand are mixed, 
formula (i) must be employed. 

The more practical formula may be expressed as follows, employing 
similar notation to that given above, and letting 

r = ratio of the absolute volume of the water plus the air entrained in 
gaging, to the absolute volume of cement plus sand, 

then 

W 1i = c+s+r{c+s) + g+pg 

or 

Wi=(i + r) (c + s) + (i + p)g ( 2 ) 

♦Absolute volumes are defined on p. 135. 


QUANTITIES OF MATERIALS 


223 


Substituting average values for r and p, which the authors have selected 
by analyzing the results of a number of exact records in the United States 
and Europe of the volumes of concrete and mortar, the formula becomes 

w i = I -34 (c + s) + 1.08 £ (3) 

The comparison of this formula with actual experiments is shown on page 
227. The formula may be readily reduced to practical working form if 
the characteristics of the cement, sand, and stone are known. The cement 
may be expressed in pounds by substituting for the absolute volume, c, 
the number of pounds of cement divided by its specific gravity (which 
may be taken as 3.1) times the weight of a cubic foot of water (62.3 lb.). 
It may also be expressed in barrels by substituting for the absolute 
volume, c, the number of barrels, B , multiplied by the net weight per 
barrel, 376 pounds, and divided, as above, by the specific gravity times 
the weight of a cubic foot of water [see formula (4)]. The terms re¬ 
lating to sand and stone may be expressed in pounds in a way similar 
to that just shown for cement, or they may be expressed in measured 
volume by substituting for the absolute volume, j or g, the measured 
volume, S or C, multiplied by the proportion of solid material con¬ 
tained in it. Expressing this algebraically, if 

Q = quantity of concrete made with B barrels cement, 

Q x = quantity of concrete made with one barrel cement, 

B = number barrels cement, 

B x = number barrels cement per cubic yard of concrete, 

S = volume of loose sand in cubic feet, 

S 1 = volume of loose sand in cubic yards per cubic yard of concrete, 

G = volume of broken stone or gravel or cinders in cubic feet, 
v = absolute voids in sand determined by weight method (p. 166), 

v' = absolute voids in stone determined by weight method (p. 167), 

376 

then from formula (3), since c = B —--- 

3- 1 x 62.3 

Q = T, 34 X 376 ^ 4-1.34 (1 — v) S + 1.08 (1 — v f )G 

62.3 X 3 - 1 

Q = 2.61 B + 1.34 (1 — v) S + 1.08 (1 — v f ) G (4) 

The volume of concrete in cubic feet made by one barrel of cement, 
assuming that a cubic foot of average loose, moist sand contains 89 
• pounds of dry sand, and that its specific gravity dry is 2.65, is, 

Q t = 2.61 + 0.723 S + 1.08 (1 — v f ) G 


( 5 ) 




224 


A TREATISE ON CONCRETE 


This formula is applicable to average concrete made with Portland 
cement of good quality, coarse bank sand measured loose and containing 
ordinary moisture, and any broken stone or gravel of known voids. For¬ 
mula (5) has been used in compiling tables on pages 233 to 235, except in 
the first twelve proportions, which contain no sand. 

If the volume of concrete made from a barrel of cement plus the sand 
and other aggregate which accompanies it is known, the number of 
barrels of cement per cubic yard is readily calculated. In formula (5), 
Q x represents the number of cubic feet of concrete made with one 
barrel cement, hence the number of barrels cement per cubic yard of 
concrete is 27 divided by Q 1 




Assuming a cubic foot of average sand to contain 89 pounds of dry sand 
produces the formula employed in calculating tables on pages 230 to 232, 
and substituting in formula (6) the value of Q t from formula (5), 

27 

2.61 + 0.723 A + 1.08 (1 — v r ) G ^ 

The formulas may be expressed in parts by volume (such as 1:2:4) by 
multiplying the coefficient of S and G by the assumed volume of a barrel, 
say by 3.8. 

Knowing the number of barrels of cement, B l , per cubic yard of concrete, 
the number of cubic yards of sand per cubic yard of concrete, S v is 
evidently 

~ _ B x X quantity sand in cubic feet per barrel of cement 

Cq--- ; -- (8) 

2 7 

The quantity of stone is similarly obtained. 

If two or more coarse materials, such as broken stone and gravel, are 
used, they must be mixed in the selected proportions, before weighing, to 
determine their voids. 

In mortars of extremely fine sands the density (c + 5) is apt to be about 
0.60 (see Feret’s table, sand C, p. 136) and the coefficient of first term of 

1.00 

formula (3) becomes = 1.67 instead of 1.34. In plastic mortars 

of standard Ottawa sand the density (c + s), by tests of the authors, 

averages about 0.71, hence the coefficient becomes — ° Q = 1.41 instead of. 

0.71 

T.34. Substituting these values, or any others which may be obtained by 







QUANTITIES OF MATERIALS 


225 


experiment, in formula (2), the working formulas which follow it may be 
readily deduced. It is evident from the variation in the coefficient with 
different sands, that the variation in volume of mortar and concrete ob¬ 
tained by different experimenters is due chiefly to the difference in the 
materials employed. 

The coefficient of (c + s) is also affected, though to a less degree, by 
the character of the cement, some cements requiring more water than 
others and therefore producing a greater bulk of paste for a given weight 
of cement. 

In concrete mixtures of cement and coarse stone, with no sand or screen¬ 
ings, formulas (2) to ( 8 ) are inapplicable because apparently the air voids 
do not increase with the leanness of the mixture until the point is 
reached at which the paste fails to fill the voids in the stone. It is therefore 
necessary to go back to formula (1), page 222. Since 5 is zero, the formula 
becomes 

W 2 = (1 + m) c + (1 + p) g (9) 

An average value of (1 + m) for a first-class American Portland cement 
has been found by experiment to be 1.65. It varies with the quantity of 
water required to gage the cement to such a consistency that the voids will 
be filled, but no free water will exist upon the surface. The selected value, 
assuming 1% voids in the paste, corresponds to 20% of water by weight. 
The value of (1 — p) is usually 1.04 to 1.08. An average formula for a 
concrete of cement and coarse stone may thus be taken as 

W 2 = 1.65c + i.o8g (10) 

which is readily reduced to practical forms by the method adopted in 
evolving formulas (4) to (8) from formula (3). 

If the stone is a mixture of sand and gravel, or broken stone and screen¬ 
ings, the coefficient of g must be increased and a figure selected whose 
value depends upon the relative proportion of fine and coarse material. 

TABLES AND CURVES OF QUANTITIES OF MATERIALS AND 

VOLUMES 

Tables on pages 229 to 235 are calculated from formulas (5), (6), 
(8), and (9). These formulas are used not merely because of their 
theoretical worth, but because, as stated on pages 216 and 227, the 
results from them agree with actual experiment. 

The values are average values of sufficient exactness for practical 
ase, although, as suggested on pages 222 and 224, variations in the 


226 A TREATISE'ON CONCRETE 

quality of the materials largely affect the resulting volumes, especially 
of the mortar. 

The tables on pages 231 and 234 are recommended for general use 
in determining the quantities of materials for concrete, or the volume 
of concrete made with known materials, and where the percentage of 
voids in the coarse aggregate is unknown the 45% columns should be 
adopted. The curves on page 228 are also in convenient form for prac¬ 
tical use. 

All except the first item in the table on page 229 and the first 12 
items in tables on pages 230 to 235 are calculated from formulas (5), 
(6), and (8), page 223, with the assumption there outlined. The 
broken stone in the first twelve items in the concrete tables, pages 230 
to 235, except where the voids are 40% or over, is assumed to contain 
fine material, and the coefficient selected for g, formula (9), varies from 
1.08 for 50%, 45%, and 40% voids to 1.14 for 20% voids. , 

Use of Curves. The use of the curves on page 228 is best illus¬ 
trated by the following examples: 

Example 1. — Find quantities of materials required for 1 000 cubic 
yards 112^:5 concrete. 

Solution. — Intersection of dotted horizontal line corresponding to 
2\ barrels sand with dotted vertical line corresponding to 5 barrels 
stone falls on diagonal curve 1.30; hence, 1.30 barrels cement are 
required per cubic yard, or 1 300 barrels cement for 1 000 cubic yards 
concrete. From Note 4 of diagram 1300X0.141X2^=460 cubic 
yards sand will be required, and 1300X0.141X5 = 920 cubic yards 
stone required. 

Example 2. — Find number of barrels cement required for 1000 
cubic yards concrete in proportions one barrel cement to 9 cubic feet 
sand to 18 cubic feet stone. 

Solution. — Intersection of full cross section horizontal line corre¬ 
sponding to 9 cubic feet sand with vertical line for 18 cubic feet stone 
gives 1.37 barrels cement per cubic yard or 1 370 barrels for 1 000 
cubic yards concrete. 

Example 3. — Find volume of concrete of Example 1 made from one 
barrel of cement. 

Solution. — By Note 5 of diagram volume of concrete per barrel 
cement is 27 divided by the quantity of cement per cubic yard of con 

crete, or —— = 20.8 cubic feet. 

1.30 


QUANTITIES OF MATERIALS 


227 


Comparison of Table Values with Actual Experiments. Comparatively 

few experimenters have recorded complete data with reference to the ma¬ 
terials entering into their specimens of concrete and mortar. The most 
comprehensive records of this nature that have come to the knowledge of 
the authors are those by Mr. William B. Fuller,* which are tabulated in full 
•on page 258, his proportions ranging from 1:0 to 1:6:10. The actual 
volumes obtained by him, having been found to agree closely with 
other carefully made experiments, are used in the determination of the 
constants employed in the above formulas and in compiling the tables 
and curves on pages 228 to 235. Volumes calculated from the formulas 
employing these constants agree with Mr. Fuller’s tests with an average 
variation of 0.2 of 1% and a maximum variation of 6%. 

Other records which have been compared with results calculated by our 
formulas, and with which they usually agree within less than 5% after 
making allowance for different materials and units, are those by Messrs. 
George W. Rafter,f Edwin Thacher,| J. E. Howard,§ E. Candlot,|| and 
E. S. Wheeler,If C. A. Matcham,** E. S. Larnedff and Leonard Met¬ 
calf.yf 

Experiments by Mr. Edwin Thacher show the rammed volume of 
dry facing mortar (that is mortar mixed with a small proportion of 
water) to be about 12%, less than the volume of slush mortar made from 
the same materials, and the quantity of cement per cubic yard to be cor¬ 
respondingly greater for the dry mortar. 

The volume of mortar or concrete is affected by the character of the 
cement as well as by the sand and method of mixing, since some cements 
require more water and will make more paste to a unit weight of cement 
than others even of the same class. In one series of experiments, for ex¬ 
ample, 85 pounds of a certain first-class American Portland cement 
were required to make one cubic foot of paste, while for another 
standard American Portland cement of a different brand 107 pounds 
were required. Average values for wet or plastic mortars are given in 
the table on page 229. 

*See page 261. 

•j-Transactions American Society of Civil Engineers, Vol. XLII, p. 104. 

^Johnson’s “The Materials of Construction,” 1903, p. 610a. 

§Tests of Metals, U. S. A., 1899, p. 7 86. 

||Ciments et Chaux Hydrauliques, 1898, p. 446. 

^[Report Chief of Engineers, U. S. A., 1895, pp. 2922 to 2931. 

**Engineering Record, April 15, 1905, p. 434. 

ffPersonal Correspondence. 


228 


XI 

XI 

o 


X 


X 

_ l 

JO 

_ l 

X 


X 


0 

X 

X 

X 

X 

X 

X 

X 

X 

X 

X 

X 

•Hn 

X 

-l« 

X 

Hn 

X 

«-J<N 

X 

-JCM 

X 

X 

vO 

o 

10 

N- 

-t 

to 

ro 

CO 

CSI 

04 

o 

CN 

— 

— 

Hcm 

CN 




r- 






CJ 



"Tj ^ 

o 


to 


-d 
c i; 

pj 

OJ 

c 

c 

4^ 

a 

V 

cn vo 

4-) 

cfi 

B 


D 


T3 

(<N 

U 

C/J 5P 

B 

cd 

~a 

p| 

M-* *“• 

73 

a3 

ej 

£J 


a 

c3 

-4— > 

Ui 

u, OJ 
o £ 

C/} 

<4-4 

O 

O 

P4 

aj C 
£ 

+-> 

<u 

<l> 

*4-« 

«+H 

o 

C/} 

«J £ 

o 

"a 

u- 

a; 

O 

-Q 

M 

4—> 

£ -rj 
<V X 
c/i 5 
<U TO 

CJ 

-M 

a 

rO 

o 


X 

X 

X 

X 

X 

-Q XI 

X 

X 

X 

X 

X 

XI ja 

H«N 



CO 

H<n 

Cvl -l« 



co 

CN 

— 




•Id 

■no qnvs 3sooi 

























































































































































































































































































































































































































































































































































































































2 2Q 


MORTAR WITH ORDINARY COARSE BANK 


1 olume of Plastic Mortar and Quantities of Materials per Cubic Yard. 


SAND 

(See p. 226.) 




Volume of Compacted Plastic Mortar 



n 1. vrl. 




Relative 

propor- 







Materin 1«; for t 

nmmrt PlnQtir \1nrtsr 

from 1 

cu. ft. Cement 

from 

1 bbl. Cement 


Based on 

barrel of 


tions bv 













volume* 

Based on Portland 

Based on barrel 









Cement weighing 


of 


3-5 cu. ft. 

3.8 cu. rt.\ 

4 cu 

. ft. 




•b- 













• 

40 





q-i 


Ho 






3 

u 

U 

$3 

6 

u 


-t— 

So 


a 

0 

£ 

d 

_ 3 

73 Q) 

Q) 3 

73 

3 

3 

r + 

<D 

E 

V 


• 4 — > 

a 

V 

£ 

<D 

d 

a 

ri 

ft 

in 

00 

O 

O ° 
O Ri 
qj 

0 

ft 

in 

«*-« 

3 

U 

ko 

3 

O 

°° 

d 

O 

d 

0 

a 

C/I 

0 

r. 

r 

S 

O 

O 

u 

d 

^4 

a 

C 

~ 

m 

0 

C /5 

8 

u 

C/I 

M 


ft 


fo 


ft 

►3 


0 

t-H 




cu. ft. 

cuJt. 

cu. ft. 

cu. ft. 

cu.ft. 

cu. ft. 

bbl. 

cu. vd. 

' 

bbl. 

CU . 

yd. 

bbl. 

cu. yd. 

1 

0 

o -93 

0.86 

0.80 

3-2 

3-2 

3-2 

8.31 


8.31 


8.31 


1 

JL 

2 

1.12 

1.06 

1.02 

3-9 

4.0 

4.1 

6.92 

0.46 

6.73 

0.47 

6.61 

0.49 

1 

I 

1.48 

1.42 

1.38 

5-2 

5-4 

5-5 

5.22 

0.68 

5 -oi 

0.71 

4.88 

0.72 

1 

ii 

1.84 

1.78 

1.74 

6.4 

6.7 

7.0 

4.20 

0.81 

4.00 

0.84 

3-87 

0.86 

I 

2 

2.20 

2.14 

2.11 

7-7 

8.r 

8.4 

3 - 5 i 

O.9I 

3-32 

0.93 

3.21 

0.0/ 

1 

22 

2.56 

2.50 

2.47 

9.0 

9-5 

9.9 

3.01 

0.98 

2.84 

1.00 

2.74 

1 01 

I 

3 , 

2.92 

2.86 

2.83 

10.2 

IO.9 

11 -3 

2.64 

1.03 

2.48 

1.05 

2-39 

1.06 

I 

32 

3.28 

3 -23 

3-19 

11 -5 

12.2 

12.8 

2-35 

1.06 

2.20 

1.08 

2.1 2 

I.IO 

1 

i 

3-64 

3-59 

3-55 

12.8 

13.6 

14.2 

2.12 

I.IO 

1.98 

1.11 

I.9C 

I-I 3 

X 

4 b 

4.01 

3-95 

3-91 

14.0 

15.0 

15.6 

1.92 

1.12 

1.80 

1.14 

1.72 

I-I 5 

I 

5 

4-37 

4-31 

4.28 

153 

16.4 

17.1 

1-77 

iiS 

1.65 

I.l6 

1.58 

1.17 

I 

si 

4-73 

4.67 

4.64 

16.6 

17-7 

18.5 

1.63 

I.l6 

1-52 

I.l8 

1.46 

1.19 

I 

6 

5-09 

5 03 

5.00 

17.8 

19.1 

20.0 

1.52 

1.18 

1.41 

1.19 

i -35 

1.20 

I 

£)b 

5-45 

5-39 

5-36 

19.1 

20.5 

21.4 

1.41 

1.19 

1.32 

1.2 I 

T .26 

1.21 

I 

7 

5.81 

5.76 

5-72 

20.3 

21.9 

22.9 

i -33 

1.21 

1.23 

1.21 

I.l8 

1.22 

I 

72 

6.18 

6.7 

6.08 

21.6 

23.2 

24-3 

1.25 

1.21 

1.16 

1.22 

I. I I 

1.23 

I 

8 

6.S4 

6.48' 

6.44 

22.9 

24.6 

25.8 

I.l8 

T .22 

I .TO 

1.24 

1.0, 

T.24 


Note. — Variations in the fineness of the sand and the cement, and in the consistency of the mortar 
may affect the values bv to% in either direction. 

*C.ement as packed hv manufacturer. sand loose, 

t Use these columns ordinarily. 

MORTAR WITH VERY FINE SAND 

Volume of Plastic Mortar and Quantities of Materials per Cubic Ya'd. (See p. 226.) 


Relative 
propor¬ 
tions l y 


Volume of Compacted Plastic Mortar 


Materials for 1 cu. yd. Compact Plastic 


c 

CJ 

£ 

4J 

o 


m 


1 
1 
1 

1 2 




1 2^ 

1 3 

1 3 b 
1 4 


4 i 

5 

5 h 
6 " 


from 1 

cu. ft. Cement 

from 1 bbl. Cement 

Mortar Based on barrel of 

1 

Based on Portland 
Cement weighing 

Based on barrel 
of 

I 3.5 cu. ft. 

3.8 cu. ft. f 

4 cu. ft. 

108 lbs. per cu. ft. 

2 

ft 

CD 

0 

0 

** 

O 

O 

DO 

jO 

LO 

4 —> 

V 

iO 

CO 

d— 

8 

4 cu. ft. 

Packed Cement 

Loose Sand 

Packed Cement 

1 

Loose Sand 

Packed Cement 

d 

r: 

m 

0 

■ 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

bbl. 

cu. yd. 

bbl. 

cii.yd. 

b jl. 

u. yd. 

1.26 

1.19 

1. i 5 

4.4 

. 

4.D 

4.6 

6.16 

0.40 

6.01 

0.42 

, 

D . 9 I 

0.44 

1.62 

i .56 

1. 5 1 

5 .7 

5 .9 

6.0 

4. 78 

0.62 

4. 59 

o .65 

4.40 

0.66 

1.98 

1.92 

1.88 

6.9 

7-3 

7.5 

3-79 

0. 76 

3-72 

0.78 

3.61 

0.80 

2.35 

2.28 

2.24 

8.2 

8.6 

8.9 

3-29 

o .85 

3-12 

0.88 

3-02 

0.90 

2.71 

2 .65 

2. 5 1 

9.5 

10.0 

10.4 

2 .85 

0.92 

2.69 

0.95 

2.60 

0.96 

3.08 

3 -oi 

2.97 

10.8 

11.4 

11.8 

2. 5 1 

0.98 

2.37 

1.00 

2.28 

1.01 

3-44 

3.38 

3-33 

12.0 

12.8 

13-3 

2.24 

1.02 

2. 11 

1.04 

2.03 

1. o 5 

3.80 

3-74 

3-70 

13-3 

14.2 

14.8 

2.03 

1 • 03 

1.90 

1.07 

I.83 

1.08 

4.17 

4.10 

4.06 

14.6 

1 5.6 

16.2 

i .85 

1.08 

1.74 

1. 10 

I . 67 

1.11 

4.03 

4-47 

4-43 

ID .9 

16.9 

17-7 

1. 70 

I.IO 

1.59 

1. 12 

1.03 

i-13 

4.90 

4-33 

4-79 

17 . I 

18.3 

19. 1 

1.58 

1.12 

1-47 

1. 14 

1.41 

1. i 5 

5 .26 

5 .20 

5 .1 5 

18.4 

19.7 

20. 6 

1.47 

1.14 

i -37 

1. 16 

1. 3 i 

1 .17 


* Cement as packed by manufacturer, sand loose, 
t Use these columns ordinarily. 




























































































230 


Quantities of Materials for One Cubic Ya-rd of Rammed Concrete 
Based on a Barrel of 3.5 Cubic Feet. 

(See important foot-notes, also p. 225.) 


PROPOR¬ 

TIONS 

BY PARTS 

PROPOR¬ 

TIONS 

BY VOLUMES 

V olumeof mortar 

in terms of per¬ 

centage of vol¬ 
ume of stone 



PERCENTAGES 

OF VOIDS 

IN BROKEN STONE 

OR GRAVEL 


!>•>%* 

45%t 

40%t 

3 °% § 

20 %§ 

•*-* 

C 

V 

6 

0 

u 

T3 

d 

CtJ 

co 

d 

0 

in 

■0 c 

jij y 

0 £ 
rt <u 

§ 5 

co 

to g 
§ § 
-4co 

-+-» 

a 

<u 

a 

CD 

O 

*"d 

d 

G 

c n 

4) 

0 

0 

-*-» 

CO 

0 ) 

£ 

4) 

O 

d 

G 

C/3 

<0 

a 

0 

-*-» 

CO 

4—* 

G 

<D 

£ 

u 

T3 

g 

g 

m 

§ 

0 

in 

4—* 

d 

<D 

£ 

1 

U 

q 

d 

CO 

d 

0 

4-» 

CO 

-4 -> 

d 

oj 

£ 

<D 

U 

"d 

G 

g 

in 

O 

G 

O 

in 

bbl. 

cu. 

ft. 

cu. 

ft. 

% 

bol 

cu. 

yd. 

cu. 

yd. 

bbl 

cu 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd 

bbl 

cu. 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

I 


1 

I 


3-5 

101 

5-25 


0.68 

5-07 


0.66 

4.89 


0.63 

4-51 


0.58 

4.19 


o -54 

X 


2 

1 


7.0 

54 

3-84 


1.00 

3-64 


0.94 

3-47 


0.90 

3-09 


0.80 

2.80 


0.73 

1 


3 

1 


10.5 

39 




2.85 


1.11 

2.69 


1.05 

2-35 


0.91 

2.10 


0.82 

I 


4 

1 


14.0 

3 i 










x.90 


0.99 

1.69 


o .83 

X 


s 

1 


1 7-5 

27 










1 -59 


1.03 

1 41 


c.91 

I 


6 

1 


21.0 

24 










i -37 


1.07 

1.21 


0.94 

I 


7 

1 


24-5 

21 













1.06 


0.96 

I 


8 

1 


28.0 

20 













0.94 


0.98 

I 


9 

1 


3 i -5 

18 













0.84 


0.98 

I 


10 

1 


35 -° 

17 













0.77 


1.00 

I 


11 

1 


38.5 

16 













0.70 


I.OO 

I 


12 

1 


42.0 

16 













0.65 


1.01 

I 

1 

lit 

1 

3-5 

S -2 

104 

3-37 

0.44 

0.65 

3.26 

0.42 

0.63 

3-15 

0.41 

0.61 

2-95 

0.38 

o -57 

2.78 

0.36 

0.54 

I 

1 

2 

1 

3-5 

7.0 

78 

3.02 

0.39 

0.78 

2.89 

c.38 

0.75 

2.78 

0.36 

0.72 

2.58 

o -33 

0.67 

2.41 

0.31 

0.62 

I 

1 

2 i 

1 

3-5 

8.7 

64 

2-73 

o -35 

0.88 

2.60 

o -34 

0.84 

2.49 

0.32 

0.80 

2.29 

0.30 

0.74 

2.12 

0.28 

0.68 

I 

1 

3 

1 

3-5 

IO.5 

54 

2.49 

0.32 

0.97 

2-37 

0.31 

0.92 

2.25 

0.29 

0.88 

2.06 

0.27 

0.80 

1.90 

0.25 

0.74 

I 

12 

2 

X 

5-2 

7.0 

95 

2.64 

0.51 

0.68 

2-55 

0.49 

0.66 

2.46 

0.47 

0.64 

2.30 

0.44 

0.60 

2.16 

0.42 

0.56 

I 

i* 

2 i 

1 

5-2 

8-7 

78 

2.42 

0.47 

0.78 

2.32 

o -45 

0.75 

2.23 

o -43 

0.72 

2.07 

0.40 

0.67 

1-93 

0.37 

0.62 

I 


3 

1 

S -2 

IO.5 

65 

2.23 

o -43 

0.87 

2.13 

0.41 

0.83 

2.04 

o -39 

0.79 

1.88 

0.36 

0.73 

1.74 

0.34 

0.68 

I 

12 

32 

1 

5-2 

12.2 

56 

2.07 

0.40 

0.94 

x.97 

0.38 

0.89 

1.88 

0.36 

0.85 

1.72 

o -33 

0.78 

i -59 

0.31 

0.72 

I 


4 

X 

5-2 

14.0 

SO 

i -93 

0-37 

I.OO 

1.83 

o -35 

o -95 

1.74 

o -34 

0.90 

1-59 

0.31 

0.82 

1.46 

0.28 

0.76 

I 


4 i 

I 

S-2 

iS -7 

45 

1.81 

o -35 

x.05 

1.71 

o -33 

0.99 

1.62 

0.31 

0.94 

1.47 

0.28 

0.86 

i -35 

0.26 

0.78 

I 

1 i 

5 

I 

S-2 

I 7 -S 

4 i 

1.70 

o -33 

1.10 

1.60 

0.31 

1.04 

1.52 

0.29 

0.99 

i -37 

0.26 

0.89 

1.25 

0.24 

0.81 

I 

2 

3 

I 

7.0 

10.5 

77 

2.02 

0.52 

0.79 

1.94 

0.50 

0-75 

1.86 

0.48 

0.72 

i -73 

o -45 

0.67 

1.61 

0.42 

0.63 

I 

2 

3 i 

I 

7 -o 

12.2 

67 

1.89 

0.49 

0.85 

1.80 

0-47 

0.81 

i -73 

o -45 

0.78 

i -59 

0.41 

0.72 

1.48 

0.38 

0.67 

I 

2 

4 

I 

7.0 

14.0 

59 

1.77 

0.46 

0.92 

1.69 

0.44 

0.88 

1.61 

0.42 

0.83 

1.48 

0.38 

0.77 

i -37 

o -35 

0.71 

I 

2 

42 

I 

7.0 

15-7 

53 

1.67 

o -43 

0.97 

1.58 

0.41 

0.92 

I * 5 I 

o -39 

0.88 

1.38 

0.36 

0.80 

x 27 

o -33 

0.74 

I 

2 

5 

I 

7.0 

1 7-5 

48 

i -57 

0.41 

1.02 

1.49 

0-39 

0-97 

1.42 

0-37 

0.92 

1.29 

°-33 

0.84 

1.18 

0.31 

0.76 

I 

2 

si 

I 

7.0 

19.2 

44 

1.49 

o -39 

1.06 

1.41 

0.36 

I.OO 

1 -34 

o -35 

0-95 

1.21 

0.31 

0.86 

1.11 

0.29 

0.79 

I 

2 

6 

I 

7 -o 

21.0 

4 i 

1.42 

0.37 

1.10 

1-34 

0-35 

1.04 

x.27 

0-33 

0.99 

1.14 

0.30 

0.89 

1.04 

0.27 

0.81 

I 

^2 

3 

I 

8-7 

10.5 

90 

1.84 

o -59 

0.72 

1.78 

0-57 

0.69 

1.71 

o -55 

0.66 

1.60 

0.52 

0.62 

1.50 

0.48 

0.58 

I 

2 i 

3 i 

I 

8.7 

12.2 

78 

i -73 

0.56 

0.78 

1.66 

o -53 

0-75 

1.60 

0.52 

0.72 

1.48 

0.48 

0.67 

1.38 

0.44 

0.62 

I 

2 ? 

4 

I 

8.7 

14.0 

68 

1.63 

0.52 

0.85 

x- 5 b 

0.50 

0.81 

1-50 

0.48 

0.78 

1.38 

0.44 

0.72 

1.28 

0.41 

0.66 

I 

2\ 

4 i 

I 

8-7 

15-7 

61 

i -55 

0.50 

0.90 

1.47 

0.47 

0.86 

1.41 

0.45 

0.82 

1.29 

0.42 

o -75 

1.20 

o -39 

0.70 

I 

2\ 

5 

I 

8-7 

17-5 

55 

1.47 

0.47 

0.95 

i -39 

o -45 

0.90 

i -33 

0.43 

0.86 

1.22 

o -39 

0.79 

1.12 

0.36 

0.73 

I 

2i 

si 

I 

8-7 

19.2 

5 i 

i -39 

o -45 

0.99 

x -32 

0.42 

0.94 

1.26 

0.41 

0.90 

i-iS 

0-37 

0.82 

1.06 

o -34 

o -75 

I 

2i 

6 

I 

8.7 

21.0 

47 

i -33 

o -43 

1.03 

1.26 

0.41 

0.98 

1.20 

o -39 

0-93 

1.09 

0-35 

0.85 

1.00 

0.32 

0.78 

I 

2\ 

6i 

T 

8-7 

22.7 

44 

1.27 

0.41 

1.07 

1.20 

o -39 

1.01 

1.14 

0-37 

0.96 

1.03 

o -33 

0.87 

0.94 

0.30 

0.79 

I 

2i 

7 

1 

8.7 

24-5 

4 i 

1.22 

0-39 

1.11 

I.I5 

0-37 

1.04 

1.09 

o -35 

0.99 

0.98 

0.32 

0.89 

0.90 

0.29 

0.82 

I 

3 

4 

X 

10.5 

14.0 

77 

1.52 

0-59 

0.79 

1.46 

o -57 

0.76 

1.40 

o -54 

o .73 

1-30 

0.50 

0.67 

1.21 

0.47 

0.63 

I 

3 

4 i 

I 

10.5 

15-7 

69 

1.44 

0.56 

0.84 

1.38 

o -54 

0.80 

1.32 

0.51 

0.77 

1.22 

0.47 

0.71 

1.13 

0.4V 

o .56 

I 

3 

S 

I 

10.5 

17-5 

62 

i -37 

o -53 

0.89 

1 - 3 i 

0.51 

0.85 

1.25 

0.48 

0.81 

i-iS 

0-45 

o -75 

1.07 

0.42 

0.69 

I 

3 

si 

I 

10.5 

IQ.2 

57 

I -31 

0.51 

o -93 

x.25 

0.4& 

0.89 

1.19 

0.46 

0.85 

x.09 

0.42 

0.78 

1.01 

°-39 

0.72 

I 

3 

6 

I 

10.5 

21.0 

53 

1-25 

0.48 

0 97 

1.19 

0.46 

o -93 

I-I 3 

0.44 

0.88 

1.03 

0.40 

0.80 

0.95 

o -37 

0.74 

I 

3 

62 

I 

10.5 

22.7 

49 

T.20 

0.47 

x.ox 

1.14 

0.44 

0.96 

1.08 

0.42 

0.91 

0.98 

0.38 

0.82 

0.90 

o -35 

0.76 

I 

3 

7 

I 

10.5 

24-5 

46 

i-i 5 

o -45 

1.04 

1.09 

0.42 

0-99 

x.03 

0.40 

0-93 

0.94 

0.36 

0.85 

0.86 

o -33 

0.78 

I 

3 

7 i 

X 

10.5 

26.2 

43 

1.11 

0.43 

1.08 

1.05 

0.41 

1.02 

0.90 

0.38 

0.96 

0.90 

o -35 

0.87 

0.82 

0.32 

0.80 

I 

3 

8 

I 

10.5 

28.0 

40 

1.06 

0.41 

1.10 

1.01 

o -39 

1.05 

o -95 

0-37 

0.99 

6.86 

o -33 

0.89 

0.78 

0.30 

c.81 

I 

4 

S 

I 

14.0 

17-5 

77 

1.22 

o.6j 

'■’•79 

1.17 

0.61 

0.76 

1.12 

0.58 

o -73 

1.04 

o -54 

0.67 

0.97 

0.50 

0.63 

I 

4 

6 

I 

14 0 

21 0 

65 

T.12 

0.58 

0.87 

1.07 

o -55 

0.83 

1.02 

o -53 

0.79 

0.94 

0.49 

o -73 

0.87 

0-45 

0.68 

I 

4 

7 

I. 

14.0 

24-5 

56 

1.04 

o -54 

0.94 

0.99 

0.51 

0.90 

0.94 

o -49 

0.85 

0.86 

0.44 

0.78 

0.80 

0.41 

0-73 

I 

4 

8 

I 

14.0 

28 0 

50 

o -97 

0.50 

1.ox 

0.92 

0.48 

0-95 

0.87 

o -45 

0.90 

0.80 

0.41 

0.83 

0-73 

0.38 

0.76 

I 

4 

9 

I 

14-0 

31-5 

45 

0.91 

0.47 

1.06 

0.86 

0.44 

1.00 

0.81 

0.42 

0.94 

0-74 

0.38 

0.86 

0.68 

o -35 

0.79 

I 

4 

10 

I 

14.O 

35-0 

4 i 

0.85 

0.44 

1.10 

0.81 

0.42 

1.05 

0.76 

o -39 

0.98 

0.69 

0.36 

0.89 

0.63 

o -33 

0.82 

I 

5 

10 

I 

17-5 

3 S-o 

48 

0.79 

0.51 

1.02 

0-75 

0.49 

0.97 

0.71 

0.46 

0.92 

0.65 

0.42 

0.84 

o -59 

0.38 

0.76 

I 

6 1 

12 

I 

21.0 

42.0 

46 

0.67 

0.52 

1.04 

0.63 

0.49 

0.98 

0.60 

0.47 

o -93 

0-54 

0.42 

0.84 

0.50 

0-39 

0.78 


Note. — Variations in the fineness of the sand and the compacting of the concrete may affect the quantities 
by 10% in either direction. 

*Use 50% columns for broken stone screened to uniform size. 

tUse 45% columns for average conditions and for broken stone with dust screened out. 

JUse 40% columns for gravel or mixed stone and gravel. 

§Use these columns for scientifically graded mixtures. 
































































































Cement 


231 


USE THIS TABLE ORDINARILY. 


Quantities of I,Materials for One Cubic Yard of Rammed Concrete. 
Based on a Barrel of 3.8 Cubic Feet. 

(See important foot-notes, also p. 225.) 


propor¬ 

tions 

BY PARTS 


13 

fl 

cj 

CO 


4 ) 

1 

o 

CO 


I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 

1 2 

I 2§ 


i I 3 

1 ii 2 

1 ij 2 \ 


I 

T 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

J 


ii 
ii 
11 

I* 

2 

2 

2 

2 

2 

2 

2 

2 b 

2-j 

2 ^ 


3 


3 i 


4 

4 i 

5 

3 

3 1 

4 

4 * 

5 

5 * 

6 

3 

32 

4 


1 

T 

I 


2S 
21 


4 i 

5 

5^ 


1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 


*4 

25 

2 i 

3 

3 

3 

3 

3 

3 

3 

3 

3 

4 
4 
4 

4 

4 

4 

5 

6 I 


6 

6i 

7 

4 

4 a 

5 

5 * 

6 

61 

7 


5 

6 

7 

8 

9 

ic 

10 
12 


PROPOR¬ 

TIONS 

BY VOLUME 

Volume of mortar 

in terms of per¬ 

centage of vol¬ 
ume of stone 

PERCENTAGES OF VOIDS IN BROKEN STONE OR CRAVEL 

50 %* 


45 % t 

40% J 

30% § 

20% § 

Packed 

Cement 

Loose 

Sand 

Loose 

Stone 

Cement 

-o 

c 

a 

co 

i> 

a 

0 

CO 

Cem’nt 

Sand 

Stone 

Cement 

13 

a 

d 

CO 

a; 

a 

0 

-*-■ 

CO 

Cement 

c 

a 

CO 

0 

c 

0 

tn 

Cement 

T 3 

G 

CJ 

CO 

e 

0 

CO 

bbl 

cu. 

ft. 

cu. 

ft. 

% 

bbl 

cu. 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

1 


3-8 

94 

5-09 


0.72 

4.90 


0.69 

4-73 


0.67 

4-33 


0.61 

4.02 


0-57 

1 


7-0 

51 

3-67 


1-03 

3.48 


0.98 

3-3 0 


0-93 

2-93 


0.82 

2.65 


0-75 

1 


11.4 

36 




2.69 


1.14 

2-54 


1.07 

2.22 


0.94 

1.98 


0.84 

I 


15.2 

29 










1.78 


I.OO 

1.58 


089 

1 


I Q.O 

25 










1.40 


1.03 

i- 3 i 


0.92 

1 


22.8 

22 










i.28 


1.08 

1.12 


o -95 

1 


26.6 

20 













0.98 


0.97 

1 


30.4 

19 













0.87 


0.98 

1 


34-2 

18 













0.78 


0.99 

1 


38.0 

17 













0.71 


1.00 

I 


41.8 

16 













0.65 


I.OI 

I 


45-5 

15 













0.60 


I.OI 

1 

3-8 

5-7 

99 

3-19 

0.45 

0.67 

3.08 

0.43 

0.65 

2.97 

0.42 

0.63 

2.78 

o -39 

0.50 

2.62 

0.37 

0.55 

1 

3-8 

7-6 

75 

2.85 

0.40 

0.80 

2.73 

0.38 

0.77 

2.62 

0.37 

0.74 

2-43 

o -34 

0.68 

2.26 

0.32 

0.64 

1 

3-8 

9-5 

61 

2-57 

0.36 

0.90 

2.45 

0.34 

0.86 

2-34 

o -33 

0.82 

2.15 

0.30 

0.76 

1.99 

0.28 

0.70 

1 

3-8 

11.4 

51 

2-34 

033 

0.99 

2.22 

0.31 

0.94 

2.12 

0.30 

0.90 

1-93 

0.27 

0.82 

1.77 

0.25 

0.75 

1 

5-7 

7.6 

93 

2.49 

0.53 

0.70 

2.40 

0.51 

0.68 

2.31 

0.49 

0.65 

2.16 

0.46 

0.61 

2.03 

0.43 

0.57 

1 

5-7 

9-5 

76 

2.27 

0.48 

0.80 

2.18 

0.46 

0.77 

2 . 0 Q 

0.44 

0.74 

1.94 

0.41 

0.68 

1.80 

0.38 

0.63 

I 

5-7 

11.4 

64 

2.09 

0.44 

0.88 

2.00 

0.42 

0.84 

1.01 

0.40 

0.81 

1.76 

0-37 

0.74 

1.63 

0.34 

0.69 

1 

5-7 

T 3-3 

55 

1.94 

0.41 

0.96 

1.84 

0.39 

0.91 

1.76 

0-37 

0.87 

T.61 

o -34 

0.79 

1.48 

0.3^0.73 

1 

5-7 

15.2 

49 

1.80 

0.38 

1.01 

1.71 

0.36 

0.96 

1.63 

0-34 

0.92 

T.48 

0.31 

0.83 

1-36 

0.29 0.77 

I 

5-7 

17.1 

44 

1.69 

0.36 

1.07 

1.60 

0.34 

1.01 

1.51 

0.32 

0.96 

i -37 

0.29 

0.87 

1.25 

0.26 0.79 

1 

5-7 

19.0 

40 

1.59 

0.34 

1.12 

1.50 

0.32 

1.06 

1.42 

0.30 

1.00 

1.28 

0.27 

0.90 

1.17 

0.25 

0.82 

I 

7.6 

TI.4 

75 

1.89 

0-53 

0.80 

1.81 

0.51 0.76 

1.74 

0.49 

0.74 

1.61 

0-45 

0.68 

1.50 

0.42-0.63 

I 

7.6 

13-3 

65 

1.76 

0.49 

0.87 

1.68 

0.47 0.83 

1.61 

0-45 

0.79 

1.48 

0.42 

0-73 

1.38 

0.30 

0.68 

1 

7.6 

T5.2 

57 

T.65 

0.46 

0-93 

1.57 

0.44 0.88 

1.50 

0.42 

c.84 

1.38 

0.39 

0.78 

1.27 

0.36 

0.72 

I 

7.6 

17.1 

5 i 

i -55 

0.44 

0.98 

1.48 

0.42 0.94 

1.41 

0.40 

0.89 

1.28 

0.36 

0.81 

1.18 

0.33 

0-75 

1 

7.6 

19.0 

47 

1.47 

0.41 

1.03 

1.39 

0.39 

0.98 

1.32 

0-37 

0-93 

1.20 

0-34 

0.84 

1.10 

0.31 

0.77 

1 

7 6 

20.9 

43 

i -39 

0.39 

1.08 

1 . 3110.37 

1.01 

1-25 

0-35 

0.97 

3 

0.32 

0.87 

1.03 

0.29 

0.80 

1 

7.6 

22.8 

40 

1.32 

0.37 

1.11 

1.25 

0.35 

1.06 

1.18 

0-33 

i.00 

1.06 

0.30 

0.89 

0.97 

0.27 0.02 

1 

9-5 

IT.4 

87 

1.72 

0.61 

0.73 

1.66 

0 . 5810.70 

1.60 

0.56 

0.68 

1.49 

0.52 

0.63 

1.40 

0.49 

0.59 

1 

9-5 

13-3 

75 

1.62 

0.57 

0.80 

1.55 

0.55 0.76 

1.49 

0.52 

0.73 

1.38 

0.49 

0.68 

I. 2 Q 

0.450.64 

I 

9-5 

15.2 

66 

1.52 

0.54 

0.86 

1.46 

0.51 0.82 

1.4c 

0.49 

0.79 

1.29 

0-45 

o -73 

1.19 

0.42 

0.67 

I 

9-5 

17.1 

60 

1.44 

0.51 

0.91 

1.37 

0.48 0.87 

I- 3 I 

0.46 

0.83 

1.20 

0.42 

0.76 

I.IT 

0.39 0.70 

1 

9-5 

19.0 

54 

i -37 

0.48 

0.06 

1.30 0.46 0.92 

I.24 

0.44 

0.87 

V13 

0.40 

0.80 

1.04 

0.37 0.73 

I 

9-5 

20.9 

49 

1.30 

0.46 

I.OI 

1.23 0.43 

0.95 

1.17 

0.41 

0.91 

1.07 

0.38 

0.83 

0.98 

0.340.76 

I 

9-5 

22.8 

46 

1.24 

0.44 

1.05 

1.17 0.41 

0.99 

1.11 

0-39 

0.94 

I.OI 

0.36 

0 85 

0.92 

0.32 

0.78 

1 

9-5 

24.7 

42 

1.18 

0.42 

1.08 

1.12 0.39 

1.02 

1.06 

0-37 

0.97 

0.96 

0-34 

0.88 

0.88 

0.31 

0.80 

I 

9-5 

26.6 

40 

I-I 3 

0.40 

1.11 

1 - 07 1 0.38 

1.05 

I.OI 

0.36 

0.99 

0.91 

0.32 

0.90 

0.83 

0.20 

0.82 

T 

11.4 

iS-2 

76 

1.42 

0.60 

0.80 

1.36 0.57 

0.77 

1.30 

o -55 

0-73 

1.21 

0.51 

0.68 

1.12 

0.47 

0.63 

1 

11.4 

17.1 

68 

i -34 

0.57 

0.85 

1.28 0.54 0.81 

1-23 

0.52 

0.78 

i-i 3 

0.48 

0.72 

1.05 

0.44 

0.66 

1 

11.4 

19.0 

61 

1.28 

o -54 

0.90 

1 . 22 i 0.52 0.86 

1.17 

0.49 

0.82 

1.07 

0-45 

0-75 

0.99 

0.42 0.70 

1 

11.4 

20.9 

56 

1.22 

0.52 

0.94 

1.16 0.49 0.90 

I.I I 

0.47 

0.86 

I.OI 

0-43 

0.78 

0.93 

0.39 0.72 

1 

11.4 

22.8 

52 

1.16 

0.40 

0.98 

1.11 0 . 47 | 0.94 

T.05 

0.44 

0.89 

0.96 

0.41 

0.81 

0.88 

0.37 0.74 

I 

IJ.4 

24.7 

48 

1.12 

0.47 

1.02 

1 . 00 , 0.45 

0.97 

I.OI 

0-43 

0.92 

0.92 

0-39 

0.84 

0.84 

0.35,0.77 

1 

11.4 

2O.6 

45 

1.07 

0-45 

1.05 

1 . 0 L 0.43 

0.99 

0.96 

0.40 

0-95 

0.87 

0-37 

0.86 

0.80 

0.34 0.79 

I 

11.4 

28.5 

42 

T .O'? 

0.44 

I.OQ 

0.97 0.41 

1.02 

0.92 

o -39 

0.97 

0.83 

0-35 

0.88 0.76 

0.32 

0.80 

I 

11.4 

30.4 

40 

0.99 

0.42 

T.I I 

0.93 0.39 

1.05 

0.88 

0.37 

0.99,0.80 

0-34 

0.90.0.73 

0.31 

0.82 

1 

15.2 

19.0 

76 

1.13 

0.64 

O.80 

1.08 0.61 

0.76 

1.04 

0-59 

0 73*0.06 

0.54 

0.68 

0.90 

0.51 

0.63 

1 

I 3.2 

22.8 

64 

1.04 

0-59 

0.88 

0 99 0.56 0.84 

0.95 0.54 

0.80.0.87 

0.49 

0.73 0.81 

0.46 0.68 

1 

15.2 

26.6 

55 

0.96 

0-54 

0-95 

0 . 92 i 0.52 0.91 

0.88 

0.50 

0.87 

0.80 

0-45 

0 . 79 , 0.74 

0.42 0.73 

i 

15.2 

30.4 

49 

0.90 

0.51 

I.OI 

0.85 0.48 0.96 

0.81 

0.46 

0.91 

0.74 

0.42 

0.83 

0.68 

0.38 0.77 

1 

15-2 

34-2 

44 

O.84 

0.47 

1.06 

0 80 0.45 

1.01 

0.76 

0.43 

0.96 

0.68 

0.38 

0.86 

0.63 

0.35 ! 0.80 

1 

15-2 

38.0 

40 

O 79 

0.44 

1.11 

0 . 75 , 0.42 

1.06 

0.71 

0.40 

1.00 

0.64 

0.36 

0.90 

0.58 

0.33J0.82 

1 

IQ.O 

38.0 

47 

O.73 

0.52 

1.03 

0.69 0.49 0.97 

0.66 0.46 

o -93 

0.60 

o.42'o.84 

0-55 

0.39 

0.77 

! 1 

2 2.8 

45-5 

46 

0.62 

0.52 

1.04 JO.68 0 . 49 , 0.98 

,0.56 0.47 

0.94 io.50 

0.42 io.84 

0.46 

0.3910.78 


Note. — Variations in the fineness of the sand and the compacting of the concrete may affect the quantities by 
10% in either direction. 

♦Use 50% columns for broken stone screened to uniform size. 

f Use 45 % columns for average conditions and for broken stone with dust screened out. 
jlJse 40% columns for gravel or mixed stone and gravel. 

§Use these columns for scientifically graded mixtures. 































































































% 


2 3 2 

Quantities of Material for One Cubic Yard of Rammed Concrete. 
Based on a Barrel of 4 Cubic Feet. 


(See important foot-notes, also p. 225.) 


PROPOR¬ 

TIONS 

BY PARTS 

PROPOR¬ 

TIONS 

BY VOLUMES 

Volume of mortar 

in terms of per¬ 

centage of vol¬ 
ume of stone 

PERCENTAGES OF VOIDS IN BROKEN STONE OR GRAVEL 

5 °%* 

45 %t 

4 °%t 

3 °%§ 

20%§ 

Cement 

T 3 

0 

d 

c n 

<u 

a 

0 

c /5 

Packed 

Cement 

Loose 

Sand 

Loose 

Stone 

Cement 

"T 3 

fl 

ClJ 

CO 

<D 

0 

0 

-*-> 

m 

Cement 

T 3 

0 

d 

r n 

<u 

c 

0 

■*-> 

CO 

Cement 

*0 

0 

d 

in 

<D 

0 

O 

in 

Cement 

"O 

0 

d 

in 

0 

c 

0 

c /5 

Cement 

"O 

a 

CO 

0 

a 

0 

CO 

bbl 

cu. 

ft. 

cu. 

ft. 

% 

bbl 

CU. 

yd. 

cu. 

yd 

bbls 

cu. 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

bbl 

cu 

yd. 

cu. 

yd. 

bbl 

cu. 

yd. 

cu. 

yd. 

I 


I 

I 


4 

89 

4.90 


0.74 

4.80 


0.71 

4.62 


0.69 

4-23 


0.63 

3 - 9 i 


0.58 

I 


2 

1 


8 

49 

3-57 


1.06 

3-37 


1.00 

3.20 


0.95 

2.84 


0.84 

2.56 


0.76 

I 


3 

1 


12 

35 




2.60 


1.16 

2-45 


1.09 

2.13 


o -95 

1.90 


0.84 

I 


4 

1 


l6 

28 










1.71 


I.OI 

i- 5 i 


0.89 

I 


5 

I 


20 

24 










i -43 


1.06 

1.26 


o -93 

I 


6 

1 


24 

22 










1.22! 


1.08 

1.07 


0-95 

I 


7 

I 


28 

20 













0.94 


0.98 

I 


8 

1 


32 

18 













0.83 


0.98 

I 


9 

I 


36 

17 













0.75 


1.00 

I 


10 

1 


40 

16 













0.68 


I.OI 

I 


II 

I 


44 

15 













0.62 


I.OI 

I 


12 

I 


48 

15 













0-57 


I.OI 

I 

1 

ii 

I 

4 

6 

96 

3.08 

0.46 

0.68 

2-97 

0.44 

0.66 

2.87 

0.42 

0.64 

2.69 

0.40 

0.60 

2-53 

0.38 

0.56 

I 

1 

2 

I 

4 

8 

73 

2.74 

0.41 

0.81 

2.63 

0.39 0.78 

2.52 

0-37 

0.75 

2-33 

o -34 

0.69 

2.17 

0.32 

0.64 

I 

1 

2 2 

1 

4 

10 

59 

2.47 

0.37 

O.Q I 

2-35 

0.35 0-87 

2.25 

0-33 

0.83 

2.06 

0.31 

0.76 

I .90 

0.28 

0.71 

I 

T 

3 

I 

4 

12 

50 

2.2 S 

0-33 

I.OO 

2.13 

0.32 0.93 

2.03 

0.30 

0.00 

1.Sc 

0.27 

0.82 

1.70 

0.25 

0.76 

I 

ii 

2 

I 

6 

8 

92 

2-39 

0.33 

0.71 

2.30 

0.51 

0.68 

2.22 

0.49 

0.66 

2.07 

0.46 

0.6 T 

T.94 

0.43 

0.58 

I 


22 

I 

6 

IO 

74 

2.18 

0.48 

0.81 

2.0Q 

0.46 0.77 

2.01 

o -45 

0.74 

1.86 

0.41 

O.69 

1-73 

0.38 

0.64 

I 

1$ 

3 

I 

6 

12 

62 

2.0 T 

0.45 

0.89 

t.91 

0.42 

0.85 

1.83 

0.41 

0.81 

1.68 

0-37 

0-75 

1.56 

0.35 

0.69 

I 

ii 

32 

1 

6 

14 

54 

1.86 

0.41 

0.96 

1.77 

0.39 0.92 

1.68 

0-37 

0.87 

1 54 

0-34 

O.80 

1.42 

0.32 

0.74 

I 

1 h 

4 

I 

6 

16 

48 

i -73 

0.38 

1.03 

1.64 

0.36 0.97 

1.56 

0-35 

0.92 

1.42 

0.32 

O.84 

1.30 

0.29 

0.77 

I 

ih 

42 

1 

6 

18 

43 

1.62 

0.36 

1.08 

i -53 

0.34 

1.02 

i -45 

0.32 

0.97 

1- 3 1 

0.2Q 

O.87 

1.20 

0.27 

0.80 

I 

ii 

5 

1 

6 

20 

39 

1.52 

o -34 

I - r 3 

i -43 

0.32 

1.06 

t -35 

0.30 

1.00 

1.22 

0.27 

0.90 

I.I I 

0.25 

0.82 

I 

2 

3 

1 

8 

12 

74 

1.81 

0-54 

0.80 

1.74 

0.52 

0.77 

1.67 

0.50 

0.74 

1-54 

0.46 

0.68 

1.44 

0.43 

0.64 

I 

2 

32 

I 

8 

14 

64 

1.69 

0.50 

0.88 

1.61 

0.48 0.83 

i -54 

0.46 

0.80 

1.42 

0.42 

0.74 

1 - 3 1 

0.39 

0.68 

I 

2 

4 

1 

8 

l6 

56 

T.58 0.47 

0.94 

i- 5 i 

0.45 0.89 

1.44 

0.43 

0.85 

1.32 

0-39 

0.78 

1.21 

0.36 C.72 

I 

2 

42 

I 

8 

18 

51 

1.49 

0.44 

0.99 

1.41 

0.42 0.94 

i -34 

0.40 

0.89 

1.23 

0.36 

0.82 

1 .I 3 

o -34 

0-75 

I 

2 

5 

I 

8 

20 

46 

1.40 

0.42 

1.04 

i -33 

°-39 

0.98 

1.26 

0-37 

o -93 

I-I 5 

0-34 

0.85 |i. 05 

0.31 

0.78 

1 

2 

sh 

I 

8 

22 

42 

i -33 

0-39 

1.08 

1.26 

0-37 

1.03 

1.19 

0-35 

0.97 

1.08 

0.32 

0.8810.98 

0.29 

0.80 

I 

2 

6 

I 

8 

24 

39 

1.26 

0-37 

1.12 

1.19 

0-35 

1.06 

I-I 3 

0.34 

T.OO 

1.02 

0.30 

0.91 

P 93 

0.28 

0.83 

I 

2 % 

3 

1 

IO 

12 

86 

1.65 

0.61 

o -73 

i -59 

0-59 

0.71 

1-53 

0-57 

0.68 

1.42 

0.52 

0.63 

i -33 

0.49 

0-59 

I 

2* 

32 

I 

10 

14 

75 

i -55 

0-57 

0.80 

1.48 

0-55 

0.77 

1.42 

0.52 

0.74 

1.32 

0.49 

0.68 

1.23 

0.46 

0.64 

I 


4 

I 

IO 

16 

66 

1.46 

0-54 

0.87 

r -39 

0.51 

0.82 

1-33 

0.49 

0.79 

1.23 

0.46 

0-73 

1.14 

0.42 

0.68 

I 

0 X 

z 2 

4 * 

I 

10 

18 

59 

r.38 

0.51 

0.92 

r - 3 T 

0.48 

0 87 

1.25 

0.46 

0.83 

I.i 5 

0.43 

0.77 

1.06 

o -39 

0.71 

I 

22 

5 

1 

IO 

20 

54 

i- 3 i 

0.48 

0.97 

1.24 

0.46 

0.92 

1.18 

0.44 

0.87 

1.08 

O.^O 

0.80 

0.99 

0-37 

o -73 

I 

2 h 

52 

I 

IO 

22 

49 

1.24 

0.46 

I.OI 

I.l8 

0.44 

0.96 

1.12 

0.41 

O.9I 

1.02 

0.38 

0.83 

0-93 

0-34 

0.76 

I 

22 

6 

I 

IO 

24 

45 

I.l8 

0.44 

1.05 

r.12 

0.41 

I.OO 

1.06 

0-39 

0.94 

0.96 

0.36 

0.85 

0.88 

0-33 

0.78 

1 

22 

6& 

I 

IO 

26 

42 

i-i 3 

0.42 

1.09 

1.07 

O.40 

1.03 

I.OI 

037 

0.97 

0.92 

0.34 

0.89 

0.84 

0.31 

0.81 

I 

2% 

7 

1 

IO 

28 

39 

1.08 

0.40 

1.12 

1.02 

0.38 

1.06 

0.96 

0.36 

1.00 

0.87 

0.32 

O.9O 

0.79 

0.29 

0.82 

1 

3 

4 

1 

12 

16 

75 

1.35 

0.60 

0.80 

1.30 

0.58 

0.77 

1.25 

0.56 

0.74 

I-I 5 

0.51 

0.68 

T .08 

0.48 

0.64 

I 

3 

42 

I 

12 

18 

67 

1.28 

0-57 

0.85 

1.23 

0-35 

0.82 

'1.18 

0.52 

0.79 

1.08 

0.48 

0.72 

I.OI 

0-45 

0.67 

I 

3 

5 

I 

12 

20 

60 

1.22 

0-54 

0.90 

I .l6 

0.52 

0.86 

I.II 

0.49 

0.82 

1.02 

o -45 

0.76 

O.94 

0.42 

0.70 

1 

3 

ri 

52 

I 

12 

22 

55 

1.16 

0.52 

o -95 

I .1 I 

0.49 

0.90 

1.06 

0.47 

0.86 

0.97 

0-43 

0.79 

O.89 

0.40 

0.72 

I 

3 

6 

I 

12 

24 

50 

1.11 

0.49 

0.90 

1.06 

0.47 

0.94 

I.OI 

0.45 

0.90 

0.92 

0.41 

0.82 

O.84 

o -37 

0-75 

1 

3 

6J 

1 

12 

26 

48 

1.06 

0.47 

1.02 

I.OI 

0-45 

0.97 

0.96 

0-43 

0.92 

0.87 

o -39 

0.84 

O.80 

0.36 

0.77 

1 

3 

7 

1 

12 

28 

44 

1.02 

0.45 

1.06 

0-97 

0-43 

I.OI 

0.92 

0.4T 

0.95 

0.83 

0-37 

0.86 

O.76 

o -34 

0.79 

1 

3 

7-2 

I 

12 

3 ° 

42 

0.98 

0.44 

1.09 

o -93 

0.41 

1.03 

0.88 

o -39 

0.98 

0.79 

0-35 

0.88 

0-73 

0.32 

0.81 

1 

3 

8 

I 

12 

32 

39 

0.94 

0.42 

I.II 

0.89 

0.40 

1.05 

0.84 

0-37 

1.00 

0.76 

0-34 

0.90 

O.69 

0.31 

0.82 

1 

4 

5 

I 

l6 

20 

75 

1.08 

0.64 

0.80 

1.03 

o.6t 

0.76 

0.99 

0.50 

o -73 

O.Q 2 

0.55 

0.68 

0.86 

0.51 

0.64 

1 

4 

6 

I 

l6 

24 

63 

O.Q 9 

o -59 

0.88 

0.95 

0.36 

0.84 

0.91 

0-54 

0.81 

O.83 

0.49 

0.74 

0.77 

0.46 

0.68 

1 

4 

7 

I 

16 

28 

55 

0.92 

0-54 

0.95 

0.88 

0.32 

0.91 

0.83 

0.49 

0.86 

O.76 

0-45 

0.79 

,0.70 

0.42 

0-73 

I 

4 

8 

I 

l6 

32 

48 

0.86 

0.51 

1.02 

0.81 

0.48 

0.96 

0.77 

0.46 

0.91 

0.70 

0.42 

0.83 

0.64 

0.38 

0.76 

1 

4 

9 

I 

16 

36 

43 

0.80 

0.47 

1.07 

0.76 

0-45 

I .OI 

0.72 

0-43 

0.96 

0.65 

o -39 

0.87 

[0.60 

0 36 

0.80 

1 

4 

10 

I 

16 

40 

40 

0-75 

0.44 

1.11 

0.71 

0.42 

1.05 

0.67 

0.40 

0.99 

0.6l 

0.36 

0.90 

P -55 

0-33 

0.81 

1 

5 

10 

I 

20 

40 

47 

0.70 

0.52 

I.04 

0.66 

0.49 

0.98 

0.63 

0.47 

o -93 

0-57 

0.42 

0.84 

0.52 

0.3S 

0.77 

1 

6 

12 

T 

24 

48 

46 

0.59 0.52 

t -OS '0.56 

0.30 

T .OO 

0.5s 

0.47I0.94 

O.48 O.43 

0.85 

o.44'o.30 0.78 


Note. — Variations in the fineness of the sand and the compacting of the concrete may affect the quantities 
by to% in either direction. 

*Use 50% columns for broken stone screened to uniform size. 

+Use 45% columns for average conditions and for broken stone with dust screened out. 

JUse 40% columns for gravel or mixed stone and gravel. 

§Use these columns for scientifically graded mixtures 








































































































Volume of Concrete Based on a Barrel of 3.5 Cubic Feet 

(See important foot-notes, also p. 225.) 


233 


PROPORTIONS 

PROPORTIONS 

*-• * » 

AVERAGE 

VOLUME OF RAMMED 

CONCRETE 

MADE 


BY 



BY 


b a > 

§ 0 

c ^3 0- c 


FROM ONE 

BARREL CEMENT 



PARTS 


VULUML 













0 0 

PorrpntnnrpQ nf VniHc in UrnLrpn S>tnr»P nr ( iravpl 


1 





0 £ to 


5 V “ ’ V * V4W 




4 -i 



a 

a 

0 

0 

a 

rt 

CO 

<D 

C 

O 

c /5 

Volume 

in tern 

centage 

ume of 

50%* 

45 %t 

40 % t 

30 % § 

20% § 

d> 

s 

cu 

1 

<D 

fl 

O 

bbl. 

cu. ft. 

cu. ft. 

% 

cu. ft. 

cu. ft. 

cu. ft. 

CU. ft. 

cu. ft. 

CJ 

CO 

CO 









1 


X 

I 


3-5 

IOI 

5 -i 

5-3 

5-5 

6.0 

6.4 

T 


2 

I 


7.0 

54 

7.0 

7-4 

7.8 

8.7 

9.6 

I 


3 

1 


10.5 

39 


9-5 

10.0 

x i -5 

12.8 

1 


4 

1 


14.0 

3 i 




14.2 

16.0 

1 


5 

I 


17-5 

27 




17.0 

19.2 

1 


6 

x 


2 L O 

24 




19.7 

22.4 

1 


7 

T 


24-5 

21 





25.6 

1 


8 

1 


28.0 

20 





28.8 

1 


9 

1 


3 i -5 

18 





32.0 

1 


IO 

I 


35 -o 

17 





35-2 

I 


I I 

I 


38.5 

l6 





38.4 

1 


12 

I 


42.0 

l6 





41.6 

1 

I 

i* 

I 

3-5 

5-2 

104 

8.0 

8.3 

8.6 

9 1 

9-7 

I 

I 

2 

I 

3-5 

7.0 

78 

8.9 

9-3 

9-7 

10.5 

I I .2 

I 

I 

2i 

I 

3-5 

8-7 

64 

9.9 

10.4 

10.8 

11.8 

12.7 

I 

I 

3 

I 

3-5 

10.5 

54 

10.8 

11.4 

12.0 

131 

14.2 

I 

1 4 

2 

I 

5-2 

7.0 

95 

10.2 

10.6 

II.O 

11 -7 

12.5 

1 


2 2' 

I 

5-2 

8.7 

78 

11.2 

11.6 

12.1 

13.0 

14.0 

I 

i\ 

3 

I 

5-2 

10.3 

65 

12.1 

12.7 

13.2 

14.4 

15-5 

I 

lb 

3 i 

I 

5-2 

12.2 

56 

13.0 

13-7 

14.4 

15-7 

17.0 

1 

ii 

4 

I 

5-2 

14.0 

50 

14.0 

14.8 

15-5 

17.0 

18.5 

I 


42 - 

I 

5-2 

15-7 

45 

140 

13.8 

16.6 

18.3 

20.0 

I 

1^ 

5 

1 

5.2 

17-5 

4 t 

159 

16.8 

17.8 

-20.0 

21.6 

I 

2 

3 

1 

7.0 

10.5 

77 

1 . 3-4 

13 9 

14-5 

1 . 5-6 

16.8 

I 

2 

3-2 

4 

I 

7 0 

12.2 

67 

14-3 

15.0 

1 . 5-6 

17.0 

18.3 

I 

2 

x 

7.0 

14.0 

59 

15-3 

16.O 

16.8 

18.3 

19.8 

I 

2 

42 

I 

7.0 

i 5-7 

53 

16.2 

17.0 

17.9 

19.6 

21.3 

I 

2 

5 

I 

7.0 

i 7-5 

48 

17.1 

18.1 

19.0 

20 Q 

22.8 

1 

1 

2 

2 

5 i 

6 

I 

I 

7.0 

7 0 

IQ.2 

2 I .O 

a 4 

41 

l8.1 

IQ.O 

XO-I 

20.2 

20.2 

2 1.3 

22.2 

23.6 

24-3 

25.8 

I 

2 2 

3 

I 

8.7 

10.3 

90 

14.6 

15.2 

13.8 

16.9 

18.0 

I 

2$ 

3 i 

I 

8.7 

12.2 

78 

13.6 

l6.2 

16.9 

18.2 

19.6 

I 

2 2 

4 

I 

8.7 

14.0 

68 

16.5 

17-3 

18.0 

19.6 

21.1 

I 

2* 

4 i 

I 

8.7 

15-7 

61 

17-5 

18.3 

IQ .2 

20.9 

22.6 

I 

2* 

5 

I 

8.7 

17-5 

55 

18.4 

10.4 

20.3 

22.2 

24.I 

25.6 

1 

2-2 

52 

I 

8.7 

19.2 

5i 

19.4 

20.4 

21.4 

23-5 

I 

2 I 

6 

I 

8.7 

21.0 

47 

20.3 

21-4 

22.6 

24.8 

27.1 

I 

2 \ 

67 

I 

8.7 

22.7 

44 

21.2 

22.5 

23-7 

26.2 

28.6 

1 

2 \ 

7 

I 

8-7 

24-5 

4 i 

22.2 

23-5 

24.8 

27-5 

3 °.1 

x 

7 

4 

I 

10.5 

14.0 

77 

17-8 

18.3 

19-3 

20.8 

22.3 

23.8 

I 


4 i 

I 

10.3 

15-7 

69 

18.7 

19.6 

20.4 

22.1 

1 

3 

5 

X 

10 5 

17-5 

62 

19.7 

20.6 

21.6 

23-4 

25-3 

I 

I 

3 

7 

52 

6 

I 

I 

10.5 
10 5 

19.2 

2 T .O 

57 

53 

20.6 

21.6 

21:7 

22.7 

22.7 

23.8 

24.8 

26.1 

26.8 

28.4 

1 

3 

64 

I 

10.5 

22-7 

49 

22.5 

23 7 

23.0 

27.4 

29.9 

I 

7 

7 

72 

8 

I 

10.5 

24-5 

46 

23-5 

24.8 

26.1 

28.7 

3 i -4 



I 

IO-5 

26.2 

43 

24 4 

25.8 

27.2 

30.1 

32-9 

1 

3 

I 

10.5 

28.0 

40 

25-3 

26.9 

28.4 

3 i -4 

34-4 

I 

4 

5 

6 

I 

I 

14.0 

14.0 

17-5 

21.0 

77 

65 

22.2 

24.I 

23.2 

25.2 

24.1 

26.4 

26.0 

28.6 

27.9 

30-9 

1 

4 

7 

X 

14.0 

24-5 

56 

26.0 

27-3 

28.6 

3 i -3 

33-9 



8 

I 

14.0 

28.0 

50 

27.9 

39-4 

30.9 

33-9 

36-9 


A 

Q 

I 

14.0 

31-5 

45 

29.8 

3 i -5 

33-2 

36.6 

40.0 

1 

4 

IO 

I 

14.0 

35 -o 

4 i 

31-7 

33-6 

35-4 

39-2 

43 -o 

1 

1 

5 

6 

10 

12 

I 

I 

17-5 

21.0 

•S. Co 

10 Ul 

b b 

48 

46 

34-2 

40. c 

36.1 

42.8 

38.0 

45 -° 

41.8 

49.6 

45-5 

54 -i 


Note. _ Variations in the fineness of the sand and me compacting oi me . 

times by 10% in either direction. 

*U«e co% column for broken stone screened to uniform size. , 

tUse 45% column for average conditions and for broken stone with dust screened out. 
lUse 40% column for gravel or mixed stone and gravel. 

§Use these columns for scientifically graded mixtures 



























































234 


USE THIS TABLE ORDINARILY. 

Volume of Concrete Based on a Barrel of 3.8 Cubic Feet. 

(See important foot-notes, also p. 225.) 


PROPORTIONS 

BY 

PARTS 

PROPORTIONS 

BY 

VOLUME 

Volume of mortar 

in terms of per¬ 

centage of vol¬ 
ume of stone. 

AVERAGE 

VOLUME OF RAMMED CONCRETE MADE 
FROM ONE BARREL CEMENT 

Percentages of Voids in Broken Stone or 

Gravel 

Cement 

Sand 

Stone 

Cement 

Sand 

Stone 

50%* 

45 % t 

4°%t 

3°%§ 

20% § 

bbl. 

cu. 

ft. 

cu. 

ft. 

% 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

r 


1 

I 


3-8 

94 

5-3 

5.5 

5-7 

6.2 

6.7 

I 


2 

1 


7.6 

51 

7-4 

7.8 

8.2 

9.2 

10.2 

1 


3 

1 


11.4 

36 


10.0 

10.6 

12.2 

13.6 

1 


4 

1 


15-2 

29 




15.2 

17.1 

1 


5 

1 


19.0 

25 




l8.2 

20.6 

1 


6 

1 


22.8 

22 




21.1 

24.0 

I 


7 

1 


26.6 

20 





27-5 

1 


8 

1 


3°-4 

19 





31.0 

I 


9 

1 


34-2 

18 





34-4 

I 


10 

1 


38.0 

17 





37-9 

X 


11 

X 


41.8 

16 





41.4 

1 


12 

1 


45-5 

IS 





44.8 

I 

1 

ii 

X 

3-8 

5-7 

99 

8-5 

8.8 

9.1 

9-7 

10.3 

I 

i 

2 

I 

3-8 

7.6 

75 

9-5 

9.9 

10.3 

11.1 

11-9 

I 

1 

si 

I 

3-8 

9-5 

61 

10.5 

11.0 

II-5 

12.6 

13.6 

1 

I 

3 

I 

3-8 

11.4 

51 

11-5 

12.2 

12.8 

14.0 

15.2 

I 

ii 

2 

I 

5-7 

7.6 

93 

10.8 

11.3 

11-7 

12.5 

1.3-3 

I 

ii 

si 

I 

5-7 

9-5 

76 

11-9 

12.4 

12.9 

13-9 

15.0 

I 

ii 

3 

I 

5-7 

11-4 

64 

I 2.9 

13.5 

14.1 

15.4 

16.6 

I 

ii 

3i 

I 

5-7 

13-3 

SS 

13-9 

14.6 

15-4 

16.8 

18.2 

1 

12 

4 

I 

5-7 

15.2 

49 

15.0 

15.8 

16.6 

18.2 

19.9 

I 

ii 

4i 

X 

5-7 

17.1 

44 

16.0 

16.9 

17.8 

19.7 

21.5 

I 

ii 

. 5 

I 

5-7 

19.0 

40 

17.0 

18.0 

19.1 

21.1 

23.2 

I 

2 

3 

I 

7.6 

11 4 

75 

14-3 

14.9 

15-5 

16.7 

18.0 

I 

2 

3i 

I 

7.6 

13-3 

65 

15-3 

16.0 

16.8 

18.2 

19.6 

1 

2 

4 

I 

7.6 

IS-s 

57 

16.3 

17.2 

18.0 

19.6 

21.3 

1 

2 

4i 

I 

7.6 

17.1 

5i 

17.4 

18.3 

19.2 

21.0 

22.9 

1 

2 

5 

I 

7.6 

19 0 

47 

. 18.4 

19.4 

20.4 

22.3 

24-5 

I 

2 

si 

I 

7.6 

20.9 

43 

19.4 

20.5 

21.7 

239 

26.2 

I 

2 

6 

I 

7.6 

22.8 

40 

20.4 

21.7 

22.9 

25-4 

27.8 

1 

»i 

3 

I 

95 

IT.4 

87 

15-7 

16.3 

16.9 

18.1 

19-3 

X 

si 

3i 

I 

9-5 

13-3 

75 

16.7 

17.4 

18.1 

19.6 

21.0 

I 

si 

4 

I 

9-5 

15-2 

66 

17.7 

18.5 

19-3 

21.0 

22.6 

I 

si 

4i 

I 

9-5 

17.1 

60 

18.7 

19.6 

20.6 

22.4 

243 

I 

si 

5 

I 

9-5 

19.0 

54 

19.8 

20.8 

21.8 

23-9 

25-9 

I 

si 

Si 

I 

9-5 

20.9 

49 

20.8 

21.9 

23-0 

25-3 

27.6 

I 

si 

6 

X 

9-5 

22.8 

46 

21.8 

23.0 

24-3 

26.7 

29.2 

I 

si 

6i 

I 

9-5 

24.7 

42 

22.8 

24.2 

25-5 

28 2 

30.8 

I 

si 

7 

I 

9-5 

26.6 

40 

2 3-9 

25.3 

26.7 

29.6 

32.5 

I 

3 

4 

I 

11.4 

15.2 

76 

19.1 

19.9 

20.7 

22.4 

24.0 

I 

3 

4i 

I 

ii -4 

17.1 

68 

20.1 

21.0 

21.9 

23.8 

25.6 

I 

3 

5 

I 

ii *4 

19.0 

61 

21.1 

22.1 

23.2 

25.2 

27.2 

X 

3 

Si 

I 

II-4 

20.9 

50 

22.1 

23.3 

24.4 

26.7 

28.9 

I 

3 

6 

I 

ii -4 

22.8 

52 

23.2 

24.4 

25.6 

28.1 

30.6 

I 

3 

6i 

I 

11-4 

24.7 

48 

24.2 

25.5 

26.9 

295 

32.2 

I 

3 

7 

X 

11-4 

26.6 

45 

25.2 

26.7 

28.1 

3T.O 

33-8 

I 

3 

7i 

I 

11-4 

28.5 

42 

26.2 

27.8 

29-3 

32.4 

35-5 

I 

3 

8 

I 

11-4 

304 

40 

27-3 

28.9 

30.6 

33-8 

37-1 

I 

4 

5 

I 

15-2 

19.0 

76 

2 3-9 

24.9 

25-9 

28.0 

30.0 

I 

4 

6 

I 

15.2 

22.8 

64 

25-9 

27.2 

28.4 

30.8 

33-3 

I 

4 

7 

I 

15.2 

26.6 

55 

28.0 

29.4 

30-8 

33-7 

36-6 

X 

4 

8 

I 

15.2 

30.4 

49 

30.0 

31.7 

33-3 

36.6 

390 

I 

4 

9 

I 

15-2 

34-2 

44 

32.1 

33.9 

35-8 

39-4 

43. 1 

I 

4 

10 

I 

15-2 

38.0 

40 

34-1 

36.2 

38.2 

42.3 

46.4 

I 

S 

10 

I 

IQ.O 

38.0 

47 

36-9 

38.9 

41.0 

45-i 

49 2 


6 

12 

I 

22.8 

45-5 

46 

43-7 

46.2 

48.6 

53-6 

58.5 


Note. Variations in the fineness of the sand and the compacting of the concrete may affect the vol 
umes by 10% in either direction. 

*Use 50% column for broken stone screened to uniform size. 

tJTse 45 % column for average conditions and for broken stone with dust screened out. 
IUse 40% column for gravel or mixed stone and gravel. 

§Use these columns for scientifically graded mixtures. 










































Volume of Concrete Based on a Barrel of 4 Cubic Feet 

(See important foot-notes, also p. 225.) 


235 


PROPORTIONS 

BY 

PARTS 

PROPORTIONS 

BY 

VOLUME 

U « • 

5 0 0 

s ^ 

£ * * 3 * a 
° 0 2 

0 a „ « 

AVERAGE 

VOLUME OF RAMMED CONCRETE 
FROM ONE BARREL CEMENT 

MADE 

Percentages of Voids in Broken Stone or Gravel 

Cement 

1 

| Sand 

I 

Stone 

t 

Cement 

Sand 

Stone 

— G P 

0 fl U £ 

£ -a 0 p 

5 °%* 

45 %t 

40 % t 

3 °% § 

20% § 

bbl. 

cu. 

ft. 

cu. 

ft. 

% 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

CU. ft. 

1 


1 

1 


4 

89 

5-4 

5-6 

5-8 

6.4 

6.9 

1 


2 

I 


8 

49 

7.6 

8.0 

8.4 

9-5 

10 5 

1 


3 

1 


12 

35 


10.4 

11.0 

12.7 

14.2 

1 


4 

1 


16 

28 




15-8 

17.8 

I 


5 

1 


20 

24 




18.9 

21.5 

1 


6 

1 


24 

22 


k 


22.1 

25.1 

1 


7 

1 


28 

20 


0 



28.8 

1 


8 

1 


32 

18 





32-4 

1 


9 

1 


36 

17 





36.1 

1 


10 

1 


40 

16 





39-7 

1 


IX 

1 


44 

15 





43-4 

1 


12 

1 


48 

IS 





47-0 

1 

1 

ii 

1 

4 

6 

96 

8.8 

9.1 

9.4 

10.0 

10.7 

I 

1 

2 

1 

4 

8 

73 

9.8 

10.3 

10.7 

11.6 

12.4 

I 

X 

2 i 

X 

4 

10 

59 

10.9 

n -5 

12.0 

i 3 -i 

14.2 

1 

1 

3 

1 

4 

12 

50 

12.0 

12.7 

13-3 

14.6 

15-9 

1 

ii 

2 

1 

6 

8 

92 

11 -3 

11 7 

12.2 

13.0 

13-9 

1 

ii 

2| 

1 

6 

10 

74 

12.4 

12.9 

13-5 

14-5 

15-6 

i 


3 

I 

6 

12 

62 

13-5 

14.1 

14.8 

16.0 

17-3 

1 

ii 

3 i 

1 

6 

14 

54 

14.5 

15-3 

16.0 

17.6 

19.1 

I 

ii 

4 

1 

6 

16 

48 

15 -u 

16.5 

17-3 

19.1 

20.8 

1 

ii 

4 * 

1 

6 

18 

43 

16.7 

17.7 

18.6 

20.6 

22.5 

I 

l| 

5 

1 

6 

20 

39 

17.8 

18.9 

19.9 

22.1 

24-3 

1 

2 

3 

X 

8 

12 

74 

14-9 

15-6 

16.2 

17-5 

18.8 

1 

2 

3 i 

I 

8 

14 

64 

16.0 

16.7 

17-5 

19.0 

20.5 

I 

2 

4 

I 

8 

16 

56 

17.X 

17.9 

18.8 

20.5 

22.3 

T 

2 

4 * 

I 

8 

18 

51 

18.1 

19.1 

20.1 

22.0 

23-9 

1 

2 

5 

J 

8 

20 

46 

19.2 

20.3 

21.4 

23-5 

25-7 

1 

2 

si 

I 

8 

22 

42 

20.3 

21.5 

22.7 

25.1 

27.4 

1 

2 

6 

I 

8 

24 

39 

21.4 

22.7 

24.0 

26.6 

2Q.2 

1 

2 $ 

3 

I 

TO 

12 

86 

16. t 

X 7.0 

17.6 

18.9 

20.2 

I 

22 

3 i 

I 

IO 

14 

75 

17.4 

lS.2 

189 

20.5 

22.0 

1 

2^ 

4 

I 

IO 

16 

66 

18.5 

19 4 

20.2 

21.9' 

23-7 

1 

22 

4 i 

I 

IO 

18 

59 

19.6 

20.6 

21.5 

23-5 

25-4 

I 

2^ 

5 

I 

IO 

20 

54 

20.7 

21.8 

22.8 

25.0 

27.2 

1 

2 \ 

si 

1 

IO 

22 

49 

21.8 

22.9 

24.1 

26. s 

28.9 

I 

2^ 

6 

I 

XO 

24 

45 

22.8 

24.I 

25-4 

28.0 

30.6 

I 

2^ 

6i 

I 

IO 

26 

42 

23-9 

25-3 

26.7 

29-5 

32-3 

1 

2i 

7 

I 

10 

28 

39 

25.0 

26.5 

28.0 

3 i-o 

34 -o 

I 

3 

4 

I 

12 

16 

75 

20.0 

20.8 

21.7 

23-4 

25.1 

I 

3 

4 i 

I 

12 

18 

67 

21.0 

22.0 

23.0 

24-9 

26.8 

1 

3 

5 

I 

12 

20 

60 

22.1 

23.2 

24-3 

26.4 

28.6 

I 

3 

si 

I 

12 

22 

55 

23.2 

24.4 

25.6 

28.0 

3°-3 

I 

3 

6 

I 

12 

24 

50 

24-3 

2^.6 

26.9 

29-5 

32.1 

1 

3 

6i 

1 

12 

26 

48 

25-4 

26.8 

28.2 

31.0 

33-8 

I 

3 

7 

I 

12 

28 

44 

26.4 

27.9 

29.4 

32-5 

35-5 

I 

3 

7 i 

I 

12 

3 ° 

42 

27-5 

29.1 

30.8 

34 -o 

37-2 

1 

3 

8 

I 

12 

32 

39 

28.6 

30-3 

32.0 

35-5 

39 -o 

I 

4 

s 

I 

l6 

20 

75 

25.0 

26.1 

27.2 

29-3 

3 i -5 

I 

4 

6 

I 

l6 

24 

63 

27.2 

28.5 

29.8 

32-4 

35 -o 

1 

4 

7 

I 

l6 

28 

55 

29-3 

30.8 

32-4 

35-4 

38-4 

I 

4 

8 

I 

l6 

32 

48 

3 i -5 

33-2 

34-9 

38.4 

41.9 

I 

4 

9 

I 

l6 

3 6 

43 

33-6 

35-6 

37-5 

41.4 

45-3 

1 

4 

10 

I 

l6 

40 

40 

35-8 

38.0 

40.1 

44.4 

48.8 

I 

5 

10 

I 

20 

40 

47 

38.7 

400 

43 -o 

47-3 

5 i -7 

I 

6 

12 

I 

24 

48 

46 

45-9 

1 485 

1 5 i-i 

56.3 

61.4 


Note. — Variations in the fineness of the sand and the compacting of the concrete may affect the 

volumes bv 10% in either direction. 

*Use 50% column for broken stone screened to uniform size. 

tUse 45% column for average conditions and for broken stone wnn dust screened out. 

§Use 40% column for gravel or mixed stone and gravel. 

§Use these columns for scientifically graded mixtures. 























































236 


MATERIALS FOR RUBBLE CONCRETE. 

Quantities of Materials for One Cubic Yard Based on a Barrel of 3.8 Cubic Feet. 
{See important footnotes , also pp. 238 and 296.) 


Percentage of Rubble in Total 
Volume of Concrete. 

PROPOR¬ 
TIONS OF 

PLAIN 

CONCRETE 
BY PARTS 

PROPORTIONS 
OF PLAIN CON¬ 
CRETE BY 
VOLUME* * * * § 

PERCENTAGES OF VOIDS IN BROKEN STONE OR GRAVEL. 

5 o%* 

45 %t 

40 % t 

3 °%§ 

4-5 

C 

0 ) 

a 

® 

0 

bbl. 

G.S Sand 

0 

a 

0 

m 

cu. 

yd. 

4 -> 

a 

<v 

a 

V 

0 

bbl. 

•a 

a 

cS 

C /3 

CU. 

yd. 

4 ) 

a 

0 

-kk 

CO 

cu. 

yd. 

o' Cement 

a 

d 

m 

cu. 

yd. 

a> 

a 

0 

-kJ 

m 

cu. 

yd. 

cr Cement 

'd 

c 

c 3 

Ci 

CU. 

yd. 

cLo Stone 

• • 

Cement 

T 3 

a 

d 

02 

0 ) 

c 

0 

-kJ 

m 

1 o* 

o' Packed Cement 

Loose Sand 

Loose Stone 

(.1) 

(2) 

( 3 ) 

( 4 ) 

( 5 ) 

( 6 ) 

( 7 ) 

( 8 ) 

(9) 

(10)|(11) 

(12) 

(13) 

(14) 

(1 5 ) 

(16) 

(17) 

(18) 

(19) 



1 

2 

3 

1 

7.6 

11.4 

1 . 5 1 

0-43 

0.64 

1.45 

0.41 

0.61 

i -39 

0. 39 

0.59 

1.29 

0.36 

0. 54 



I 

2 

4 

I 

7.6 

l 5 . 2 

1 • 32 

0. 37 

0.74 

1.25 

0. 35 

0. 70 

I . 20 

0. 34 

0.67 

1.10 

0. 31 

0. 62 



I 

2 

5 

I 

7.6 

19 . 0 

I . l8 

0. 33 

0.82 

1 . 11 

0.31 

0. 78 

1 . 06 

0. 30 

0.74 

0.96 

0.27 

0. 67 



I 

22 

4 

I 

9.5 

I 5 . 2 

1.22 

0.43 

0.69 

1.17 

0.41 

0. 66 

I . 12 

0. 39 

0.63 

1.03 

0. 36 

o .58 

20% 


1 

22 

5 

I 

9.5 

19 . 0 

I . IO 

0. 38 

0. 7 r 

1 . 04 

0. 37 

0. 74 

0.99 

0. 35 

0.70 

0.90 

0. 32 

0. 64 



I 

2^ 

6 

I 

9.5 

22.1 

0. 99 

0. 35 

0.84 

0. 94 

0. 33 

0. 79 

0.89 

0.31 

0.75 

0.81 

0. 29 

0. 68 



I 

3 

5 

I 

11.4 

19.0 

I . 02 

0.43 

0. 72 

0. 98 

0.42 

0. 69 

0.94 

0. 39 

0. 66 

0. 86 

0.36 

0. 60 



I 

3 

6 

I 

11.4 

22.8 

0.93 

0. 39 

0.78 

0. 89 

0. 38 

0.75 

0.84 

0. 35 

0.71 

0. 77 

O. 33 

0. 65 



l 1 

3 

7 

I 

11.4 

26.6 

0.86 

0. 36 

0.84 

0.81 

0-34 

0. 79 

0.77 

0. 32 

0. 76 

0. 70 

0. 30 

0. 69 



1 

2 

3 

I 

7.6 

11.4 

1.32 

0. 37 

0. 56 

1.27 

0. 36 

0. 53 

1.22 

0. 34 

O. 52 

1. 13 

0. 32 

0. 48 



1 

2 

4 

I 

7.6 

I 5 . 2 

1. i 5 

0. 32 

0. 65 

1. 10 

0.31 

0. 62 

1. o 5 

0. 29 

0. 59 

0.97 

0.27 

0. 55 



1 

2 

5 

I 

7.6 

19 . 0 

1.03 

0. 29 

0. 72 

0. 97 

0.27 

0. 69 

0. 92 

0. 26 

0. 65 

0. 84 

0. 24 

0. 59 



1 

si 

4 

I 

9.5 

I 5 . 2 

1.06 

0. 38 

0. 60 

I . 02 

0. 36 

0.57 

0. 98 

0. 34 

o .5 5 

0. 90 

0. 32 

0. 5 i 

30 % 


1 

2i 

5 

I 

9.5 

19 . 0 

0.96 

0. 34 

0. 67 

0.91 

0. 32 

0. 64 

0. 87 

0.31 

0.61 

0. 79 

0. 28 

0. 56 



I 

9 1 

2 2 

6 

I 

9 .5 

22.1 

0. 87 

0. 31 

0. 74 

0.82 

0. 29 

0. 69 

0. 78 

0.27 

0. 66 

0.71 

0.2 5 

0. 60 



I 

3 

5 

I 

11.4 

19.0 

O. 90 

0. 38 

0. 63 

o .85 

0. 36 

0. 60 

0. 82 

0. 34 

0. 57 

0.75 

0. 32 

0. 53 



I 

3 

6 

1 

11.4 

22 . c 

0.81 

0. 34 

0. 69 

0. 78 

0. 33 

0. 66 

0. 74 

0.31 

0. 62 

0. 67 

0. 29 

0.57 



I 

3 

7 

I 

11.4 

26 . t 

0. 75 

O. 32 

0. 74 

0.71 

0. 30 

0. 69 

0. 67 

0. 28 

0. 67 

0.61 

0. 26 

0. 60 



I 

2 

3 

I 

7.6 

II.4 

i. 13 

0. 32 

0. 48 

1.09 

0.31 

0.46 

1.04 

0. 29 

0. 44 

0.97 

0.27 

0.41 



I 

2 

4 

I 

7.6 

I 5 . 2 

0. 99 

0. 28 

0. 56 

0.94 

0. 26 

0. 53 

0. 90 

0.25 

0. 5 o 

0. 83 

0.23 

0.47 



1 

2 

5 

I 

7.6 

19 . O 

0. 88 

0.25 

0. 62 

0. 83 

0. 23 

0. 59 

0. 79 

0.22 

0. 5 C 

0.72 

0.20 

0. 5 o 



I 

si 

4 

I 

9.5 

15 .2 

0.91 

0. 32 

0.52 

0.88 

0.31 

0.49 

0. 84 

0.29 

0.47 

0. 77 

0.27 

0. 44 

40 % 


I 

22 

5 

I 

9.5 

19.0 

0. 82 

O. 29 

0. 58 

0. 78 

0. 28 

0. 55 

0. 74 

0.26 

0. 5 c 

0. 68 

O. 24 

0. 48 



I 

2* 

6 

I 

9.5 

22.8 

0. 74 

0. 26 

0. 63 

0. 70 

O. 25 

0. 59 

0. 67 

0.23 

0. SC 

0.61 

0.22 

0. 5 i 



1 

3 

5 

1 

11.4 

19 . O 

0. 77 

0. 32 

0. 54 

0. 73 

0. 31 

O. 52 

0. 70 

0.29 

0.4 c 

0. 64 

0.2 7 

0.45 



1 

3 

6 

1 

11.4 

22.8 

0. 70 

O. 29 

0. 5 g 

0. 67 

0. 28 

0. 56 

0. 63 

0.26 

0.53 

0. 58 

0.2 5 

0. 49 



1 

3 

7 

1 

11.4 

26.6 

0. 65 

0.27 

0. 63 

0.61 

0. 26 

0. 59 

0. 58 

0.24 

0.57 

O. 52 

0.22 

0.52 



1 

2 

3 

I 

7.6 

11.4 

0. 94 

0. 27 

O. 40 

0. 90 

0. 26 

0. 38 

0.87 

0.24 

0.37 

0. 80 

O. 22 

0. 34 



1 

2 

4 

I 

7.6 

i 5 . 2 

0. 82 

0. 23 

0.46 

0. 78 

0. 22 

0.44 

0.75 

0.2 1 

0.42 

0. 69 

0.20 

0. 39 



I 

2 

5 

1 

7.6 

19 . O 

0. 74 

0. 20 

0.52 

0. 70 

0. 20 

0.49 

0. 66 

0.18 

0. 4 c 

0. 60 

0.17 

0. 42 



I 

2j 

4 

I 

9.5 

l 5 . 2 

0. 76 

0.27 

0.43 

0. 73 

0. 26 

0.41 

0. 70 

O. 24 

0. 40 

0. 64 

0.22 

0. 36 

So% 


1 

2i 

5 

I 

9. 5 

19.0 

0. 68 

0. 24 

0.48 

0. 65 

0.23 

0. 46 

0. 62 

0.22 

0. 44 

0. 56 

O. 20 

0. 40 



I 

2i 

6 

I 

9.5 

22.8 

0. 62 

0.22 

0.52 

0. 58 

O. 20 

0. 5 o 

0. 56 

O. 20 

0.47 

0. 5 o 

0.18 

0.42 



1 

3 

5 

I 

11.4 

19 . O 

0. 64 

0.27 

0. 45 

0.61 

0.26 

0. 43 

0. 58 

0.24 

0.41 

0. 54 

0.22 

0. 38 



1 

3 

6 

I 

11.4 

22.8 

0. 58 

0. 24 

0.40 

0. 56 

O. 24 

0.47 

0.52 

0.22 

0.44 

0. 48 

0.20 

0. 40 



I 

3 

7 

1 

11.4 

26.6 

0. 54 

0.22 

O. 52 

0. 5 o 

0.22 

0.49 

0. 48 

O. 20 

0. 48 

0.44 

0.18 

0-43 



r 

1 

2 

3 

1 

7.6 

II.4 

0. 76 

0.2 1 

0. 32 

0. 72 

0.20 

0. 30 

0. 70 

0.20 

0. 30 

0. 64 

0.18 

0.27 



I 

2 

4 

I 

7.6 

i 5 .2 

0. 66 

0.18 

0. 37 

0. 63 

0.18 

0. 35 

0. 60 

0.17 

34 

0. 55 

0.16 

0.31 



1 

2 

5 

I 

7.6 

19.0 

0. 58 

0.16 

0.41 

0. 56 

0.16 

0. 39 

0.53 

0. i 5 

0. 37 

0. 48 

0.14 

o. 34 



1 

22 

4 

1 

9.5 

l 5 .2 

0.61 

0.22 

0. 34 

0. 58 

0.20 

0. 33 

0. 56 

0. 20 

0. 32 

0.52 

0.18 

0. 29 

60% 


1 

22 

5 

1 

9.S 

19.0 

0. 55 

0.19 

0. 38 

0.5 2 

0.18 

0. 37 

0. 5 o 

0. 18 

0. 35 

0. 45 

0.16 

0. 32 



1 

2I 

6 

I 

9.5 

22.8 

0. 5 o 

0.18 

0.42 

0.47 

0.16 

0.40 

0.44 

0. 16 

0. 38 

0. 40 

0.14 

34 

•. 


1 

3 

5 

1 

11.4 

19 . O 

0. 51 

0.22 

0. 36 

0.49 

0.2 1 

0. 34 

0.47 

0. 20 

0. 33 

O. 43 

0.18 

0. 30 



1 

3 

6 

1 

11.4 

22.8 

0.46 

0.20 

0. 39 

0. 44 

0.19 

0. 38 

0.42 

0. 18 

0. 36 

0. 38 

0.16 

0. 32 



1 

3 

7 

I 

11.4 

26.6 

0.43 

0.18 

0.42 

0.40 

0.17 

0.40 

0. 38 

0. 16 

0. 38 

0. 35 

0. i5 

0. 34 


Note.—V ariations in the fineness of the sand and the compacting of the concrete may affect the quan¬ 
tities by 10% in either direction. 

* Use 5 o% columns for broken stone screened to uniform size. 

t Use 45% columns for average conditions and for broken stone with dust screened out. 

J Use 40% columns for gravel or mixed stone and gravel. 

§ Use 30% columns for scientifically graded mixtures. 















































































VOLUME OF RUBBLE CONCRETE 


Based on a Barrel of 3.8 Cubic Feet (see important footnotes, also pp. 238 

and 296). 


PERCENTAGE 

OF RUBBLE 

IN TOTAL 

VOLUME 

OF CONCRETE. 

PROPORTIONS OF 
PLAIN CONCRETE 
BY PARTS. 

PROPORTIONS OF 
PLAIN CONCRETE 

BY VOLUME. 

AVERAGE VOLUME OF RUBBLE 
CONCRETE MADE FROM ONE 
BARREL CEMENT. 

Percentages of Voids in Broken 
Stone or Gravel. 

Cement. 

Sand. 

Stone. 

Cement. 

Sand. 

Stone. 

50 %* 

45 %t 

40 %t 

30 %§ 

bbl. 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

cu. ft. 

(I) 

(2) 

(3) 

( 4 ) 

( 5 ) 

( 6 ) 

( 7 ) 

( 8 ) 

(9) 

(10) 

(11) 



I 

2 

3 

1 

7.6 

11.4 

17.9 

18.6 

19.4 

20.9 



I 

2 

4 

1 

7.6 

i 5 . 2 

20.4 

21.5 

22.5 

24 .5 



1 

2 

5 

1 

7.6 

19.0 

23.0 

24.2 

25.5 

28. I 



1 

2? 

4 

I 

9.5 

i 5 . 2 

22.0 

23.1 

24. 1 

26.2 

20 % 


I 

22 

5 

1. 

9.S 

19.0 

24.8 

26.0 

27.2 

29.9 



I 

22 

6 

I 

9.5 

22.8 

27-3 

28.8 

30.4 

33-4 



I 

3 

5 

I 

11.4 

19.0 

26.4 

27.6 

29.0 

3 i -4 



I 

3 

6 

I 

11.4 

22.8 

29 . O 

30. 5 

32.0 

35 . 1 


L 

I 

3 

7 

I 

11.4 

26.6 

31-5 

33-4 

35 .1 

38.8 


r 

I 

2 

3 

I 

7.6 

11.4 

20.4 

21.3 

22.2 

23-9 



I 

2 

4 

I 

7.6 

i 5 .2 

23-3 

24.6 

25.7 

28.0 



I 

2 

5 

1 

7.6 

19.0 

26.3 

27.7 

29.2 

32. 1 



I 

2 \ 

4 

I 

9.5 

i 5 . 2 

25.3 

26.4 

27.6 

30.0 

30 % 


I 

22 

5 

I 

9.5 

19.0 

28.3 

29.7 

31-2 

34-2 



I 

2 i 

6 

I 

9.5 

22.8 

3 i- 2 

32.9 

34.7 

38.2 



I 

3 

5 

I 

11.4 

19.0 

30. 2 

31.6 

33-2 

36.0 



I 

3 

6 

I 

11.4 

22.8 

33-2 

34-9 

36.6 

40. 2 



I 

3 

7 

I 

11.4 

26.6 

36.0 

38.2 

40.2 

43 -o 


f 

I 

2 

3 

I 

7.6 

11.4 

23-8 

24.8 

25.8 

27.8 



I 

2 

4 

I 

7.6 

i 5 .2 

27.2 

28.7 

3 °- 0 

32.7 



I 

2 

5 

I 

7.6 

19.0 

30 . 7 

32.3 

34 -o 

37 - S 



I 

2 2 

4 

I 

9.5 

i 5 .2 

29 .5 

30.8 

32.2 

35.0 

40 % 


I 

2 b 

5 

I 

9.5 

19.0 

33 -o 

34-7 

36.3 

39-8 



I 

9 1 

2 2 

6 

I 

9 .5 

22.8 

36.3 

38.4 

40. 5 

44.5 



1 

3 

5 

I 

11.4 

19.0 

35 .2 

36.8 

38.7 

42.0 



I 

3 

6 

I 

11.4 

22.8 

38.7 

40. 7 

42.7 

46.8 



I 

3 

7 

I 

11.4 

26.6 

42.0 

44.5 

46.8 

5 1 • 7 


c 

I 

2 

3 

I 

7.6 

11.4 

28.6 

29.8 

31.0 

33-4 



I 

2 

4 

I 

7.6 

i 5 .2 

32.6 

34-4 

36.0 

39-2 



I 

2 

5 

I 

7.6 

19.0 

36.8 

38.8 

40.8 

45 .0 



I 

2 2 

4 

I 

9 .5 

i 5 .2 

35.4 

37 -o 

38.6 

42.0 

5 o% 


I 

2I 

5 

I 

9.5 

19.0 

39-6 

41.6 

43-6 

47.8 



I 

22" 

6 

I 

9.5 

22.8 

43-6 

46.0 

48.6 

53-4 



I 

3 

5 

I 

11.4 

19.0 

42.2 

44.2 

46.4 

5 o. 4 



I 

3 

6 

I 

1 1.4 

22.8 

46.4 

48.8 

5 1. 2 

56.2 



I 

3 

7 

I 

11.4 

26.6 

5 o. 4 

53-4 

56.2 

62.0 



I 

2 

3 

I 

7.6 

11.4 

35.8 

37-2 

38.8 

41.8 



I 

2 

4 

I 

7.6 

i 5 . 2 

40.8 

43 -o 

45 .0 

49.0 



I 

2 

5 

I 

7.6 

19.0 

46.0 

48.5 

5 1.0 

56.3 



I 

2b 

4 

I 

9 . 5 

i 5 . 2 

44-3 

46.3 

48.3 

5 2.5 

60% 


I 

2 % 

5 

I 

9.5 

19 . 0 

49. 5 

5 2.0 

54 . 6 

59.8 



I 

2 i 

6 

I 

9 . 5 

22.8 

5 4 .5 

57.5 

60.8 

66.8 



I 

3 

5 

I 

11.4 

19 . 0 

52.8 

55.3 

58 .o 

63.0 



1 

3 

6 

I 

11 4 

22.8 

58 .o 

61.0 

64.0 

7 o -3 



I 

3 

7 

1 

11 . 4 

26.6 

63.0 

66.8 

70. 3 

77.5 


Note:—V ariations in the fineness of the sand and the compacting of the 


concrete may affect the quantities by 10% in either direction. 

*Use 50% column for broken stone screened to uniform size. 

fUse 45% column for average conditions and for broken stone with dust 

screened out. 

JUse 40% column for gravel or mixed stone and gravel. 

§Use 30% column for scientifically graded mixtures. 














































238 


A TREATISE ON CONCRETE 


TABLES OF RUBBLE CONCRETE 

The tables on pages 236 and 237 give the quantities of materials and the 
volumes of concrete mixed in different proportions and with different per¬ 
centages of rubble. The values are made up as described on pages 298 
and 299, where illustrations are given of the methods of computing the cost. 

The percentages of rubble are based on the ratio of the volume of the 
concrete after it is laid, to the actual volume of the large stone contained 
in it. In other words, it is the percentage of the finished concrete occupied 
by the large stone. 


PREPARATION OF MATERIALS FOR CONCRETE 239 


CHAPTER XIII 

PREPARATION OF MATERIALS FOR CONCRETE 

The various operations relating directly to the laying of concrete are 
discussed in detail in this, and several succeeding chapters. While the 
selection of the special methods and machinery, which are described at 
length in the succeeding chapters, are determined by local conditions, 
certain general principles apply to all classes of work. The preparation 
of the materials relates to the storing of cement, the screening of sand and 
gravel, and the crushing of stone. 

STORING CEMENT 

Portland cement is not injured by storing in a dry place for an indefinite 
length of time; in fact, contrary to former belief, instead of deteriorating, 
the quality is often improved by storage. Cement manufacturers when 
rushed with orders sometimes ship material which, not being sufficiently 
air-slaked, contains free lime that exposure to air may change to a hydrate 
and thus render harmless. 

Recognition of the fact that exposure to dry atmosphere does not injure 
cement has led to packing it in bags instead of in barrels, thus saving both 
the cost of the barrel and the extra freight upon it. If, however, the work 
is in a damp location, as in marine construction, barrel shipments are 
advisable. 

The economy of storing the cement as near as possible to the mixing 
platform or mixing machine is obvious, but since, on the other hand, it is 
more easily handled and is always less in volume than sand and stone, 
these should be given the preference in the matter of location. 

SCREENING SAND AND GRAVEL 

The three most common methods of screening are (1) by hand, that is, 
by throwing shovelfuls of the material on to an inclined screen, (2) by 
dumping or hoisting the material on to a fixed inclined screen, (3) by a 
revolving screen. 

Cost of Hand Screening. The cost of hand screening depends upon 
the total amount of material handled rather than upon the quantity of 
sand or gravel produced. A material most of whose particles run through 
the screen can be most cheap 1 v screened, because the screen can be moved, 


240 


A TREATISE ON CONCRETE 


or arranged over a hole, while if a large proportion of the particles are 
caught they must be shoveled from the foot of the screen. 

An average laborer, properly superintended, will throw about 24 cu. yd. 
of material against a screen in a ten-hour day, but in estimating the cost, 
allowance must be made for shoveling the material out of the way, moving 
screen, and superintendence. 

The following are approximate costs of screening sand and gravel by 
hand under ordinary conditions. The prices are from actual records on 
a number of jobs and are based on labor at $1.50 for ten hours, with a 
suitable allowance for superintendence and contractor’s profit. The min¬ 
imum prices apply to first-class men. 


Screening sand, coarse stuff wasted. 

Screening gravel to remove large stones. 

Screening gravel to remove sand,sand wasted. 

Screening gravel coarse, and fine stuff, both measured 


Average 

Minimum 

cost 

cost 

per cu. yd. 

per cu. yd. 

$0.11 

$0.08 

0.15 

0.10 

0.24 

0.17 

0.18 

0.12 


If laborers are working alone with no foreman in sight, as is often the 
case on concrete work, 50% should be added to the average costs. 

Inclined Screen fed by Carts, Derrick Buckets, or Endless Chain. The 
slope of an elevated screen may vary from 35 0 to 45 0 from the horizontal, 
according to the character of the material. Coarser screens are required 
to pass material of a certain size than for hand screening. 

At the new Cambridge Bridge, Boston, the contractors employed a 
screen about 15 feet long, hinged at the top so that the slope could be 
varied to suit the material. A hopper located above the screen fed on to a 
3-inch bar screen, consisting of parallel iron bars about 3 inches apart, 
supported by iron cross pieces about 5 inches apart. The stones too large 
for the concrete ran down this coarse screen, and rolled off one side, while 
the remainder of the material fell through it on to a screen with i-inch by 
J-inch mesh, which separated the medium gravel from the sand. 

On another large job in Everett, Mass., where an inclined screen was 
fed by a bucket elevator supplied by carts, 300 to 350 cu. yd. of sand and 
gravel were screened in ten hours, and an even larger quantity could have 
been handled had it been supplied with absolute regularity. 

The cost of screening by this method depends both upon local conditions 
and the quantity screened. The average cost may be assumed to be from 
4 to 8 cents per cubic yard when large quantities of sand or gravel are 
handled at once. 

Rotating Screens. Rotating screens, cylindrical or hexagonal in shape, 
although most frequently employed for separating crushed stone 





PREPARATION OF MATERIALS FOR CONCRETE 241 


(see p. 245), are also adapted, if power is available, for separating sand 
from gravel, or for separating gravel into several sizes to remix in the theo¬ 
retical proportions required for a dense, impervious concrete. 

While the first cost of a rotating screen is more than that of an inclined 
screen, less elevation is required and it may be fed with a bucket conveyor. 

A plant for ordinary concrete made from two aggregates, sand and 
gravel, requires a screen with only two sizes of mesh, the smaller about 
f-inch and the larger 2, 2\ or 3-inch mesh, as desired. Often no screening 
is required except to remove the sand, as a few large stones do no harm. 
The screen may be about 3 feet in diameter by 12 feet in length. 

The present tendency, for concrete which is to be subjected to severe 
stress or to water pressure, is to require more scientific proportioning by 
separating the aggregate into - several sizes and remixing them so as to 
produce the greatest density. This separation may be accomplished in 
practice by adding more sections, and thus lengthening the screen, or by 
employing a double cylinder, which occupies about half the space of a 
single cylinder. 

The inner cylinder of a double-cylinder screen is composed of two or 
more sections of different sized mesh, and the outer cylinder is composed 
of two or more corresponding sections which are entirely separate from each 
other so that each may discharge into a separate bin. Each outer section 
has a finer mesh than the corresponding section of the inner cylinder. 
The material, after passing through a section of the inner cylinder, falls 
upon the outer wire and is again separated, the part which is caught rolling 

* 

out through an annular opening into one bin and the remainder passing 
through the mesh into another bin. 

STONE CRUSHING 

The crushing of stone for concrete must be approached from a different 
standpoint than the preparation of material for macadam paving, although 
the costs will not vary materially from those of a well-arranged portable 
crushing plant used on road construction. 

For city or town macadam paving, where a suitable ledge is available, 
it is possible to establish a fixed plant with stationary engine, large stone 
bins, and economical machinery for handling cars, so that the stone can 
be hauled over a system of movable tracks directly from the ledge to the 
crusher, while for country road building the plant is arranged with a view 
to its portability, sometimes even resting on wheels. 

For concrete work a plant intermediate in style between these is usually 
required. Its design is governed bv the local conditions and by the quan- 


242 


A TREATISE ON CONCRETE 


tity of concrete to be made. In some cases where the concrete is laid in 
excavation it is possible to locate the crusher on the bank, and allow the 
stone to pass by gravity on to and through an inclined screen, or, if “crusher 
run” is used, to fall directly into a pile below. Generally the stone from 
the crusher must be taken by bucket or belt conveyors to bins, located, if 
possible, above the concrete mixer, or where the stone can be conveniently 
conveyed to the mixer without shoveling. 



NAME AND NUMBER OF PARTS 







1 Main Frame II Upper Half Cheek Plate 21 Balance Wheel 30 Spring Rod 

2 Round Back 12 Lower Half Cheek Plate 22 Bolt for Sw ing Jaw Shaft 31 Spring Bar 

3 Fixed Jaw Plate 13 Bolt for Cheek Plate Cover 32 Washer 

4 Swing Jaw Plate 14 Toggle 23 Bolt for Main Bearing 33 Washer 

5 Swing Jaw 15 Toggle Bearing 24 Pulley 34 Hand Wheel 

6 Pitman < 16 Bolt for Wedge 25 Grease Box Cover 35 Thumb Nut 

7 Toggle Block 17 Bolt for Toggle Block 26 Bolt and Thumb Screw 36 Rubber Spring 

8 Wedge 18 Cover for Main Bearing 27 Bolt for Swing Jaw Plate 37 Bolt for Pulley 

9 Eccentric Shaft 19 Cover for Swing Jaw Shaft 28 Shackle Pin 38 Grease Box Cover on 

10 Swing Jaw Shaft 20 Grease Cup 29 Spring Rod Shackle Main Bearing 

Fig. 77. — Jaw Crusher. ( See p. 242.) 


Stone Crushers. Stone crushers are of two general types, jaw crushers 
and gyratory crushers. 

The size of a jaw crusher is designated by the opening into which the 
stone is introduced. A 16 by 10-inch crusher has jaws 16 inches in width, 
and the space between the two jaws at the top is 10 inches. A “duplex” 
crusher has two pairs of jaws operated by the same shaft, but working 
alternately by means of different eccentrics. Single jaw crushers range 
in size from 3 by 1^ inches to 36 by 24 inches. 

The operation of a typical jaw crusher is shown in Fig. 77. One of the 
jaws is fixed, and the other is hinged at the top, and swung back and forth 














































PREPARATION OF MATERIALS FOR CONCRETE 243 

through a very small arc. The motion is imparted by the eccentric shaft, 
which, in revolving, raises and lowers the “pitman,” whose lower end is 
connected by toggles with the lower end of the movable jaw. The size of 
the stone passing through the jaws, that is, the size of the largest particles, 
is regulated by the opening at the bottom of the swing jaw, which is changed 
by using longer or shorter toggles. 

The capacity of any crusher — that is, the quantity of broken stone 
which it will turn out per hour or per day — is dependent not only upon 
the size of the crusher, but upon the texture of the stone and the sizes of 
the largest particles. From the following catalogue capacities for a 16 
by 10-inch jaw crusher per day of ten hours, it may be inferred that the 
quantity turned out is nearly in the ratio of the sizes of the stones. 

120 tons crushed to 2^-inch size 
100 “ “ “ 2 “ “ 

80 “ “ “ « “ 

« « « J “ U U 

In estimating the actual daily output of a crusher, — and this is in fact 
true for most machinery, — all catalogue figures are likely to be misleading 
because they are based on maximum capacity with continuous feeding, 
while in practice there are likely to be unavoidable delays. An average 
day’s work of ten hours, — based on actual records obtained by the authors 
from a number of jobs, — for a 15 by 9-inch crusher set for 2j-inch stone, 
with a small percentage of tailings, may be taken at 65 cu. yd. or, say, 
78 tons, in ten hours. This estimate applies to continuous running of the 
crusher, allowing only for occasional unavoidable delays.* 

A section of a gyratory crusher, which is adapted for more stationary 
plants, is shown in Fig. 78, page 244. It consists essentially of a cone 
with a gyratory motion within an inverted conical chamber or shell. The 
size of the crusher is determined by the width of the opening between the 
top of the cone and the shell, and the circumference. The gyratory motion 
of the cone shaft is produced by an eccentric keyed to its lower end. As 
the shaft revolves, the cone is given a kind of a rocking motion which con¬ 
tinually directs it toward, and then away from, different portions of the 
shell. The size of the broken stone is regulated by raising or lowering 
the cone on the shaft. 

For a concrete plant producing 200 cubic yards per day, manufac¬ 
turers recommend a No. 4 gyratory crusher with openings 8x27 inches. 

The horse-power required to drive a crusher and its attendant machinery 

*The Annual Report of the Newton, Mass., City Engineer for 1891 gives interesting data op 
detail costs of stone crushing, a portion of which are here summarized on page 249. 


244 


A TREATISE ON CONCRETE 


varies largely with the material handled. It is advisable to make ample 
allowance above the figures given in manufacturers’ catalogues. It is, 
also, economical to use a wider and heavier belt than is generally specified, 



Hopper 


Bottom 

Shell 


double Counter 


Driving i Pulley 


iBreakPin 


-I,.:.:i 


* Counter Shaft 


—-%—~r 




lWheel 


"-"gJ 


Weari it& Ring 


-Boptom Plate. 


Lighter Screw 


Fig. 78.—Gyratory Crusher. (See p.243.) 


in order to avoid delays and shutdowns. When ordering almost any kind 
of machinery the authors make it a practice to require a wider and heavier 
pulley than the standard width. It is wise to make a pulley at least 
2 inches wider than the belt which is to be run upon it. 








































































































































































PREPARATION OF MATERIALS FOR CONCRETE 245 

Crusher Screens and Bins. A typical design, by Mr. Earle C. Bacon* 
for bins suitable for a plant where the concrete mixer or mixing platform is 
located at a distance from the crusher is shown in Fig. 79. With slight 
changes they may be arranged to discharge into hoppers over a concrete 
mixer. The dimensions of timber employed in the construction may be 
used as a basis for bins of other sizes. 



Fig. 79.—Small Crushing Plant with Elevator, Screen, and Portable Bins. (See p. 245.) 


A safe slope for the bottom of stone bins is 45 0 , although if lined with 
sheet iron this may be decreased to 35 0 or 40°. 

Screens for broken stone as shown in Fig. 80, page 246, are usually made 
in sections varying in length from 3 to 5 feet, so that they can be bolted to¬ 
gether and give as many divisions of sizes as are required. The diameters 
vary from 24 to 48 inches. The mesh of a rotating screen should be about 
20% smaller in diameter than the required size for the stone, as there is 
more or less wear on the screen, which enlarges the holes, and this allow¬ 
ance will also assist in excluding the oblong pieces whose longest dimen- 




















































































































































246 


A TREATISE ON CONCRETE 


sion is above the limit. For concrete, unless two or more sizes of stone 
are mixed, no more than two sizes of mesh are required, one, J-inch to 
remove the dust, and the other, 2, 2j, or 3-inch to remove the coarse stuff. 
Often it is necessary only to remove the dust which may then be used as 
sand. 

Stone Bin Gates. A gate designed by Mr. C. S. MacHenry, of the 
Greene Consolidated Copper Co., has proved extremely satisfactory for 
cutting off the flow of materials of the nature of broken stone, gravel, and 
sand. A detail drawing of this is shown in Fig. 81. 

Cost of Stone Crushing. The cost of stone crushing is so dependent 



r'lG. 80 — Rotating Screen. {See p. 245.) 


upon local conditions and upon the character of the rock, that only approxi¬ 
mate estimates based upon actual experience can be given. There are, 
in general, two classes of work, — one where the rock is blasted from a 
ledge near at hand, and the other where the crushers are supplied with 
boulders or other loose rock. The gang at the .crusher is similar in both 
cases, and the chief difference in operation is the extra gang for drilling 
and breaking up the stone in the ledge. On the other hand, usually more 
permanent, and therefore more economical, arrangements for hauling the 
stone can be made in ledge excavation than when th'e stone is obtained 
from various sources. 




247 


i 

£ 

$ 

£ 

$| 

I 


5 

1 

< 5 . 

1 

I 







tlG. 81.—Gate for Stone or Sand Bins. (See i). 246.) 











































































































































248 


A TREATISE ON CONCRETE 


A typical gang* for operating a 15 by 9-inch crusher, turning out, say, 
65 cubic yards of broken stone in ten hours, is as follows: 

One foreman. 

One engineman. 

Two men feeding crusher. 

One other man at crusher on odd work. 

Three men loading stone into carts to supply crusher. 

Two single carts with one teamster hauling stone to crusher. 

The number of teams required to haul stone to crusher depends, of 
course, upon the length of haul. Sometimes additional men will be needed 
to pass the stone to the men feeding the crusher; on the other hand, if the 
stone is dumped directly into a hopper above the crusher so as not to re¬ 
quire handling, two men are capable of supplying a crusher whose capacity 
is 200 cubic yards per day. 

The labor of drilling a ledge obviously depends upon the quality and 
seaminess of the rock and the depth of the holes. Under ordinary condi¬ 
tions, a steam drill with two men can be counted upon to loosen consider¬ 
ably more rock than can be handled by a 15 by 9-inch crusher. The cost 
of barring out and sledging the blasted rock may be estimated on the basis 
of about 10 cubic yards (measured after crushing) per man per day of ten 
hours. If the crusher is a large one, say a No. 6 rotary (n by 36 in.), 
a man will bar and sledge about double this quantity because it does not 
need to be broken so fine. The figures are averaged by the authors from 
actual observed speeds on a number of jobs. 

In estimating the cost of crushing stone, the original cost of the plant is 
an important item. The allowance for this per yard of rock is dependent 
upon the length of time the plant is to be operated, and the probable value 
of the machinery when the work is complete, as well as upon the interest 
on the investment and the cost of repairs. A plant similar to that shown in 
Fig. 79, page 245, with a 16 by 10-inch jaw crusher, may be estimated to 
cost from $2,000 to $2,5oo.f 

A very careful analysis of the actual cost of crushing stone for macadam 
in a large gyratory crusher was made by Mr. Albert F. Noyes, City Engi¬ 
neer of Newton, Mass. His prices are based on common labor at $1.75 
per day of nine hours, drill men at $3.00, drill helpers at $1.75, engineman 
for crusher at $2.00, and two one-horse carts with driver at $5.00. The 
detail costs per cubic yard of crushed stone were as follows: 

♦Actual gang employed on a concrete contract for the Metropolitan Water Works, Mass. 

f Estimated by Earle C. Bacon. 


PREPARATION OF MATERIALS FOR CONCRETE 249 

Cost per cubic yard 0} Quarrying and Crushing Hard Green Trap at Newton , Mass* 


Labor of steam drilling. $0,092 

Coal, oil, waste, powder, drilling and repairs for drilling and blasting. 0.084 

Shaipening drills and tools. 0.069 

Breaking stone for crusher. 0.279 

Filling carts with rough stone. 0.098 

Carting stone to crusher. 0.072 

Feeding crusher. 0.05 3 

Engineman of crusher. 0.031 

Coal, oil, and waste for crusher. 0.079 

Repairs . 0.041 

Total cost per cubic yard of crushed stone. $0,898 


The total cost of crushing in a jaw crusher conglomerate ledge stone 
drilled by hand, Mr. Noyes gives as $1,113 P er cubic yard; of trap cobble 
stone wheeled to crusher in barrows, as $0,445 P er cubic yard; and of 
granite cobble stone hauled in carts, as $0,372 per cubic yard. 

These costs, which, as well as the wages paid per day, must be taken into 
account when estimating under other conditions, are based upon an output 
per hour of 7.7 cubic yards hard green trap, 8.9 cubic yards conglomerate 
ledge, 11.8 cubic yards trap cobble stone, and 9 cubic yards granite cobble 
stone, j* 

Data on Broken Stone. Broken stone is often sold by weight instead of 
by the cubic yard, because of the variation in volume due to handling or 
transporting. A cubic yard of broken trap stone may vary in weight 
from 2 400 to 2 700 pounds. J If measured after carting some distance, 
broken stone will weigh about 10% heavier per cubic yard than at the 
crusher, because of the settling. The authors have found by repeated 
measurements that 100 pounds per cubic foot is a fair average weight for 
screened trap rock after it has been shaken down by hauling, although 
when measured loose in a small measure an average weight is about 90 
pounds. Crusher run stone is about 10% heavier than this because it 
contains less voids. Stones having lower specific gravities than trap are 
correspondingly lighter in weight. § 

On macadamized or paved roads, if no steep hills are to be encountered, 
two horses will haul from 6 000 to 7 000 pounds of broken stone to a load. 
Very high side boards are of course necessary to carry this quantity. 


*Annual Report of City Engineer for 1891. 

fCost per cubic yard of stone crushing for pavement in various towns is given in Report Mass. 
Highway Commission, 1895, p. 38, and further data in Engineering News, March 27, 1902, p. 
258, and Jan. 15, 1903, p. 55. 

jFor data on weights, see article by W. E. McClintock in Journal Association Engineering 
Societies, Vol. XI., p. 424. 

§See table, p. 163. 













250 


A TREATISE ON CONCRETE 


Numbers are used to designate the sizes of stone on road construction, 
and stone bought from a crusher is likely to be sold in this way. In such 
cases it must be borne in mind that these numbers are of local significance. 
Some plants call their finest product, including dust, No. i stone, while 
others commence to number from their coarsest size or tailings. 

WASHING SAND AND STONE 

Gravel frequently requires washing to remove the coating of clay or loam 
from the pebbles. Crushed stone may require removal of the dust. Sand 
sometimes has too much silt to produce a strong concrete, or may contain 
vegetable matter (see p. 154b) which renders it absolutely unfit for concrete. 
Washing also may be employed to assist in the separation of aggregates 
into the sizes required for accurate proportioning. 

The most satisfactory plan for washing appears to be to wash the mate¬ 
rial down a trough over screens in the bottom of the trough, or against and 
through screens inclined in the opposite direction from the trough. Screens 
with round punched holes are better for this purpose than wire mesh. 

Bellows Falls Canal Company’s Plant. The method used by the Aber- 
thaw Construction Company for washing both the crushed stone and gravel 
consisted of shoveling the material from an elevated platform into inclined 
chutes over the upper end of which were placed eight i-inch pipes with 
their lower ends hammered together to form a spray. The water from these 
pipes washed the gravel and stone down the chute into storage bins below, 
the dirty water passing through screens near the bottom of the chute into 
troughs lined with tarred paper which carried it away. For washing 
stone or gravel, |-inch screens were used, and for sand, No. 20 mesh screens, 
the latter requiring frequent cleats to support the wire cloth! 

Rockingham Power Company Washing Plant.* In this plant the gravel 
was dumped as it came from the pit into hoppers forming the upper end of 
an inclined sluice carried on a light pole trestle. Enough water was then 
drawn from an elevated tank to float the gravel down the chute to the lower 
end which terminated in an inclined screen with ^-inch mesh. The water 
and sand passed through the screen into hoppers below, while the pebbles 
rolled along the screen and passed over the end into a gondola car. The 
water overflowing the sides of the sand hopper carried off the loam and 
lighter material while the sand settled, and when the hopper was filled 
it could be drawn off into cars beneath. 


* Engineering-Contracting, May, 13, 1908, p. 292. 


MIXING CONCRETE 


251 


« 

CHAPTER XVI 

MIXING CONCRETE 

The method employed for mixing concrete is immaterial, provided the 
result is a homogeneous mass of the required uniform consistency, con¬ 
taining the various aggregates and cement in proper proportions. If the 
color of the mass is not absolutely uniform, that is, if uncoated particles 
of sand or stone are visible, if masses of stones are separate from the 
mortar, or if some portions of the mortar are dryer than others, the mixing 
has not been thorough. 

Hand vs. Machine Mixing. First-class concrete may be produced, with 
careful superintendence, by either hand or machine-mixing. 

The relative cost of the two methods depends entirely upon circum¬ 
stances, and must be estimated for each individual case. If the job is a 
small one, so that the cost of erecting the plant plus the interest and de¬ 
preciation, divided by the number of cubic yards to be made, is a large item, 
or if frequent moving is required, concrete may be and often is mixed 
cheaper by hand than by machinery. The information which follows 
concerning both methods will serve as a guide for comparison in special 
cases. 

MIXING CONCRETE BY HAND 

The methods employed by different engineers and contractors for 
handling the materials and arranging the men are nearly as varied with 
hand-mixed as with machine-mixed concrete. Concrete mixing is seem¬ 
ingly so simple an operation that it is often neglected by the inspector, 
and poor workmanship escapes detection. 

The inspector should lay the greatest stress upon (a) exact measurement 
of the gravel or broken stone, ( b ) thorough mixture of the cement and 
sand, (c) thorough mixture of the mass, and (d) care in dumping the con¬ 
crete into place. The quantity of water used in the mixing and the proper 
ramming or puddling of the concrete in place are equally important but 
are less likely to be overlooked. 

In proportioning the ingredients, it is poor economy to make allowance 
for insufficient mixing or improper handling of the materials. The addi¬ 
tional cement will be much more expensive than the extra time expended 
by laborers in securing a homogeneous mixture. 

In the first place the mixing platform should be located as near the work 


252 


A TREATISE ON CONCRETE 


as possible, and so situated that the coarse materials can be conveniently 
dumped on one side of it and the sand on the other. It should be not less 
than 15 to 20 feet square if all the work is to be done upon it, and except 
for a very small job should be of 2-inch plank, planed one side, spiked to, 
say, 2 by 4-inch stringers about 5 feet apart, so that it can be moved from 
place to place as required. A 2 by 3-inch strip around the edge will pre¬ 
vent loss of material. If the sand and cement are made into a mortar 
before mixing with the stone, the platform may be narrower and a mortar 
box employed in addition. 

Methods of Measuring Material. Cement should invariably be meas¬ 
ured by weight. In practice this is accomplished not by weighing on 
scales but by counting packages, since bags or barrels of cement have 
standard weights.* 

The volumes of sand and stone or other aggregate should be distinctly 
stated in the proportions in terms of the number of cubic feet of each 
material to a barrel of cement, or else by parts, coupled with the explana¬ 
tion that one part, or barrel, represents a definite volume, such as 3.8 cubic 
feet. In specifications where the proportions are given by parts with no 
unit of measurement, the contractor undoubtedly has the legal right to 
base the volumes of aggregate on the loose measurement of cement, hence 
the necessity of exact statement of units, as prescribed on page 217. 

The sand measure preferred by the authors is a bottomless box similar 
to the gravel box shown in Fig. 5, page 18, having a depth of about 6 inches, 
and other dimensions determined by the required volume. The filling of 
cement barrels or half-barrels with sand is a slower and less accurate process. 
If the sand cannot be conveniently unloaded close to the measuring plat¬ 
form, it may be measured in a barrow or other wheeled vehicle so con¬ 
structed that it can be accurately leveled off after filling. For rough 
measurement ordinary contractors’ barrows, whose approximate “large” 
capacities are given on page 9, are suitable. If more exact quantities are 
required, however, it takes only a few more seconds to dump the sand 
from the barrows into a bottomless box. 

For gravel or broken stone a bottomless box about 8 or 9 inches deep, 
shown in Fig. 5, page 18, is a convenient measure. Special barrows built 
to exact dimensions are more exact measures than ordinary contractors' 
barrows and, in some cases, than the bottomless box, because an unscrupu¬ 
lous contractor can more easily heap the material in the latter when the 
inspector’s back is turned. Cement barrels are accurate measures, but 
time is wasted in lifting the shovels when filling, and in dumping them. 

♦See page 2. 


MIXING CONCRETE 


253 

A measuring barrow car,* built so that it can be handled with a derrick, 
is sometimes convenient. 

Hand Mixing. A detailed description of one of the best ways to mix 
concrete by hand is given in Chapter II for the benefit of those not familiar 
with concreting. It is the general opinion of concrete experts that the 
particular order adopted for mixing the materials has little effect upon the 
strength of the concrete, provided the materials are turned a sufficient 
number of times to incorporate them thoroughly. Some engineers prefer 
to make the cement and sand into a mortar, while others do not add the 
water until the final turning. The authors have seen excellent work pro¬ 
duced by both methods, but prefer the latter chiefly because shoveling the 
mortar on to the stone involves more labor than handling the dry mixed 
cement and sand; in fact, comparative tests show that it costs less to mix 
the cement and sand dry, shovel the mixture on to the stone and mix three 
times, than to make a mortar, shovel it on to the stone and mix only twice. 

Methods variously employed, the first of which is described in detail on 
page 21, are outlined as follows: 

(1) Cement and sand mixed dry and shoveled on to the stone or gravel 
leveled off, and wet as the mass is turned. 

(2) Cement and sand mixed dry, and the stone or gravel dumped on 
top of it, leveled off, and wet as the mass is turned. 

(3) Cement and sand mixed with water into a mortar which is shoveled 
on to the gravel or stone, and the mass turned with shovels. 

(4) Cement and sand mixed with water into a mortar, the gravel or 
stone spread on top of it, and the mass turned with shovels. 

(5) Gravel or stone, sand, and cement, spread in successive layers, 
mixed slightly and shoveled into a circle or crater, water poured into the 
center, and the mass mixed with shovels and hoes. 

The last method is applicable only where a small amount of concrete is 
to be mixed on the ground with no mixing platform or mortar box. 

Sand and cement must never be mixed up in advance, as lime and 
sand are often mixed, because the natural moisture which all sands contain 
will make the cement set and cake. 

The systematic arrangement of the men in pairs, as described on page 
21, and insistence upon their shoveling from the bottom of the pile and 
then turning their shovels completely over, are essentials for thoroughly 
mixed concrete. In the final wet mixing the materials should be turned 
in this way two or three times. 

For wetting the concrete some engineers specify spraying with the hose, 

*See illustration in Engineering News, April 23, 1896, p. 268 


254 


A TREATISE ON CONCRETE 


but in practice there appears to be no special advantage in this over ordinary 
galvanized iron buckets, while with the latter the quantity can be gaged 
more accurately by filling the required number of buckets in advance. 
Nearly all the water can be poured on the dry materials before commencing 
to turn, and the remainder used to wed up occasional dry spots. 

The quantity of water is regulated according to the appearance of the 
concrete after placing. In a thin wall the water will rise to the surface 
through successive layers so that the first batches in a day’s work require 
the most water. Whatever the quantity, it should be thoroughly incor¬ 
porated with the other ingredients, and the amount which can be thus 
incorporated may sometimes be taken as the allowable limit in hand¬ 
mixing. The best consistency for different classes of concrete is dis¬ 
cussed on page 279. 

Distribution of Mixing Gang. Whatever the methods of mixing, the 
chief requisites for economy are such an arrangement of the gang that each 
man will have definite duties, and that the number of men on one set of 
operations will perform their work in the same length of time required by 
another set of men to perform a different operation or set of operations. 
A gang should be as large as practicable in order to lessen the cost of 
superintendence and the general expense. 

The best plan, where the size of the gang can be regulated to suit, is to 
give each man a single operation to perform. For example, let one man 
or set of men wheel and measure all the sand; let another set of men mix 
the sand and cement; let a third set be continually employed measuring 
the gravel or stone; a fourth mixing the mass, while one or two of their 
number supply water; a fifth filling the barrows and wheeling the con¬ 
crete to place, and still another set leveling the concrete and ramming or 
puddling. 

It is generally economical to have two batches of concrete in preparation 
at once, although one set of men usually can measure and mix the sand and 
cement for two mixing gangs. While one batch of concrete is being 
shoveled to place or wheeled in barrows, the other batch, either in a different 
location on the same platform or on a separate platform, may be spread 
and mixed. 

The method of handling a small gang is described on page 21. The 
arrangement of gangs on two well managed actual jobs is illustrated in 
the following outline: 

(1) Gang on a core wall for a dike where the sand and cement were 
mixed dry and spread on to the stone, then wet as the mass was 
turned. 


MIXING CONCRETE 


2 55 

The large mixing platform was located 30 to 50 feet distant from the 
excavation, and the concrete was handled in wheelbarrows. 

One foreman. 

One man wheeling sand to measuring box. 

Two men, working alternately at the two ends of the mixing platform, 
opening cement, and mixing sand and cement dry. 

Three or four men, working alternately at each end of platform, shoveling 
gravel into bottomless boxes. 

Six men working alternately at each end of platform, mixing concrete 
(turning it three times). 

Two men handling water. 

Four men wheeling concrete, each filling his own barrow. 

four men leveling and ramming. 

The average quantity of concrete in proportions 1:2:5 laid by this gang 
per day of ten hours was about 65 batches or 47 cubic yards, with a maxi¬ 
mum of about 90 batches or 65 cubic yards. 

(2) Gang for a 6-inch foundation for a street pavement, where the sand 
and cement were made into a mortar and spread on to the stone, and 
where two mixing platforms were used, one on each side of the street, 
with a mortar box between them. 

One foreman. 

Two men mixing mortar in one mortar box. 

Four men shoveling stone alternately into two measuring boxes. 

Four men working alternately on the two mixing platforms, spreading 
mortar on stone, mixing concrete, and shoveling to place. 

Three men leveling and ramming concrete and also assisting to shovel 
to place. 

One man carrying water and doing other odd work. 

The total quantity of concrete in proportions 1:2:5 laid per day of ten 
hours averaged from 40 to 46 batches or 29 to 33 cubic yards per day 
for the gang. The gang was not quite up to the average, for under given 
conditions they ought to have turned out regularly 34 cubic yards per day 
of ten hours. 

Approximate costs of concrete mixing are discussed on page 25. 

MIXING BY MACHINERY 

On all large contracts, machinery for mixing concrete is universally 
replacing hand labor. The economy of this usually is due as much to 
the appliances introduced for handling the raw materials and the concrete 


256 


A TREATISE ON CONCRETE 


as to the saving in the actual labor of mixing. Any arrangement which 
requires the measuring and spreading of materials by shovelers before 
entering the mixer results simply in saving the process of hand turning 
of the concrete and the labor of shoveling it into the vehicle, and this saving 
is partly balanced by the cost of maintaining and operating the mixer. 
On a small job this last item almost invariably exceeds the saving in hand 
labor and renders the expense with the machine greater than without it. 

The design of the appliances or plant for handling the materials, and to 
some extent the selection of the type of mixer, depends upon local condi¬ 
tions, the quantity to be mixed per day, and the total volume of concrete. 
For a large mass of concrete masonry it is evident that it pays to invest a 
considerable sum in machinery to reduce the number of men and horses, 
but if for any reason only a small quantity, we will say not over 50 cubic 
yards, can be deposited in a day, the cost of expensive machinery cuts a 
very large figure and hand labor is generally cheaper. In estimating the 
interest on the cost of the plant which must be charged against a cubic 
yard of concrete, instead of dividing the interest per day by the usual 
daily output, the interest for the year must be divided by the total amount 
of concrete to be laid in the year. In other words, allowance must be 
made for the days when inclement weather prevents work. To find the 
depreciation, the value of the entire plant when new, minus its value after 
the job is completed, is divided by the total number of yards of concrete. 
Some of the other running expenses, such as the wages of the engineman, 
may continue from day to day whether or not any concrete is being laid. 

Concrete Mixers. An effective concrete mixer not only stirs the mass, 
which may tend to separate the light and heavy particles, but cuts it again 
and again, and repeatedly transfers the materials from one part of the 
machine to another, so that in whatever order they are introduced, the 
product will be homogeneous. Continuous turning alone does not ac¬ 
complish the result so quickly or thoroughly as the more complicated 
motions. The appearance of the concrete as it falls from the mixer will 
often distinguish the better of two machines. 

The larger the machine, the more economical it will be, provided the 
arrangements for supplying it with material and conveying the concrete to 
the work permit running at full capacity. 

Concrete mixers are of two general classes: (1) continuous mixers into 
which the materials are fed constantly, usually by shovelfuls, and from 
which the concrete is discharged in a steady stream, and (2) batch mixers, 
designed to receive at one charge, say, a barrel or a bag of cement with its 
proportionate volume of sand and stone, and after mixing to discharge it 


MIXING CONCRETE 


*57 


in one mass. It is impossible to separate these two classes very distinctly 
because many of the machines are adapted to either continuous or batch 
mixing. 

The authors are opposed, as a rule, to the use of continuous mixers, 
unless the materials are measured and fed mechanically, because of the 
difficulty of uniform feeding. When the ingredients are measured out by 
hand, spread in layers one above another, and then, starting at one edge, 
are shoveled into the mixer, the proportions of the materials in the resulting 
concrete are regulated by the thickness of the layers of the different in¬ 
gredients rather than by the dimensions of the measuring barrels or boxes. 
If in one portion of the pile the layer of cement is thicker than in another, 
the resulting concrete will be proportionally richer. With batch mixers 
all the materials enter the machine at once; the homogeneity of the product 
depends upon the character and length of time of mixing rather than upon 
the care exercised by the laborers in feeding, and less inspection is neces¬ 
sary. 

The regulation of the water supply in machine-mixing as in hand¬ 
mixing is largely a matter of judgment. Even if the materials were all 
supplied under absolutely uniform conditions, the same volume of water 
would not produce from each batch a concrete of uniform consistency, 
because, as the concrete is laid, the water works up through from one layer 
to the next, so that more water may be necessary early in the morning than 
later in the day. It is well, nevertheless, to roughly measure the quantity 
each time, varying the amount from batch to batch as the condition of the 
materials and the state of the mass require. 

The selection of the type of mixer is often governed by local conditions. 
If, for example, there is to be a large quantity of concrete, and the machinery 
can be located at one place, a stationary machine, mounted perhape on 
timber framework, with derricks, elevators, or belts, to raise the materials, 
may be economical. On running work, like a conduit or retaining wall, 
more portable machines are required, while for thin layers, like pavement 
foundations, if any machine is used it must be very light or easily moved. 
If stone for the aggregate is to be broken on the spot, a stationary plant 
may be built, or the stone may be hauled from the crusher bin to the mixer. 
In some cases the conformation of the ground will permit of dropping the 
materials into or through the machine by gravity. Frequently the volume 
of concrete to be laid is limited by the construction of forms, and a machine 
of small size is sufficient. 

Mixers may be classified in three general types: 

Rotating mixers. 


258 


A TREATISE ON CONCRETE 


Paddle mixers. 

Gravity mixers. 

Rotating or rotary mixers, as they are usually termed, sometimes mix 
the materials by simply tumbling them in an oblong or cubical box, and 
in other cases by throwing them against the deflectors, blades, or plows. 

The cubical box is one of the simplest forms of rotating mixers, and 
formerly was used largely on extensive concrete construction, but is now 
giving place to modified forms which permit more thorough mixing and 
the inspection of the material during mixing. The cubical box is of steel, 
generally mounted on a timber frame similar to the plan in Fig. 94, page 
272. The shaft for revolving it runs through two opposite corners and 
consists of a perforated [hollow tube which supplies the water. The 
measured materials are dropped in from above through a hinged door in 
the side of the mixer, and the machine after some twelve or fifteen revolu¬ 
tions is stopped, the door is opened, and the concrete dropped into carts or 
cars When most of the concrete is out, the box is revolved once again to 
empty it more completely. The mixer itself is inexpensive, but the cost 
of erection and of raising the stone and sand often renders it less eco¬ 
nomical than more expensive machines. 

Cube mixers are also made on a frame and geared so that they may rotate 
while filling and dumping as illustrated in Fig. 85. 

The rotating mixers illustrated in Figs. 82 and 83 which contain deflec¬ 
tors, or blades, are usually mounted by the manufacturers upon a suitable 
frame, although in certain cases it is preferable to construct special timber 
framework, so that materials may be introduced and the concrete taken 
away more economically. The larger machines of this type are so con¬ 
structed that the materials can be introduced from derrick buckets, carts, 
or barrows. The rotating of the drum tumbles the material and also throws 
it against the mixing blades which cut and throw it from side to side. Most 
of these machines can be dumped while running, by tilting either them or 
their chutes. They are also provided with hoppers as shown in Fig. 83, 
or with loading skips or trays, operated by the engine that runs the mixer, 
which lift the materials from the ground up to the charging hopper as in 
Figs. 82 and 85. 

A different style of rotary machine is shown in Fig. 84. It consists of 
an open revolving pan in which are stationary plows which mix the concrete. 
The outlet is through trap doors in the bottom. 

Of the paddle mixers, those adapted to mix a batch at a time can be 
more surely depended upon to produce good concrete than the continous 
machines. Fig. 86 shows a duplex paddle mixer to be placed upon a 


MIXING CONCRETE 


259 


raised platform and fed by hand wheelbarrows or derrick buckets. The 
mixing paddles, on two shafts, revolve in opposite directions, and the concrete 
falls through a trap door in the bottom of the machine into carts, cars, or 
wheelbarrows, or upon a platform whence it is shoveled to place. 

The continuous paddle mixer with a single shaft and an open end is some¬ 
times used for a volume of concrete ranging from 75 to 150 cubic yards per 
day. Care should be taken that the materials are thrown in near enough the 
upper end to be thoroughly mixed. The water is usually fed near the 
middle of the machine so that the materials are first partially mixed dry. 
They may be measured by shovelfuls, or by spreading in layers before 
shoveling into the mixer, or by automatic machinery which feeds the cement 
and each aggregate in the proper proportions. 



Fig. 82.—Rotary Mixer. (See p. 258.) 


Measuring the materials by shovelfuls would seem at first thought likely 
to give a poorer quality of concrete than measuring in boxes or barrels, 
but with a properly trained gang and periodic checking of the number 
of barrels of cement to a given volume of concrete, fair results may be 
obtained. At the Charlestown Bridge piers in Boston (see Fig. 92, p.270), 
the contractors, by changing off the men who shoveled into the mixer so 
as to give them light work half the time, turned out (by steady work) 
concrete at the rate of about 17 cubic yards per hour. Each feeding 
gang consisted of five men, three shoveling gravel, one shoveling sand, 

























260 a TREATISE ON CONCRETE 


Fig. 83.—Rotary Mixer. 


{Seep. 258.) 


Fig. 84.—Revolving: Pan Mixer. (See p. 258.) 





















MIXING CONCRETE 


261 


and one shoveling cement, the size of shovels being so arranged that when 
all worked together the proper proportions were introduced. The two 
gangs changed off every half-hour. 



Fig. 85.—Rotary Cube Mixer. (See p. 258.) 



Fig. 86.—Duplex Paddle Mixer. (See p. 259.) 


When the materials are measured and spread in layers before shoveling 
into the mixer, the machine should be below the measuring platform, and 
two gangs of men employed, one on each side of the machine, so that one 









262 


A TREA TISE ON CONCRETE 



batch may be prepared while another is entering the mixer. This seems 
like a very simple requirement, yet the authors have often seen a single 
gang measure out the materials on the ground while the machine stood 

idle, and then lift them to a 
height of perhaps 3 or 4 feet, 
while the mixed concrete fell 
to the ground to be shoveled 
into barrows. With such an 
arrangement, hand-mixing is 
cheaper than machine-mixing. 

Gravity machines, properly 
so-called, require no power, 
the materials being mixed by 
striking obstructions which 
throw them together in their 
descent through the machine. 
A gravity concrete mixer is il¬ 
lustrated in Gillmore’s “Treat¬ 
ise on Limes, Hydraulic Ce¬ 
ments and Mortars,”* first 
published in 1863. In this 
machine the concrete fell into 
successive hoppers opened and 
closed by hand-levers. 

A well-known modern type 
of the gravitv machine, shown 
in Fig. 87, may be increased 
in length from 4 to 10 feet 
by adding different sections. 
In falling through the slant¬ 
ing tube the materials are 
thrown by the deflectors on 
the sides and the curved 
back — the deflectors also 
acting as tables upon which 
Fig. 8 7 .-Gravity Mixers. (See P . a 63.) the stones are coated with 

mortar against several series of iron rods which mix them violently 
together. The inventor claims that by this violence the cement is pounded 
into the fractures and indentations of the sand and stone so as to increase 


*Page 229. 



MIXING CONCRETE 


263 


the strength of the concrete produced. The materials generally are 
measured in layers on a platform above the machine and fed by shovels, 
but may be fed by a tipping box or by a derrick bucket. In the latter 
case the mixer becomes practically a batch machine. 

Another gravity mixer is illustrated in Fig. 88. Four cone-shaped 


3 STORAGE BINS EACH 4 FT. X 13 FT. 





FOUR HOPPERS,ONE MAN TO EACH 



SIDE ELEVATION 


Fig. 88.—Gravity Mixer. (See p. 263.) 

hoppers at the top of the machine receive the materials in layers, with 
the cement at the bottom and the coarsest material at the top. From 
these, on the opening of gates, the mixture falls into a single cone below, 
and thence at the will of an operator into a still lower cone, whence it 
drops into the car or other receptacle. The same type of mixer is used 

























































































264 


A TREATISE ON CONCRETE 


with a derrick so that the mixing progresses while the material is being swung 
to place. A series of cone-shaped buckets, telescoping each other when 
at rest, are connected with chains so that the concrete materials may be 
placed in the upper one and will fall when this is raised through an open¬ 
ing in the bottom to the next, and so on to the lowest bucket, from which 
it is dumped into the work by the operator at the place where it is needed. 

Portable Concrete Mixing Machinery. Nearly all the types of con¬ 
crete mixers described are made, at least in their smaller sizes, so that 
they can be readily transported from one part of a job to another. A 
few of them are adapted for such work as laying a thin foundation for 
street paving, while the heavier machines are sometimes arranged upon 
cars running on a track, so that the concrete can be dropped directly into 
place from the mixer, or conveyed to place by an endless belt. 

On the Chicago & Western Indiana R. R.* a train was made up for 
preparing and depositing concrete for retaining walls. Three or four 
cars carried the stone, sand, and cement, and from these the materials 
u. were conveyed by wheelbarrows to the mix- 

o 

ing car, where the sand and stone were 
measured, dumped into the mixer, and thence 
onto a belt conveyor mounted upon a swing¬ 
ing steel boom like a derrick boom, which 
deposited at any point within derrick swing. 
The train was hauled by the winding drum 
on the same engine which operated the 
mixer, a cable running ahead to an anchor 
or “dead-man” in the ground. 

In building a dam at Chaudiere Falls, 
P. Q.,f tracks were laid just above and below 
the site of the dam and parallel to it, and a 
traveling platform containing the mixer was 
constructed so as to straddle the dam. The 
mixer discharged the concrete into the upper 
end of a tube fitted with a lower telescoping 
section, so that it could be deposited directly on any part of the dam. 

Automatic Measurers for Concrete Materials. The accurate measur¬ 
ing of concrete materials by mechanical means has not been extensively 
developed. One difficulty, if methods of volumes are employed, lies in 
the inaccuracy of measuring cement by volume. 



SECTIONAL elevation 
OF oouble measuring 

MACHINE 


Fig. 89. —Measurer for Con¬ 
crete Materials. (Seep. 265.) 


^Engineering News, Feb. 28, 1901, p. 149. 
f Engineering News, May 7, 1903, p. 403. 








































MIXING CONCRETE 


265 

One patented device consists of several drums, one for each material 
placed directly under the bins containing the cement, sand and stone, and 
rotating upon the same horizontal shaft. The quantity of each material is 
regulated by the position of the gates in the bins and by the speed of rotation. 

Another machine delivers the different materials through separate 
troughs containing Archimedean screws. 

Another type of measuring machine, the working of which is illustrated 
in Fig. 89, consists of one or more bottomless storage cylinders, from 
under which the material flows out on to revolving discs or tables, and 
is peeled off by stationary adjustable knives which rest upon the discs 
and project into each material a distance determined by the quantity of 
each required. 

A partially automatic measuring arrangement was employed on one 
section of the Boston Subway, in 1896. Each material fell into a closed 
chute arranged with gates at such distances apart as to enclose the required 
volume, whence it dropped into a hopper above the mixer. 

Proportioning by Weight. Attention has been called on page 217 to 
the fact that not only cement, but also sand, stone, and gravel, can be more 
accurately proportioned by weighing than by volume measurement. When 
a large amount of concrete is to be mixed, it is possible to arrange apparatus 
for weighing each material in such a way that less labor will be required 
than for proportioning by volume. The first cost of the scales may often 
be more than counterbalanced by the accuracy in proportioning, which 
permits of leaner mixtures, while at the same time greater uniformity is 
assured. 

In view of these facts, the authors predict that engineers will gradually 
recognize the advantage of proportioning bv weight. In most cases ex¬ 
cessive cost may prohibit the use of standard scales, but if the materials 
are accurately screened and subdivided, the relative weights of each on 
the same job will be so nearly constant that the weighing can be performed 
by a simple system of counterweights and levers. With properly con¬ 
structed gates to the bins it might be possible to arrange for their auto¬ 
matic closing after the required weight of each material had been received 
in the hopper. 

Measurements by weight are employed to excellent advantage by War¬ 
ren Brothers Company at their various plants where the materials, which 
consist of stone, sand, and binding material, are prepared for their bitu¬ 
minous macadam pavement. Eight bins containing aggregates of different 
coarseness drop their materials through gates into a hopper which forms 
the platform of the scales and is located directly above the mixer. The 
scale-beam is compound, with as many arms as there are ingredients to 
be weighed, and each of the arms has a sliding weight and a stop so ar¬ 
ranged that the sliding weight can be moved only to the point on the beam 
which will balance the required weight of one of the materials. When the 


266 


A TREATISE ON CONCRETE 


sliding weights are all at zero and the hopper is empty, the scale balances. 
The weight on one of the arms is moved out by the laborer who operates 
the apparatus until it comes to the stop fixed at the point corresponding 
to the weight of the material to be used from a certain bin. The gate of 
this bin is opened, and the material allowed to run into the hopper until 
the scale balances. The weight on the next lever is then slid out, and the 
second material deposited in like manner upon the first. When all the 
materials are thus weighed, the entire mass is dropped into the mixer below. 

Measuring Water. The water for each batch of concrete should be 
measured. The quantity of water used in different batches must be varied 
occasionally because of the conditions of the materials, but even in such 
cases the amount can be regulated best by measurement. A tank with a 
float connected with an indicator on the outside is easily constructed. 

CONCRETE PLANTS 

The design of the plant for handling the raw materials and the concrete 
usually has more to do with an economical production than the type of 
the mixing machine. The plant should be drawn or sketched on paper 
and accurate estimates made of its cost and the expense of operation, so 
as to determine whether the volume of concrete is sufficiently large to 
warrant, its installation. The authors have occasionally seen expensive 
machinery, which could not be readily transported to another job, installed 
on a section of work where, because of the small total volume of concrete 
and on account of its distribution, hand-mixing was really more economical. 

It is evident that the arrangement of any plant must be determined by 
local conditions, such as the contour of the ground, the distance from 
which the raw materials are transported, and the class of construction. 
A description of several plants, successful and economical in operation, 
may afford suggestions for other work. The illustrations are intended to 
show the arrangement of the gang and conveying machinery rather than 
the type of mixer. 

Platform over Mixer. A common practice with mixers of various 
types, where the conformation of the ground permits, and where the 
quantity to be laid does not warrant the introduction of bins or machinery 
for handling the aggregate, is to locate the platform for measuring materials 
directly above the mixer. When ready they are shoveled through a hole 
in the planking into the machine. One gang of men can measure and 
spread the materials for a batch while another is shoveling it in. If the 
mixer is run as a batch machine, the materials may be measured directly 
into a hopper above it. 


MIXING CONCRETE 


267 


A satisfactory arrangement for a stationary batch mixer is illustrated in 
b ig. 90. The bin above the hopper is divided into two compartments for 
the sand and stone, and these are measured by feeding them to definite 
heights in the hopper, while the cement is dumped into the chute in front. 



Fig. 90.—Stationary Mixing Plant with a one-yard Rotary Fatch Mixer. 

{See p. 267.) 


Building Construction. The concrete for building construction may be 
elevated in buckets running in a light timber frame or on steel guides as 
shown in Fig. 91. 





































































































268 


A TREATISE ON CONCRETE 


A Central Plant. The establishment of a central plant from which the 
mixed concrete may be hauled to various points as required may be economi¬ 
cal in some cities or large towns. This plan has been adopted in St. Louis, 
Mo.,* for concrete, and is employed in many places for tar and asphalt 



Fig. 91.—Automatic Dumping Concrete Elevator. (See p. 267.) 

paving. The plant may be located at a gravel bank or stone crusher, 
or near a railroad siding, permanent machinery provided which will mix 
the concrete at a much lower cost than could be done by hand-mixing, 
and the concrete hauled in carts to the work at but slightly higher cost 
than the hauling of the dry materials. Most Portland cement con- 

*Engineering News, March 10, 1904, p. 231. 























MIXING CONCRETE 269 

Crete will not be injured (see page 157) if laid within an hour or twc 
after mixing. 

Charlestown Bridge Pier. An economical handling of materials and 
concrete, where the only machinery was the concrete mixer, is shown in 
Fig. 92, which illustrates the building of the foundation for the draw pier 
of the Charlestown Bridge, Boston.* The gravel and sand were brought 
on scows and deposited so near to the mixer as to require only a short 
throw or wheelbarrow haul, and were then measured by shovelfuls, as 
described on page 259. Eight wheelbarrow men, in single file, conveyed 
the concrete from the paddle mixer, which is shown just to the right of 
the central mast, along the circular run, then on to the turn-table to the 
chute for depositing it under water. The entire gang consisted of some 
thirty-five men, and when working steadily they laid at the rate of about 
170 cubic yards of concrete in ten hours, which may be considered a 
maximum output for a machine of this character, the more usual quantity 
being from 75 to 100 cubic yards per day of ten hours. The method of 
depositing concrete from the chute is described on page 303. 

Harvard Stadium. f At the Harvard Stadium the builders, the Aber- 
thaw Construction Company, erected a movable tower on each side of 
the site, and the buckets of concrete and the seat slabsj were then taken 
from cars and conveyed by the cable suspended between the towers to 
the point where they were needed. 

Chicopee River Dam. In mixing concrete for a dam across the Chic¬ 
opee River in Massachusetts, the contractors utilized a portion of the 
excavation by locating their mixer against a bank and building out over 
it a covered platform containing the hopper from which the materials 
could be dropped directly into the mixer. Stone from the excavation was 
crushed and elevated to storage bins, whence it was hauled by carts holding 
exactly the quantity required for a batch, and dumped directly into the 
hopper above the mixer. The sand was measured and wheeled to the 
hopper in an iron vehicle consisting of a bucket set on two large wheels 
which dumped into the hopper by rotating on its axis. The cement was 
emptied on top of the sand. One batch was mixing in the machine while 
another was being emptied into the hopper, and thus twenty batches could 
be handled per hour. The concrete was dumped from the mixer into 
carts which conveyed it to the dam. 

Cambridge Electric Light Station. A portable mixing plant em- 

♦Sixth Annual Report Boston Transit Commission, 1900. 
fSee Frontispiece. 
tSee chapter xxiv. 



A TREATISE ON CONCRETE 


& sajwjnas 
£ tf m&. 


Fig. 92.—Depositing Concrete of Draw Foundation Pier, Charlestown Bridge. (See p. 269.) 











MIXING CONCRETE 


2 71 


ployed on the Cambridge (Mass.) Electric Light Station is shown in Fig. 
93 . The special feature of the arrangement is the framework containing 
the mixer. This may be taken up by the derrick, which also supplies it 
with raw materials, and moved in a few minutes to any other positior 
within derrick swing, so that the concrete can be dropped from the mixer 
close to or directly upon the place where it is required. 

East Boston Tunnel. For measuring materials brought in cars to 
the work, the contractors for one of the entrance sections of the East 



Fig. 93. —Portable Mixing Plant. {Seep. 271.) 


Boston Tunnel employed a derrick bucket. The stone was first filled in 
to a height determined by a gage, then the sand was shoveled on top of it 
and struck off with a different gage, and finally the required number of 
bags of cement emptied on top of the sand. The bucket was taken by a 
derrick and dumped into a duplex mixer. 

Cambridge Bridge Piers. When the quantity of concrete to be laid 
warrants the installation of the necessary machinery, economy requires 
that the stone and sand shall not be handled at all by laborers. If the 
stone is crushed on the spot, it may be raised to bins above the mixer 










A TREATISE ON CONCRETE 


272 





jEcrm oiij/j-fi jfamonC-j) S £cimon £f 

Fig. 94.— Mixing Plant Employing Belt Conveyor. (See p. 273.) 


















































































































































































































































































































MIXING CONCRETE 


2 73 


by bucket elevators or belt conveyors, while a similar plan for elevating 
the material may sometimes be advantageously followed where gravel is 
used. In building the substructure of the Cambridge Bridge, Boston, 
Mass.,* the concrete plant was located on a pier resting on piles. The 
gravel for the concrete was dredged from the harbor and dumped from 
scows into the water close to the pier. An “orange peel” bucket, operated 
from a dredging machine on a scow, lifted the gravel, and dropped it into 
a hopper whence it ran by gravity upon the combination inclined screen 
described on page 240, which separated the sand, pebbles, and the coarse 
waste material. Bucket elevators raised the sand and pebbles to bins 
above the mixer, and from the bins, which were V-shaped, the materials 
fell by gravity into the measuring hoppers. These were arranged in two 
sets, an essential requirement for maximum output, so that one batch 
could be measured while another was being dropped into the mixer. The 
barrels of cement were brought from the cement shed by a horizontal 
endless chain, opened on the ground under the mixer, and then three 
barrels, enough for one batch, were raised at one time by a bucket elevator 
to one of the hoppers over the mixer. 

Williamsburg Bridge Pier. A method of measuring the materials in 
cars was adopted in building one of the anchorages of the East River 
Bridge, New York. The cement and sand were stored in bins, and fell 
by gravity into cars whose capacities were equal, respectively, to the volume 
of stone and sand required for a batch. Between the tracks upon which 
these cars ran were two holes in the ground into each of which could be 
lowered a box of sufficient size to hold one batch of the broken stone, sand, 
and cement. By tipping the measuring car the broken stone was dumped 
into the box, the sand fell from another car through a trap door, and the 
cement was dumped in from the bags. After filling, the box was raised 
by a derrick and dumped into the mixer. 

Parsippany Dike. An endless rubber belt furnishes an excellent means 
for.handling concrete raw materials in a stationary plant. The width 
of the belt should be not less than 18 inches and the slope no greater than 
about 22 0 , which corresponds to 2 \ feet horizontal to one foot vertical. 
Idlers for giving the proper V-shape to the belt were placed at proper inter¬ 
vals. 

The plan in Fig. 94, page 272, shows the design by Mr. William B. 
Fuller of a plant used at the Parsippany Dike of the Jersey City Water 
Supply Co., N. J. The sand was brought to the bins and the stone to 

*For full description see article by Sanford E. Thompson in Engineering News , Oct. 17, 1901, 
p. 282. 


A TREATISE ON CONCRETE 



274 

the crusher in wagons. A belt conveyor delivered the crushed stone to 
the bins. At the outlet of each bin a measuring hopper (shown in a 
detail section, in Fig. 94), containing about 8 cubic feet, received the 
sand or stone from the bin, and at the ring of a bell the proper 
quantity of each material for one batch of concrete was dropped upon 
the conveying belt. The cement was emptied from bags on top of the 
sand and stone as they were carried past the cement shed. The bin 
over the mixer had two hoppers. As soon as a batch was delivered 
to hopper No. 1, the bell was rung again and another batch started into 
hopper No 2, and while this was filling No. 1 batch was dumped into 
the mixer. 


Fig. 95. Mixing plant at Painesville Bridge. (See p. 275.) 

Blackwell’s Island Bridge Piers. At a plant of somewhat similar de 
sign built for the piers of the Blackwell’s Island Bridge, N. Y., the sand 
and stone were measured in cars running on a track below the bins, so that 
they could be moved from one gate to another and discharged at any 
point through trap doors on to the belt between the rails. The stone was 
carried up from the crusher by another belt to the top of the bins, where 
it fell off the belt on to an inclined screen, and rolled into a bin, while 
the dust, passing through, dropped on to another short belt which carried 
it to another bin to be used as sand. 







MIXING CONCRETE 


275 


Jerome Park Reservoir.* During the construction of the reservoir at 
Jerome Park, New York City, in 1906, the concreting of the large bottom 
and slope areas was systematically arranged by using a number of medium 
sized rotary batch mixers, each with a separate gang with wheelbarrows. 
The mixers were moved from time to time. 

Chalmette Docks at New Orleans. f The concrete for the slip walls of 
the Chalmette Docks, New Orleans, was handled and mixed by a portable 
plant on standard gage tracks, consisting of a flat car with a 2-cubic yard 
hopper at each end which supplied sand and gravel to inclined belt con¬ 
veyors. These discharged into a 3-cubic yard hopper with an undercut 
gate placed above a f-cubic yard rotary mixer at the center of the 
car. Cement was supplied the mixer by hand from a storage platform 
on the side of the car, and water, from a pipe laid along the wall with hose 
connection at convenient intervals. 

Painesville Bridge. A unique method of handling concrete at the 
Painesville Bridge of the L. S. & M. S. R. R., completed in 1909, is illus¬ 
trated in Fig. 95. Concrete was elevated in towers at each end of the bridge 
and flowed in movable spouts by gravity to place. 



Fig. 96.—Two-wheeled Concrete Car, {See p. 277.) 


* Engineering News, Sept. 21, 1905, p. 298. 
J Engineering Record, July 29, 1906, p. 88. 











276 


A TREA TISE ON CONCRETE 


CHAPTER XV 

DEPOSITING CONCRETE 

The actual handling and placing of the concrete after it has been mixed, 
and the construction of forms for ordinary mass work, are treated in this 
chapter. Forms for building construction and conduit construction are 
illustrated in subsequent chapters on these subjects. 

Since the introduction of concrete into engineering construction, the 
opinions of engineers regarding the best methods of placing it have com¬ 
pletely changed. For water-tight work or for the strongest construction 
it is now recognized that the concrete should resemble as nearly as possible 
one single solid mass of stone with no joints, and it is the usual practice, 
although not universal, to specify a “quaking,” jelly-like consistency, 
while many authorities go still further and require water enough to be 
“mushy” or sloppy. Formerly, for all classes of work, concrete was 
mixed but slightly more moist than damp earth and laid in alternate blocks 
6 to 12 inches thick. Then, after hardening, the forms were removed, 
and the spaces between filled in. 

HANDLING AND TRANSPORTING CONCRETE 

In handling and transporting concrete, it is essential to prevent the 
separation of the stones from the mortar. In hand-mixed concrete, 
especially for thin walls requiring the stuff to be carried in buckets, there 
is a tendency to allow the stones to separate on the mixing platform so 
that a lot of them fall together when cleaning up the last shovelfuls. 

With the modern slow-setting cement, and in view of the accepted belief 
that some time may elapse after mixing without injury to the work, there 
is less difficulty than formerly in handling the concrete, and it can be readily 
transported to a considerable distance. Moreover, a wet mixture is much 
easier to handle, because the stones do not so readily separate from the 
mass. 

The usual vehicle for transporting hand-mixed concrete is a wheel¬ 
barrow. For machine-mixed concrete, derricks are suitable if the mass is 
concentrated near the mixer, otherwise cars running on a track, or in some 
cases wagons, afford a means of conveyance. A combination of car and 
derrick work is readily effected by using flat cars with derrick buckets or 
trays upon them. Galvanized iron buckets are sometimes useful when 


DEPOSITING CONCRETE 


2 77 

building by hand a high, thin wall. A bucket elevator is a poor contrivance 
for elevating concrete. The mortar sticks to the buckets and the ingre¬ 
dients of the concrete separate as it is thrown from them. 

Volume and Weight of Loose Concrete. The volume and weight of 
loose concrete is of importance in designing the implements or vehicles for 
transporting it and in estimating the quantities which can be handled under 
different conditions. The weight of well-proportioned concrete after 
setting, as stated on page 3, generally ranges from 143 to 155 lb. per cubic 
foot. When green, it will weigh, after ramming, slightly more than this, 
say from 150 to 160 lb. The weight per cubic foot loose, that, is, in the 
vehicle which transports it from the mixer to place, depends largely upon 
the consistency. If mixed very wet, it will settle down to very nearly 
the volume it has after it is placed, perhaps within 5% of it; but if of dry 
consistency, the volume of the rammed mass is apt to be as much as 25% 
less than the loose. A fair average weight of loose concrete may be es¬ 
timated, then, at about 140 lb. per cubic foot, or 1.9 tons per cubic yard, 
when mixed wet, and 120 lb. per cubic foot, or 1.6 tons per cubic yard, 
when mixed dry. The weights and volumes vary, of course, with the pro¬ 
portions used in the mixture and the specific gravity of the stone in the 
aggregate, but for rough estimates these figures are sufficiently accurate. 
The volumes of loose mixed concrete required for a cubic yard of rammed 
concrete, based on the above percentages, are 28 cu. ft. of a very wet 
mixture and 36 cu. ft. of a dry mixture. 

The volume of concrete-contained in an iron wheelbarrow load of average 
size is 1.9 cu. ft. place measurement. A large load is about 2.2 cu. ft. 
place measurement. Special concrete barrows are also made with a capacity 
up to 6 cu. ft. (see Fig. 96, p. 275). Further data is given in Chapter I. 

A single cart on ordinary construction roads will carry about half a 
batch of concrete of average proportions, which may be assumed as 1 
barrel cement to 2\ barrels sand to 5 barrels stone, while with a properly 
constructed cart which will not overflow or leak, 50% mere than this, or 
about three-quarters of a batch, can be drawn over macadam and paved 
streets. 

DEPOSITING CONCRETE ON LAND 

The methods which may be selected for depositing concrete depend 
largely upon its consistency. If mixed wet, it can be dropped vertically 
to any depth or passed through an inclined trough or chute. On the other 
hand, the stones in a dry mixture, that is, of damp earth consistency, will 
separate from the mortar on the slightest provocation. 

To prevent the ingredients separating when passing down an incline, if 
the mixture is not plastic enough to prevent the stones running away from 


A TREATISE ON CONCRETE 


278 

the mortar, a pipe with a hopper top and composed of two or more tele¬ 
scoping sections about 15 inches in diameter is often employed. In such 
a case, the pipe must be often moved or the material shoveled away imme¬ 
diately, to prevent its forming a high cone. Sometimes it is convenient to 
run the lower end of the pipe into a hopper with a gate at its mouth, sc that 
the concrete may be drawn out into a vehicle, while the pipe and hopper 
are kept continually full.* 

The illustration in Fig. 97 shows at how flat a slope concrete of very 



Fig. 97.—Depositing Concrete through a Trough. {Seep. 278.) 

wet consistency will run through an open trough. The picture is an 
actual construction photograph of the Jersey City Water Supply Con¬ 
duit, and shows the concrete flowing directly from the mixer to the 
crown of the arch. Mr. William B. Fuller, the engineer, states that 
when the concrete is mixed of exactly the consistency he likes, it will 
easily run through an iron trough 15 inches wide by 4 inches deep, set on 
a slope of 8 feet horizontal to 1 foot vertical. 

For water-tight work or for maximum strength the concrete should be 

*Engineering News, Dec. 25, 1902, p. 537. 








DEPOSITING CONCRETE 279 


placed so as to form a monolith. To do this on a large structure two or 
three shifts are employed in twenty-four hours, so that no portion of the 
mass commences to set until fresh concrete has been laid on top of it. In 
a large reservoir wall at Little Falls, New Jersey, built en masse to sustain 
40 feet head of water, the only point where the moisture appeared on the 
surface was at a layer where the work was stopped for one hour at noon. 
In most struc¬ 
tures it is pos¬ 
sible to divide 
the work into 
sections, each 
of which is a 
mon olit h . 

Monolithic 
construction is 
necessary for 
columns,beams 
and floors. 

A tipping car 
for conveying 
concrete on a 
track and 
dumping it into 
place is shown 
in Fig. 98. 

In a thin wall 
or a structure 
requiring espe¬ 
cial care, such Fig. 98. Dumping Car. {Seep. 279.) 

as a tank, it 

may be advisable to shovel the concrete from the wheelbarrows. Stones 
which tend to separate can be thus mixed in with the mortar in the wheel¬ 
barrow and a very thin layer formed in the molds, so that even if the 
concrete is mixed very thin the mortar cannot run off from the stones. 


CONSISTENCY OF CONCRETE 

The terms for specifying the consistency, or degree of plasticity, of 
fleshly mixed concrete are variously used by different engineers. In this 






280 


A TREATISE ON CONCRETE 


treatise the term dry mixture is applied to concrete of the consistency of 
damp earth, from which the water rises to the surface only after prolonged 
ramming, and then simply in a glistening film. A medium or quaking 
mixture means a tenacious, jelly-like consistency, which shakes on ramming. 
A very wet or mushy mixture is one which will not support the weight of 
a man and into which an ordinary rammer will sink of its own weight; 
it will run off a shovel unless shoveled very quickly, and will spread out 
and settle to a level surface after wheeling about 25 feet in a wheelbarrow. 

The proper consistency, or wetness, of concrete is a disputed point among 
engineers, some still holding to the very dry mixture, while others prefer 
one nearly as liquid as grout. As a result of a series of tests and of prac¬ 
tical experience, the authors advocate varying the consistency according 
to the class of work, and present the following general conclusions: 

Medium or quaking concrete is adapted for ordinary mass con¬ 
crete, such as foundations, heavy walls, large arches, piers, and abutments. 

Very wet or mushy concrete is suitable for rubble concrete and for re¬ 
inforced concrete, such as thin building walls, columns, floors, conduits, 
and tanks. 

Dry concrete may be employed in dry locations for mass foundations 
which must withstand severe compressive strain within one month after 
placing, provided it is carefully spread in layers not over 6 inches thick and 
is thoroughly rammed. 

The experiments of the authors show that while dry concrete, very 
carefully mixed and rammed, is stronger on short time tests, medium 
mixtures will attain nearly equal strength in six months’ time. One of 
the arguments against very dry mixtures is the difficulty of obtaining a 
uniform consistency. Occasional batches will invariably be too dry, and 
it is impossible with ordinary care in placing and ramming to avoid visible 
voids or pockets of stone which form weak places and allow the penetra¬ 
tion of water. 

The 1903 specifications of the American Railway Engineering and 
Maintenance-of-Way Association are as follows: 

The concrete shall be of such consistency that when dumped in place 
it will not require tamping; it shall be spaded down and tamped sufficiently 
to level off and will then quake freely like jelly, and be wet enough on top 
to require the use of rubber boots by the workmen. 

A very wet mixture is more suitable for rubble concrete or concrete 
rubble because the large stones more readily settle into place and bed 
themselves In thin walls very wet concrete can be more easily “joggled” 


DEPOSITING CONCRETE 


281 


into position so as to conform to the molds and give a smooth surface. 
The use of a mixture sufficiently wet to flow under and around metal rein¬ 
forcement has been found by Prof. Charles L. Norton (see p. 328) to be 
one of the essentials for the preservation of the metal. 

Stone pockets may occur even with very wet concrete because of the 
mortar running away from the stones. This may appear an imaginary 
danger to many users of concrete who have never employed a very wet 
consistency, but the authors have seen concrete mixed with too much water, 
which after setting and the removal of the forms had the appearance of 
being mixed too dry. In their opinion, however, the limit of wetness for 

many classes of work is not reached until there is 
so much water that with ordinary care in hand¬ 
mixing it cannot be made to incorporate with the 
other materials. 


RAMMING OR PUDDLING 

The method of compacting the concrete or 
forcing out the air after placing, and the kind 
of tools to employ for this, depend upon the con¬ 
sistency of the material. 

In concrete mixed with a small amount of water 
the thickness of layers is usually specified at 6 to 
10 inches, the former being the most common, but 
with a very wet or mushy concrete 12 to 15 
inches may be placed at once, the chief object 
being to expel bubbles of air by puddling or 
joggling. In using very wet concrete there is 
danger of too much ramming, which results in 


* 
* I 
CD' 


7 * 


© 


© 


Fig. 99.-Rammers for wedging the stones together and forcing the finer 
Dry Concrete. (See material, the sand and cement, to the surface. 

28 ^ The style of rammers ordinarily used for dry 

mixed or medium concrete are similar to the forms shown in Fig. 99. 
The style on the left of the figure is the ordinary type, and on the right 
is a style convenient for use close to the forms. 

The rammer shown in Fig. 100, page 282, which weighs about 8 
pounds, is the design of Mr. William B. Fuller for very wet or mushy 
concrete. The handle may be lengthened, as shown, by screwing a pipe 
coupling on to the wood. 

A “post-hole” tamping bar with iron shoe, shown in Fig. 101, has been 
successfullv used by the authors for mushy concrete. A piece of 2 by 











282 


A TREATISE ON CONCRETE 


3-inch studding cut to the required length and smoothed off so as to be 
readily grasped by the hands is also a serviceable tool. 

A pneumatic rammer built on the principle of a 
pneumatic riveting machine, as illustrated in Fig. 
102, has been used upon dry mixed concrete with 
fair success. 

Mr. Rafter and Mr. Daniel F. Fulton have de¬ 
signed a rammer based on the principle of the steam 
drill which is arranged upon a traveling carriage 
resting upon cross girders which run on tracks. A 
speed of from 400 to 600 strokes per minute may be 
maintained with from 4 to 5 horse-power. For 
ramming street pavements, it should cover 600 to 
800 linear feet of a street 30 to 40 feet wide. 

Mr. Clarence R. Neher, an advocate of wet con¬ 
crete, replies to an inquiry of the authors in regard to 
rammers, as follows: 


I am governed so much by conditions that I use 
no standard tool, the principle being to use a wedge- 
shaped rammer of some kind. For the face of the 
Fig. 100.—Rammer for WO rk nothing appears much better than a common 

(5^ Sh / s P a de. This is useful in pushing back stones that. 

have separated from the mass, and also can be used 
to select the softer and finer portions of the mass 
and place at the face, while working the spade up 
and down along the face until it is thoroughly 
filled. Care must be taken not to pry with the 
spade, as it will spring the form outward unless ex¬ 
cessively strong. 

In narrow forms where a man cannot stand in the 
concrete, a piece of 2-inch by 3-inch scantling, — 
with the upper portion rounded to make a con¬ 
venient grip and the tamping end wedge-shaped, 

— of a length determined by the depth of the form, 
is convenient and cheap. 

In heavy mass work I prefer this same form of 
rammer to the ordinary type, and thoroughly in¬ 
corporate the different deposits together, avoiding as 
much as possible a smooth, flat finish, so frequently 
insisted on. I consider the use of the term “layers” 
as describing just what you do not want. I deposit 
as much concrete in a form as the rammer will 
penetrate and enter into the deposit below. The 



Fig. i 01.—Rammei 
for Mushy Concrete. 
(See. p. 281.) 



PLAN 

































DEPOSITING CONCRETE 283 

amount will thus be governed by the size of the form and method of 
filling. 

In elevator foundations we have filled columns 3 feet by 11 feet by 22 feet 
high in five hours, dumping 14 cubic feet at a time, and not trimming, but 
shoving the rammer through the mass. The work is absolutely free from 
voids. 

Labor of Ramming. The number of men required for leveling and 
ramming concrete depends upon the thickness of the wall and the con¬ 
sistency of the mass. 

In the table of concrete data 
in Chapter I, page 9, we have 
specified 11 cubic yards as the 
work of an average man in ten 
hours, including both leveling 
the material as it is dumped from 
barrows and the actual ram¬ 
ming. This figure is based 
upon actual records of a large 
number of jobs where the 
concrete was laid of the medium 
consistency most commonly 
employed in ordinary mass 
work. Similarly, a large day’s 
work is placed at 16 cubic 
yards. Mr. George W. Rafter 
writes the authors that 4 cubic 
yards is about an average day’s 
work for an Italian laborer on 
dry mixed concrete. Mr. Neher 
estimates for ordinary conditions 
10 to 15 cubic yards of 

wet concrete per man per day Fig. io 2 .-Pneumatic Concrete Rammer, 
with an average of about 12 {Seep. 282.) 

cubic yards per ten-hour day. Mr. Fuller, who employs a still wetter 
mixture, considers 25 to 50 cubic yards a day’s work for a man jog¬ 
gling. 

On the author’s basis of n cubic yards per day, the average cost of 
leveling and ramming mass concrete with labor at $1.50 per day, allowing 
tor superintendence and contractor’s profit, is about 18 cents per cubic 
yard. For a 4 or 6-inch wall the cost may be two or three times* this figure. 






284 


A TREATISE ON CONCRETE 


BONDING OLD AND NEW CONCRETE 

In a foundation or other structure where the strain is chiefly compres¬ 
sive, the surface of the concrete laid on the previous day should be cleaned 
and wet, but no other precaution is necessary. Joints in walls or in other 
locations liable to tensile stress are coated with mortar, which should be 
richer in cement than the mortar in the concrete, proportions 1: 2 being 
' commonly used. 

Some engineers spread the cement dry upon the wetted surface of the 
old concrete, while others make it into a mortar; the latter method is 
necessary in many cases to seal the joints between the top of the old concrete 
and the bottom of the raised forms. 

The adhesive strength of cement or concrete is much less than its co¬ 
hesive strength, hence in building thin walls for a tank or other work which 
must be water-tight, the only sure method is to lay the structure as a 
monolith, that is, without joints. If the wall is to withstand water pressure 
and cannot be built as a monolith, both horizontal and vertical joints must 
be first thoroughly cleaned of all dirt and “laitance” or powdery scum, 
wet, and then covered with a very thin layer of either neat cement or 1: 1 
mortar, according to the nature of the work. As an added precaution, 
one or more square or V-shaped sticks of timber, say 4 or 6 inches on an 
edge, may be imbedded in the surface, or placed vertically at the end of a 
section, of the last mass of concrete laid each day. In some instances 
large stones have been partially imbedded in the mass at night for doweling 
the new work next day. 

In the New York Subway, work was commenced with no provision for 
bonding horizontal layers, but it was soon found that more or less seepage 
occurred, and in one case where a large arch was torn down the division 
line between two days’ work was distinctly seen. Accordingly, at the end 
of each day’s concreting a tongue-and-grooved joint was formed by a 
piece of timber 4 inches square partly imbedded in the top layer. This 
was removed before resuming work. 

Roughening the surface after ramming or before placing the new layer 
will aid in bonding the old and new concrete. 

Acid* is sometimes used for cleaning and roughening the surface of the 
set concrete. The acid must be thoroughly washed off before placing the 
new concrete or mortar. 

In9reinforced concrete, joints should be made so as to least affect the 
strength. In columns, joints should be made at lower surface of girder or 
at bottom of haunch, if any. In a floor system, or in reinforced walls resist¬ 
ing pressure, it is best to make the joints perpendicular to the surfaces at 
or near the center of the span. 

* See U. S. Letters Patent No. 800942. 


DEPOSITING CONCRETE 


285 


CONTRACTION JOINTS 

Temperature changes are apt to produce contraction in concrete in air 
because in temperate climates most concrete is laid during the warm 
season. Moreover, it is generally recognized that while setting and hard¬ 
ening in air, concretes and mortars contract for a period. 

It is probable that this contraction may be due, in part at least, to the 
cooling of the cement, which when setting attains a high temperature.* 
I his is further evidenced by the fact that cracks in a thin building wall, 
4 or 6 inches thick, open up within a few weeks after being placed, while 
heavier walls may not crack for several months. The concrete in the 
interior of a mass like a large dam cools very slowly, and records at the 
Boonton, N. J., dam indicate that the contraction cracks continue to 
increase in width for several years. The interior of a large mass like 
this is but slightly affected by atmospheric changes, and the cracks are but 
slightly wider in winter than in summer. In the Boonton Damf no cracks 
were discovered during the first winter, but in the second and third winter 
seasons numerous vertical cracks developed. During the fourth and fifth 
winters all these cracks re-opened, but no new ones appeared. It was 
noticed that the cracks which were largest during one winter might be 
smaller the next, and be exceeded in width by some which were smaller the 
previous season. Approximate measurements gave: seventeen main cracks, 
2.5 inches; sixteen smaller cracks averaging ^ inch, 0.5 inch; thirty-three 
half cracks, averaging ^inch, 0.5 inch; with a sum total of 3.5 inches for 
a length of 2150 feet of masonry. The main cracks occurred at quite 
regular intervals of about 100 feet except near the ends of the dam. It was 
apparent that proportionally more cracks developed in that portion of the 
dam in which the masonry was laid during the warmer months. 

Special measurements made upon a retaining wall along the Boston and 
Albany Railroad tracks at Newton Highlands, showed that for a length of 
w r all of 673 feet the total contraction for a given period amounted to 1 ie inches. 
The range of temperature of the wall during this time was about 30°, 
which corresponds closely to the theoretical range necessary to produce 
the contractions, for assuming the coefficient of expansion to be 0.0000055, 
as given on a succeeding page, the range should be 32J 0 . 

Measurements were made by one of the authors of widths of opening of 
contraction joints in a long warehouse in Cincinnati, and found to agree 
almost exactly with that which would be expected by the range in temperature. 

In an ordinary wall, if no cracks occur after nine months’ setting there 
is apt to be no further danger, although after joints once form they will 
vary in width with the variations in temperatures. 

*See page 130. 

+ Transactions American Society Civil Engineers, Vol. LXIII, 1909. 


286 


A TREATISE ON CONCRETE 


Contraction in concrete walls is provided for by forming joints at intervals 
to divide the wall into separate sections, and confine the cracks to straight 
lines, or else by reinforcing with sufficient steel to withstand shrinkage. 1 he 
use of steel reinforcement is treated under Retaining Walls in Chapter XXVI. 

Joints in vertical walls may be made simply by placing a temporary dam 
between the molds to remain until the concrete has set, when it is removed 
and the next section is filled in. To be sure of clear-cut cracks, however, 
it is necessary to insert non-adhesive material, as indicated below. In a 
reinforced wall rods may be run through holes in the dam if it is desired to 
tie the two sections together. If the old work has thoroughly set and the 
rods project only a few inches into the new, the adhesion between the old 
and new work will be so slight that a joint which will open as the concrete 
shrinks will be formed at the desired point. For bonding the two sections, 
a V-shaped groove may be molded into the part first laid, or alternate courses 
may be lapped or toothed out. 

As a rule only contraction joints need to be provided, since expansion 
merely compresses the concrete. Sometimes, however, as in a long wall 
with recesses or in a reservoir floor with a channel in the middle, the expan¬ 
sion may cause a break at the angle. In such cases, water-tight joints 
may be made by leaving slits about ^--inch wide and filling them with a 
plastic material, one of the best for this purpose being pure asphalt of medium 
hardness. Lime dust is sometimes mixed with the asphalt. Another 
way of forming a joint is to insert two or more thicknesses of roofing paper. 

In building the concrete filter tanks at Little Falls, N. J., which are 
15 by 24 feet in horizontal area and rest upon concrete girders, the walls 
of adjoining tanks were laid on different days, and thus kept separate 
from each other. Contraction is provided for in each tank by sloping 
the ledges on which its walls rest, so that, in case of contraction, they will 
slide without cracking. 

At the same plant* occasional expansion wells or vertical openings were 
built the- entire height of the 40-foot retaining wall, to confine cracks to 
these places, and later, in cold weather, when the cracks were furthest open, 
these wells were filled with concrete. 

From practical experience it appears that heavy walls require fewer con¬ 
traction joints than light ones. In concrete retaining wall construction in 
Chicagoj* joints formed every 50 or 60 feet opened up quite noticeably in 
cold weather. Where the walls were of small cross-section a hair crack 
appeared half-way between the joints, tending to show that in thin walls 
joints should be provided about every 30 feet. 

* Transactions American Society of Civil Engineers, Vol. L, p. 406. 

-j-“The Coefficient of Expansion of Concrete,” Journal Western Society of Engineers, Vol. VI, 
p. 549; republished in Engineering News. Nov 21. iqou n. l&o. 


DEPOSITING CONCRETE 287 

By properly distributed reinforcement, cracks may be made so small as 
to be unnoticeable. (See Chapter XXI.) 

The Harvard Stadium, 575 feet in net length or 1390 feet measured 
around the U, which is illustrated in our frontispiece, is an example of the 
possibility of providing sufficient steel to withstand the contraction due to 
hardening and temperature changes. 

Prof. William D. Pence, by very careful experiments at Purdue Univer¬ 
sity, in 1899 to 1901,* determined the coefficient of expansion of concrete in 
air from changes of temperature to be 0.0000055 P er each degree Fahren¬ 
heit. He experimented with Portland cement concrete mixed in proportions 
1:2:4 broken stone and 1:2:4 gravel. The apparatus was designed to 
give extremely accurate results, and the variation in the coefficient of ex¬ 
pansion in the different tests was from 0.0000052 to 0.0000057 per degree 
Fahrenheit. Two brands of Portland cement were employed, and in the 
broken stone concrete, two different stones. The average result for the 
gravel concrete was 0.0000054 per degree Fahrenheit, and for the broken 
stone concrete 0.0000055 per degree Fahrenheit. Prof. Pence concludes 
that “the coefficient of expansion of concrete is about 0.0000055 P er degree 
Fahrenheit. (This value is conveniently remembered as five zeros fifty- 
five.) ’’ The coefficient of expansion of the limestone used in a part of the 
tests was the same as that of the concrete made from it. Experiments'}* 
under the direction of Prof. Hallock at Columbia University gave 0.00000561 
as coefficient for 1 : 2 mortar and 0.00000655 f° r 1 : 3 : 5 concrete. Prof. 
Burr calls attention to the similarity of this to the coefficient of linear 
thermal expansion of steel, which is about 0.0000066 per degree Fahrenheit. 
This fact is of great practical value to the engineer in the construction of 
reinforced concrete because it shows that the concrete and steel will be 
similarly affected by temperature changes. 

A coefficient of 0.0000055 corresponds to a contraction of J inch in 100 
feet for 50° Fahrenheit ffill in temperature. 

The effect of hardening upon the volume, although less definitely de¬ 
termined, has been experimented upon by Prof. Bauschinger,§ of Munich, 
and Prof. George F. Swain, || of the Massachusetts Institute of Technology. 
As a result, the Committee on Cements of the American Society oi Civil 
Engineers ir 1887 reached the following conclusions:^ 

First. Cement mortars hardening in air diminish in linear dimensions 
at least to the end of twelve weeks, and in most cases progressively. 

1 

* “The Coefficient of Expansion of Concrete,” Journal Western Society of Engineers, Vol. VI, 
p. 549; republisl ed in Engineering News, Nov. 21, 1901, p. 380. 

J Burr’s “Materials of Engineering,” 1903, p. 378. 

§ Transactions American Society of Civil Engineers, Vol. XV, p. 722. 

|| Transactions American Society of Civil Engineers, Vol. XVII, p. 213. 

^Transactions American Society of Civil Engineers, Vol. XVII, p. 214. 


288 


A TREATISE ON CONCRETE 


Second. Cement mortars hardening in water increase in like manner 
but to a less degree. 

Third. The contractions and expansions are greatest in neat cement 
mortars. 

Among further conclusions of the committee given in this report it is 
stated that experiments show the contraction of neat cement in air at the 
end of twelve weeks to be from 0.14 to 0.32%, and of 1: 1 mortar, 0.08 
to 0.17%. Although these values are corroborated by Bauschinger’s* ex¬ 
periments on Portland cement mortars, the results of which also indicate 
nearly the same contraction for leaner mortars as for 1:1, further data 
upon the action of concrete made of modern Portland cement is required 
before accepting the figures as applicable to this. Considerej* gives 0.03% 
to 0.05% shrinkage for lean mortars corresponding to a contraction of 
about \ inch in a wall 100 feet long. These various conclusions show that 
cracks in a newly laid concrete wall are due in part to contraction in setting. 
In fact, it has been noticed that joints open up in new concrete before it has 
been affected by external temperature. 

It must be borne in mind that this action during hardening has nothing 
to do with the temperature of the atmosphere, and does not vary with it, 
but is in addition to the effects of temperature changes. It is possible, 
however, as suggested on page 285, that the shrinkage may be due in part 
to the cooling down from the heat evolved when the cement sets. 

FACING CONCRETE WALLS 

Exposed concrete walls had best not be plastered. It is a needless ex¬ 
pense, and the results in variable climates are unsatisfactory. It is difficult 
to apply cement mortar uniformly to the face of hardened concrete, and it 
is apt to crack off and discolor, especially if the concrete behind it is porous 
enough for the water to penetrate it. For waterproofing walls not exposed 
to the atmosphere, cement plaster is sometimes serviceable, as described on 
page 341. 

Mortar for patching irregularities and pockets, which will occasionally 
occur in the best work, and for filling holes, must contain the same pro¬ 
portions of cement and sand as the concrete, or it will set a different color. 

The treatment of the face of concrete is determined by the character of 
the structure. A fair surface, suitable for work which is not exposed to 
view, and even for sheds or other buildings where the appearance need not 
be regarded, has been obtained by the authors on 4-inch and 6-inch walls 

♦Transactions American Society of Civil Engineers, Vol. XV, p. 722. 

•j-Considere’s Reinforced Concrete, 1903, p. 87. 


DEPOSITING CONCRETE 


289 


by using merely a very wet mixture of cement, sand and gravel, with care 
in placing and puddling so that none of the stones, many of which were 
2 inches in diameter, collected in pockets against the forms. Such treat- 
1 ment will result in a sandy finish, showing the joints in the 

forms less than a smoother one. 

To produce a smooth mortar surface, a thin tool like a 
spade or an ice cutter, shown in Fig. 103, may be thrust 
down next to the molds as the concrete is placed, so as to 
force the stones back from the face and allow the mortar to 
cover every stone, care being taken not to pry the molds. 

One of the best methods of finishing for a large smooth 
surface is to spade or cut the faces as described, and then 

i after the forms are removed to pick them with a hand tool, 
shown in Fig. 104, or a pneumatic tool adapted for the 
purpose. The Harvard University Stadium, illustrated in 
our frontispiece, is finished in this way, and the photo¬ 
graph in Fig. 105 shows a near view of the surface. 
p IG IO , _ On the left is the concrete showing the impressions of the 

Face Cut- plank forms, and on the right is the finished surface. If 
ter (See p * ° 

289.) this picking is performed by hand, it is done by a com¬ 

mon laborer. The surface he will cover per day depends upon the hard¬ 
ness of the concrete. It must not be too green or 
the tool will loosen the stones, while if set very hard 
the labor is unnecessarily great. On the average, 
a man may be expected to cover about 50 square feet 
per day of ten hours. The picks require frequent, 
at least daily, sharpening. For the best appear¬ 
ance, the size of stone in the concrete should be 
limited to about j inch to one inch. This method of 
picking was employed by Mr. E. L. Ransome in the 
construction of the Pacific Borax Works in New 
Jersey. A pneumatic tool suitable for this work is 
made with a circular end containing a number of 
points, using which a man should cover 400 to 500 
square feet per day. 

Mr. C. R. Neher* states that with labor at $1.50 per 
day bush-hammering will cost less than i\ cents per 
square foot. 

A surface of washed concrete is shown in the photograph, Fig. 106. 

♦Journal Association of Engineering Societies, Jan., 1902, p. 41 



I - I 

*-6//V--* 


Fig. 104.—Pick for 
Facing Concrete. 
(See p. 289.) 





















290 


A TREATISE ON CONCRETE 



Surface left by forms is shown on left and picked surface on right. 
Fig. 105.— Surface of “ Picked ” Concrete. (See p. 289.) 



Fig. 106.—Surface of Washed Concrete. (See p . 289.) 




DEPOSITING CONCRETE 


291 


p. 290. This finish, used by Mr. Henry H. Quimby* for surfacing con¬ 
crete bridges in Philadelphia, is obtained by hand or with a hose. Hand 
methods are usually preferable because of the difficulty of applying the hose 
at exactly the right stage of hardening. In either case the forms must be 
removed as soon as the concrete is sufficiently hard,—a period varying 
from 6 hours to 2 or 3 days, according to the character of the cement and 
the weather,— and the washing done immediately. For washing by hand, 
a plasterer’s float, or a small board 1 by 3 by 6 inches, is used and the cutting 
is done by sand rolled between the board and the wall, with plenty of water. 
The concrete face after this process may sometimes be too green for rinsing 
clean, when the final cleaning is deferred for a few hours. Mr. Quimby 
states that a laborer should wash and clean 100 square feet of surface in 
less than one hour. If the concrete has become too hard before washing, 
a comparatively smooth finish is obtained in a similar manner or by vigor¬ 
ously rubbing the surface with a rough brick. A green surface may be 
treated with a common scrubbing-brush and water. 

A fine sandy finish may be obtained after concrete has set by rubbing 
with a block of carborundum about 3 by 4 by i\ inches. 

Another plan for removing the skin of cement is the acid process.! 

Mr. H. P. Gillette! mentions a method employed in one case on the 
New York Central R. R. of chiseling sloping grooves, about f inch deep 
and 2 inches apart, upon an old discolored concrete surface. 

For a very smooth mortar surface, such as may be required for moldings, 
curved surfaces or carving, the interior surface of the mold may be plastered 
about f-inch thick, by hand or trowel, just in advance of the laying of the 
concrete, so that the concrete and mortar set up as one mass. 

The advocates of dry mixed concrete often require a piece of board, corre¬ 
sponding in width to the thickness of the layer of concrete, to be placed 
on edge close to the form, the concrete rammed against it, and then the 
board removed and the space filled with mortar mixed in proportions 
1 : 2 or 1 13. Another method, which can be used with mortar of a wetter 
consistency, is to place a thin board or a strip of sheet iron at the required 
distance from the form, usually about 2 inches, then to fill in the mortar 
between it and the mold, and the concrete on the other side of it, when it 
may be removed. In the best modern practice, facing mortar is omitted 
altogether, and the concrete is made wet enough to present a good surf ace. § 

Marking the surface to resemble masonry is considered unnecessary 
from an architectural point of view, for the work is actually a monolith and 

* Personal correspondence. See also Engineering News, Dec. 20, 1906, p. 656. 

■j- See paper by Linn White, Engineering Record, Feb. 2, 1907, p. 126. 
j Engineering News, July 24, 1902, p. 66. 

§ Other methods of facing are described in the Report of the Association of Railway Superin¬ 
tendents of Bridges and Buildings, 1900. 


292 


A TREATISE ON CONCRETE 


should have that appearance, but if it is desired, triangular pieces may be 
nailed to the forms, or if tongued-and-grooved plank are used, the horizontal 
molding may be formed by a strip of wood gotten out to the preferred 
shape, and planed with a tongue and groove so as to fit between two planks 
as shown in Chapter XXIV. 

The size of molding depends upon the class of masonry which is to be 
imitated. Mr. Edwin Thacher* specifies triangular moldings 2 inches 
wide by 1 inch deep. 

To give a uniform color, in Englandf it is customary to use a rather stiff 
mortar in proportions 1 : 3 applied with a plasterer’s hand float and worked 
in so thoroughly as to leave no body on the surface. In the United States 
a 1 : 2 grout is sometimes put on with a whitewash brush or small whisk 
broom. This, however, is liable to check. 

A pumice-stone paint used by Mr. H. I. Moyer has given satisfaction in 
practice. It consists of ground pumice-stone and Portland cement mixed 
in equal parts to the consistency of thick paint. After removing the board- 
marks with a block of carborundum, the surface is wet and the paint applied 
with a brush. When this first coat is hqrd, it is wet and the second coat 
applied. 

Plastering. When plastering on external surfaces must be resorted to, 
special means must be taken to make it adhere and to prevent its checking. 
The forms must be wet instead of oiled; irregularities must be removed by 
chipping or rubbing; the entire surface should be roughened; and the coat 
of plaster should be as thin as possible, preferably not over rg or J-inch. 

By throwing on plaster with considerable force, it bonds better than by 
spreading it. If the first coat is thrown on the second is more apt to adhere. 
A spatter-dash or a pebble dash finish is made by throwing on a mortar to 
leave it regular but rough. 

Lafarge cement finish has been satisfactorily used for house walls by 
Mr. Benjamin A. Howes. The process is illustrated in a photograph shown 
in Fig. 107, page 293. The surface, which must be very true, is wet, and a 
neat solution of Lafarge cement is spread on with a whitewash brush. 
Before this has dried, a second coat in proportions about 1 : 3 of Lafarge 
cement and fine sea sand is spread with a steel trowel, floated with a wood 
float, then immediately wet down with a whitewash brush. The total 
thickness of the plaster should not be over rs inch. 

If a thick plaster is necessary, the surface must be carefully roughened, 
wet, and coated with a neat cement grout, preferably spread on very thin 
with a wire brush, and then plastered immediately before it hardens. A 
plaster which has been found satisfactory is made using one-sixth to one- 

* Cement, May, 1903, p. 107. 
t Sutcliffe’s Concrete, 1893, P* 3 2 4 * 


DEPOSITING CONCRETE 


293 


third part of lime putty to one part of cement by bulk, with enough sand 
to make it work sandy. For 3-coat work the second coat may have about 
as much hair as is used in brown coat work in interior plastering. 

FORMS FOR MASS CONCRETE* 

The forms for structures, such as buildings and sewers, are illustrated 
in the chapters treating upon these subjects. 

The best lumber for forms or molds for concrete is white pine because it 
is easily worked and retains its shape after exposure to the weather. Ex¬ 
cept, however, where a very fine face is required, motives of economy 



Fig. 107. Surfacing Wall with Mortar. ( See p. 292.) 

usually prompt the use of cheaper material, such as spruce or fir, or, for 
very rough work, even hemlock. Green lumber is preferable to dry be¬ 
cause it is less affected by the water in the concrete. 

If the planks or boards are thoroughly oiled and are not exposed too 
long a time to the hot sun and dry air, which tend to warp them, they may 
be used over and over again. Long exposure, however, will throw the 
surface out of true, and open up the joints. In some instances the same 
lumber can be employed in different places. For example, in the con- 

* See also paper by Sanford E. Thompson on “Forms for Concrete Construction,” Transactions 
National Association Cement Users, 1907, reprinted as Bulletin No. 13, Association of American 
Portland Cement Manufacturers. 







294 


A TREATISE ON CONCRETE 


struction of a factory building, Mr. Thompson specified 2-inch tongued- 
and-grooved roof plank of green spruce for the forms, and after using at 
least four times, no difficulty was found in laying it on the roof. The 
planks were merely slightly gritty and discolored by the oil employed to 
prevent adhesion of cement. 

Lumber which is planed one side is essential to a smooth face, and where 
the forms must be removed within 24 or 48 hours it is sometimes advan¬ 
tageously employed for rough work because the concrete adheres less to 
planed lumber and that which does stick is easily scraped off, thus effecting 
a saving of labor which more than balances the cost of planing. Many 
concrete experts advise the use of beveled edge stuff in preference to tongued 
and grooved. The edges crush as the board or plank swells, and thL 
prevents buckling. 

Square corners and thin projections should be avoided when possible 
A beveled strip in an external corner will give it a finished appearance. 

Either i-inch boards or 2-inch plank are suitable for forms. The 
spacing of the studs depends in part upon the consistency of the concrete 
and the thickness of the walls. If the concrete is laid quite wet and the 
mass is large, there may be considerable pressure exerted before the cement 
sets. On the other hand, there is less liability of the boards being forced 
out of place by ramming than when a drier mixture is used. The authors 
have found that in comparatively thin walls laid with a wet mixture the 
stringers may be spaced 5 feet apart for 2-inch plank and 2 feet apart for 
1-inch boards. This represents about the limit if an absolutely straight 
face is desired, and even with this spacing the lumber will spring slightly in 
places where very short lengths of it are used. 

The size of the studding depends upon the height of the wall and the 
amount of bracing which it is convenient to use. For a low form of i-inch 
stuff 2 by 4 inch studs may be satisfactory. If this size is used for a higher 
wall, horizontal timbers must be placed and carefully braced at distances 
about 5 feet apart to prevent the studs from springing. For 2-inch plank, 
as the studding is spaced farther apart, it must be heavier. Common sizes 
are 4 by 6 inches, 2 by 10 inches, and 4 by 10 inches, depending upon the 
character of the work and the material at hand. The toes of the diagonal 
braces which run from the studding down to the ground must rest securely 
against stout posts or other immovable supports. The use of these diag¬ 
onals may be avoided in many cases or their number reduced by connecting 
opposite studs with through bolts or wire. An inexpensive method of 
connection is shown in Fig. 108, page 295. The wires are wound 
around, opposite studs and then twisted with a stick, as a turn-buckle, 


DEPOSITING CONCRETE 


295 

until the studs are the proper distance apart. To remove the forms the 
wires are cut and then trimmed off close to the concrete. 

If in placing the concrete the forms commence to buckle, they must 
remain in their warped position unless trueness of face is of sufficient im¬ 
portance to warrant tearing down the concrete and replacing it. A car¬ 
penter is so accustomed to truing up his lumber after it is in place that it is 



difficult for him to realize that a thin wall of concrete cannot be straightened 
in the same way. The fact that a crack once made in conctete which is 
set is almost impossible to repair cannot be too strongly impressed upon 
the woodworkers. 

Concrete forms should be nearly water-tight but need not be absolutely 
so. Cracks of noticeable width which cannot be closed by wetting and 
swelling the lumber may be battened, and vertical joints between the ends 


















296 


A TREATISE ON CONCRETE 


of planks may be stopped in the same way. Hard soap has also been used 
for this purpose.* 

In a large structure such as a dam, cement bags filled with sandf may be 
piled to form the temporary end of a layer or series of layers of concrete. 

Greasing Forms. Crude oil is an excellent and inexpensive material 
for greasing forms. This is a petroleum product sufficiently liquid to be 
readily applied with a large whitewash brush. The object is to fill the 
pores of the wood rather than to cover it with a film of grease. The oil 
must be applied every time the forms are set. Thin soft soap or a paste 
made from soap and water is also occasionally used. On an important 
job in EnglandJ the centering boards of arches were covered with strong 
packing paper soaked with linseed oil. Paper however is apt to wrinkle. 

If the concrete is to set for several weeks before removing the forms, the 
cohesion of the concrete will be greater than its adhesion to the lumber, 
and no oil or grease will be necessary, although it is well to thoroughly wet 
the plank before laying the concrete against it. Always oil metal forms. 

Removing Forms. The length of time which concrete must set before 
removing the forms depends upon the weather, the strain which is to come 
upon the work, and the consistency employed in mixing. 

A good rule to follow when laying wet concrete upon which no pressure 
is to come immediately is to determine whether it is sufficiently hard by 
pressing upon it with the broad part of the thumb. If indented, the con¬ 
crete is too soft to permit of removing the forms. It is sometimes possible 
in good drying weather, even if slow-setting Portland cement is used, to 
raise the forms within from 10 to 24 hours after placing the concrete, but 
care must be exercised that no blow or jar comes upon the fresh work. If 
the wall is very thin and is to be subjected immediately to earth or water 
pressure, it may be advisable to allow the forms to remain for several 
weeks. The setting of concrete is retarded by cold or by wet weather. 
When mixed very wet, it sets and attains its strength more slowly than 
when mixed with a small amount of*water. 

RUBBLE CONCRETE 

Rubble concrete includes all classes of concrete in which large stones are 
placed by hand or by machinery. The term concrete rubble has been ap¬ 
plied when the mass consists essentially of large stone laid in joints of 
concrete instead of mortar. 

♦George W. Lee, Engineering News, Mar. 19, 1903, p. 246. 

f Engineering News , Aug. 27, 1903, p. 185. 

tK. Leibbrand in Proceedings Institution of Civil Engineers, Vol. CXIX, p. 227 . 


DEPOSITING CONCRETE 


297 


Rubble concrete comes in competition with pure concrete on the one 
hand, and with rubble masonry, — that is, stonework laid in cement mor¬ 
tar, — on the other hand. Its cost in large masses is usually less than that 
of pure concrete, because the expense of crushing the stones used as rubble 
is saved, and each large stone replaces a mass of mixed cement and ag¬ 
gregate, thereby saving a portion of the cement. As stone is always heavier 
than concrete made from the crushed material, because of the pores in the 
concrete, the replacing of portions of the latter by large stone increases its 
weight, and therefore its value for certain classes of construction. Large 
masses of rubble concrete can usually be laid cheaper than ordinary con¬ 
crete, but where the mass is small and separate machinery or apparatus 
will be required for handling the large stones, its use may not be advan¬ 
tageous. It is especially suitable where the concrete materials are handled 
with derricks, because these may be employed to hook the stone or transport 
it in trays. 

In comparison with large masses of rubble masonry laid in cement mor¬ 
tar, rubble concrete of similar quality is almost invariably found to be 
cheaper because scarcely any skilled labor is required. In a thin wall, not 
more than 3 feet thick, the rubble masonry may be cheaper because no 
forms are required. In estimating comparative costs of rubble masonry 
laid in Natural cement mortar and rubble concrete made with Portland 
cement, the fact must be considered that a wall of Portland cement rubble 
concrete may be made thinner than one of Natural cement masonry be¬ 
cause it is stronger. The difference in strength is not merely due to the 
class of cement employed, but to the fact that in rubble concrete the stones 
are perfectly imbedded instead of being set up on small spawls in the 
manner customarily employed by stone masons. 

The amount of cement used in rubble concrete varies not only with the 
proportions of the concrete mixture, but with the percentage of rubble 
introduced. Very much less cement is required in concrete than in a simi¬ 
lar quantity of mortar of like strength, but concrete joints must be thicker 
than mortar joints, so that the result is often more cement is required per 
cubic yard for concrete than for rubble masonry. However, by employing 
a large percentage of stone, as was done at Boonton,* the quantity of 
cement may be brought below that for rubble masonry. 

The strength of rubble concrete can be compared only theoretically to 
that of concrete or rubble masonry, because there are no testing machines 
in existence of sufficient capacity to break a mass of Portland cement 
masonry containing large stones. It is generally considered less than that 

*See description, page 300. 


298 


A TREATISE ON CONCRETE 


of plain concrete, but, the authors believe, with insufficient ground. Less 
cement is contained in a cubic yard, which tends to lessen the strength, but, 
on the other hand, as stated above, the large stones add density which is 
a source of strength. 

In concrete subjected to tension or bending the introduction of large 
stones might possibly be a source of weakness by forming planes of ad¬ 
hesion. On the other hand, the stones tooth into the mass and into each 
other, forming an irregularity of breaking surface which would tend to in¬ 
crease the strength. On long-time tests, too, the strength of the large 
pieces of stone, which is naturally greater per square inch than the strength 
of small pieces of broken stone, would naturally come into play. In com¬ 
pression this extra strength of the large stones, especially in their resistance 
to shearing, has a still greater influence upon the strength of the mass, and 
besides this they must necessarily bond and wedge with each other. 

COMPARATIVE QUANTITIES OF MATERIALS FOR PLAIN 

AND RUBBLE CONCRETE 

The cement and aggregate are often expressed as percentages of the 
total mass of plain concrete or of rubble concrete. This is confusing 
because there are various ways of expressing percentages, and, as suggested 
below, it is therefore clearer in ordinary cases to employ, instead, com¬ 
mercial measurements, such as cubic feet, cubic yards, or pounds. 

Before the concrete is mixed, the volumes of materials may be compared 
by percentages, thus, proportions 1:3:6 have 10% cement, 30% sand, 
and 60% broken stone; but this is apt to be misleading, since loose vol¬ 
umes, —- because of the different voids, — and weights, — because of 
different specific gravities, —- do not exactly correspond to absolute or 
solid volumes in the finished concrete. By absolute volumes,* for example, 
a cubic foot of 1:3:6 concretef may contain 0.079 cu - ft. of solid cement 
grain, 0.278 cu. ft. of solid sand grains, and 0.491 cu. ft. of solid stone 
particles, and may be said to have 7.9% cement, 27.8% sand and 49.1% 
stone. This is an exact method, but such percentages cannot be deter¬ 
mined without very complete data. 

For comparing costs of different concrete it is therefore best to discard 
the term percentages, and instead to express the quantity of each material 
as weights or loose volumes required for a unit volume, — say a cubic 
yard, — of compacted concrete. By this method a cubic yard of average 
1:3:6 concrete (from the table on page 231) contains 1.11 bbl. cement. 

*See example, p. 139. 
fSee item (23), p. 377. 


DEPOSITING CONCRETE 


299 


0.47 cu. yd. loose sand, and 0.94 cu. yd. loose broken stone. If, now, 
rubble concrete is used and if on the average every cubic yard of this 
rubble concrete after being laid contains large rubble stone to the amount 
of 0.3 cubic yards (measured net, as solid stone), we may say that the 
rubble concrete contains 30% rubble, and each of the other materials are 
reduced by 30%, thus giving 1.11X0.70 = 0.78 bbl. cement, 0.47X0.70 = 
°*33 cu - yd- sand, and 0.94 X 0.70 = 0.66 cu. yd. broken stone per cubic 
yard of concrete. From such data, the relative costs of materials for 
plain and rubble concrete may be readily compared/}* 

Proportion of Rubble in the Mass. The proportion of large stones 
which can be placed depends upon the size of these stones and upon their 
distance apart. In a heavy wall or dam the size may be limited simply by 
the strength of the machinery employed to handle them, whereas in a 
comparatively thin wall subjected to water pressure, it is evident that the 
stones should not be large enough to run nearly through the wall 
and might be limited to one-half or one-third of its width. Larger stones 
can be used with a wet than with a dry mixture since they bed more 
readily. 

The distance between the stones varies in different specifications from 
3 to 18 inches. If the concrete is mixed of dry consistency there must 
be space enough between the stones to ram the concrete thoroughly and 
force it into all the recesses, while with a wet mixture the spaces need be 
regulated merely by the dimensions of the stones in the concrete aggregate, 
care being exercised that they do not bridge or arch across between the 
large stones. 

The quantity of rubble is usually expressed as a percentage of the total 
mass of the finished concrete. The percentage may vary from 20% to 
64%, both of these quantities being mentioned by Mr. John W. Steven* as 
used in different places in Scotland. Nearly as much space must be left 
between two small stones as between two large ones, so that the percentage 
increases with the size. Into one of the Boonton dikes (4 feet 8 inches 
thick) of the Jersey City Water Supply Company, — where the stones were 
hoisted in derrick trays and unloaded by one or two men, — 20% of stone 
was introduced, and this may be taken as a fair average quantity for con¬ 
crete containing “one-man” or “two-men” stone. In another Boonton 
dike, of the same thickness and similar in other respects, the stones were 
large enough to handle by derricks, and the quantity was increased to 33%, 
while in the large dam described below, 55% was the average quantity. 


*Proceedings Institution of Civil Engineers, Vol. CXIII. 
j- See tables of Quantities of Materials, pp. 236, 237. 


3 °° 


A TREA TISE ON CONCRETE 


The amount of rubble may sometimes be most conveniently and accurately 
measured by weighing it in cart or car-loads. 

Methods of Laying Rubble Concrete. The forms for rubble concrete 
may be built as for ordinary concrete, or the faces of the worli may be of 
cut stone or ashlar masonry. 

Ordinarily, derrick buckets are the most suitable apparatus for placing 
the concrete, because the derrick can also be conveniently used for handling 
the stone. 

One of the best examples of rubble concrete work which has come within 
the observation of the authors is the dam of the Jersey City Water Supply 
Company at Boonton, N. J.,* built in 1902-4 under the direction of Mr. 
William B. Fuller, Resident Engineer. The darn proper contains about 
240000 cubic yards of “cyclopean” or concrete rubble masonry, and the 
contract price at which this was let, which covered all labor and all ma¬ 
terials excepting the cement, was $1.98 per cubic yard. Other bids ranged 
from $2.20 to $3.60. The rubble stones, which actually averaged in size 
from 1 to 2\ cubic yards each, were brought from the quarry about three 
miles distant over a standard gage track built for the purpose, and the stone 
for the concrete aggregate was also broken at the quarry, although it was not 
touched by hand from the time it entered the crusher until it was deposited 
in concrete. One of the distinctive features of the construction was the 
consistency of the concrete, which was mixed extremely wet, in fact, about 
like pea soup, so that when dumped it spread out, forming a level bed for 
the stone. As soon as a bucket of concrete was dumped, a large stone, 
which had come from the quarry on flat cars, was picked up by one of 
the stiff-legged derricks ranged on trestles along each face of the dam, and 
dropped, — with force, not gently lowered, — usually with its smoothest 
face down, into the mushy mass. Settling into place, it bedded itself 
in the concrete, and laborers joggled it with crowbars so as to bring it 
to a firm bearing and drive out all air bubbles. A Aone lifted after placing 
left a bed conforming to the irregularities of the stone, and having the ap¬ 
pearance of mortar, no stones being visible. Scraping this mortar in places 
showed that the stones of the concrete were covered with an exceedingly 
thin film of mortar. 

The labor of actually placing the concrete and stone after bringing them 
to the dam may be estimated from the fact that each stiff-legged derrick 
supplied a gang of three or four laborers dumping concrete and joggling 
the stone, with one foreman mason, who not only looked after the depositing 


* See drawing, Chap. XXVI. See also Engineering Record, Aug. 8, 1^03, p. 152. 


DEPOSITING CONCRETE 


3 01 


of the stone in the concrete, but also spent some of his time on the face stone 
masonry. In addition to these, there were the men mixing concrete and 
handling the cars of stone. Mr. Fuller stated that seven derrick gangs 
averaged about 700 cubic yards of concrete rubble masonry in ten hours, 
or about 100 cubic yards to a derrick. A maximum day’s work for a 
derrick was about 125 cubic yards. 

The concrete was proportioned 1 part Portland cement, 2J parts sand, 
6j parts broken stone, the latter ranging in size from fine particles up to 
3 inches in diameter. The masonry contains about 55% of rubble, the 
large stones being kept at least far enough apart so that the fist could be 
thrust between them. About 0.6 barrels of cement were used per cubic 
yard of concrete rubble masonry. This quantity is less than is generally 
used in a rubble wall built of fairly well dressed stones laid in 1: 2 cement 
mortar; and where water-tight rubble is required and the stones are accord¬ 
ingly left as rough as possible, the quantity of cement is apt to average 
slightly more than one barrel per cubic yard. 

In a dam built in eastern Connecticut in 1899 1 ° 190 1 ,* where methods 
somewhat similar to those jus!: described were employed, the quantity of 
cement averaged about two-thirds barrels per cubic yard of masonry. 

The masonry dry dock at the Charlestown Navy Yard, which was begun 
in 1900, furnishes an example of rubble laid in dry mixed concrete. The 
stones, which were placed about 18 inches apart in all directions, averaged 
about \ cubic yard in volume, and had comparatively square faces and 
level beds. They occupied less than one-third of the total volume of the 
concrete. The concrete, mixed in proportions about 1 part Portland 
cement to 2 parts sand to 5 parts gravel, was deposited from buckets, and 
thoroughly rammed, and the stones, after washing with a hose, were placed 
by derrick. If a stone did not bed itself properly, the derrick picked up a 
heavy weight and allowed it to drop several times upon the stone to ram 
it into place. 

DEPOSITING CONCRETE UNDER WATER 

Although some engineers still specify that no concrete shall be laid under 
water, the many important structures which have been built of late years 
upon foundations of concrete deposited loose, to set and harden under 
water, prove that excellent work can be performed with proper selection 
of materials and care in laying. It is absolutely necessary, however, 
to lay the concrete by some means which will prevent the separation of 
the ingredients as they pass through the water. This has been accom- 

*Described by Herbert M. Knight, Engineering News , June 12, 1902, p. 470. 


302 


A TREATISE ON CONCRETE 


plished, as discussed in the succeeding pages, by the following methods: 
(i) passing the concrete through a tube in a continuous flow, (2) lowering 
it in large buckets from which the concrete may be dropped in large masses, 
(3) confining it in bags, (4) forming the concrete into blocks on land, and 
after setting placing them by machinery or by floats, and (5) allowing the 
concrete to partially set in air and then depositing it in a “plastic” condi¬ 


tion. 


For seawater construction, the cement should be carefully .tested to see 
that it is of standard quality.* Occasionally the water of a stream or pond 
may be impregnated with by-products, such as sulphuric acid from indus¬ 
trial plants, or with mineral impurities which prevent the concrete from 
setting properly. 

Cofferdams, which need not be water-tight, are almost always necessary 
to prevent the concrete from spreading and the cement from washing away. 

Laitance. “ Laitance ” is a French word, quite generally adopted in the 
United States and England for the light-colored powdery substance which 
is held in suspension by the water when cement or concrete is deposited 
below the surface. On land the same substance forms on the surface of 
concrete which has been mixed very wet. 

The analysis of a sample of laitancef showed its composition to be as 
follows: 

Silica (Si 0 2 ) . 16.06% 

Alumina and Iron (AI2O3, Fe2C>3) . 8.66 “ 

Lime (CaO). 4740 “ 

Magnesia Oxide (MgO). 2.40 “ 

Ignition loss. 23.60 “ 

If calculated to a water and carbonic acid free basis the analvsis becomes; 


Silica (Si 0 2 ). 

Alumina and Iron (AI2O3, Fe20s) 

Lime (CaO). 

Magnesia Oxide (MgO). 



Mr. Richardson notes that this composition corresponds with that of a 
normal Portland cement except that it is unusually high in alumina and 
iron, a fact which may be explained by the large amount of magma detected 
in the thin section examined. He further states: 

I have had a thin section ground, but find that it shows no structure 
which is characteristic. The section consists largely of amorphous material 
of an isotropic nature, that is to say, it does not affect polarized light. It 
reveals a considerable amount of a yellow substance which seems to be the 

* Also see Chapter XV, and page 308. 

^Analyzed for the authors by Mr. Clifford Richardson. 











DEPOSITING CONCRETE 


3°3 


undecomposed magma contained in the original cement. I have formed a 
material very similar to the “laitance” by shaking Portland cement with 
water, decanting the finer portion and allowing it to settle out and harden. 
This material, like your “ laitance,” is rather soft, and this is due to the fact 
that the Portland cement is much more thoroughly decomposed under these 
conditions than unde'* ordinary ones, and this accounts for its character. 

It is evident from these facts that the milky laitance which appears on 
concrete laid under water represents an actual loss of cement, which should 
be prevented by confining the mass until it reaches its position. 

Depositing Concrete through Chutes. In his Treatise On Limes, 
Hydraulic Cements and Mortars,* Mr. Gillmore refers to a “tremie” 
used in laying concrete under water in Chesapeake Bay. This consisted 
essentially of a tube of boiler iron about 2 feet in diameter, and long enough 
to reach the place where the concrete is to be deposited. Similar apparatus 
; s still employed for forming layers of concrete under water. 

When building the piers of the Charlestown Bridge, Boston, a cofferdam 
was first constructed, and then a tube, about 14 inches in diameter at the 
bottom and n inches at the neck, with flaring top, was suspended by a 
differential hoist from a moving platform, as shown in Fig. 92, page 270. 
The tube was made in removable sections bolted together by outside 
danges so that its length could be readily varied. Mr. William Jackson, 
Chief Engineer for the bridge, describes'j* the method of operation as 
follows: 

The foot of the chute was allowed to rest on the bottom, and was 
filled with concrete dumped from wheelbarrows. The chute was then 
raised slowly from the bottom, allowing a part of the concrete to run out 
in a conical heap at the foot, while the loss was made good by dumping in 
more concrete at the top. The truck bearing the chute was then moved 
from side to side of the dam, so as to leave a ridge or bank of concrete 
crosswise of the pier, the chute being kept always filled or nearly filled by 
dumping more concrete into the hopper. The height of the ridge of con¬ 
crete was regulated by the height to which the foot of the chute had been 
raised from the bottom. When the ridge was completed across the dam, 
the traveller supporting the truck was moved a short distance lengthwise 
of the pier, and the truck was moved back again across the dam, parallel 
to its former course, allowing the concrete to run out over the edge of the 
bank first deposited, widening it on the side to which the traveler had been 
moved, and this process was continued until the whole area of the founda¬ 
tion was covered with a layer of concrete, upon which, when it was suffi 
ciently hardened, another similar layer or course could be deposited. 

*Page 236. 

fThird Annual Report, Boston Transit Commission, 1897, p. 74. 


3°4 


A TREATISE ON CONCRETE 


The thickness of each course depended upon the height to which the 
foot of the chute was raised above the top of the preceding course. Courses 
were laid up to 6 feet in thickness, but it is thought that the best results 
were attained with a thickness of 2 or 2^ feet. 

If the bank is made too high, or if the bottom (or the top of the pre¬ 
ceding course) is very uneven, or if the piles interfere with the motion of 
the chute, or if the chute is moved along or raised too rapidly, the concrete 
is likely to run out so fast as to empty the chute entirely before the flow can 
be checked. In this event the “charge” is said to be ‘.‘lost,” and the 
chute must be lowered again to the bottom and refilled. When the charge 
is lost the water rises inside the chute to the same level as that outside, and 
into this water the concrete must be dumped until the water is wholly dis¬ 
placed or absorbed by the concrete. This has a tendency to wash the 
concrete, and to separate the cement from the sand and gravel, and as it 
generally takes a cubic yard or more of concrete to displace all the water 
in the chute, there is .danger that a rather large body of badly washed 
concrete will be deposited whenever the charge is lost. This danger 
threatens not only when the charge is accidentally lost, but whenever work 
is begun in the morning or after the mid-day intermission; for whenever 
the work stops the charge must be allowed to run out lest it set in the 
chute. 

To obviate partially the evil of washed concrete, the contractor was 
directed, whenever work was begun after an intermission, or whenever the 
charge was lost or water leaked into the chute, to throw into it, before each 
wheelbarrow-load of concrete, until the water was displaced, a quantity of 
dry cement. He was also directed to begin work after an intermission 
with the chute near the center line of the pier, so that any body of washed 
concrete resulting would be completely surrounded by sound concrete. 

After the workmen and the inspector had gained experience with the 
chute, the accidental loss of the charge was not a frequent occurrence, and 
the danger of an occasional body of partly washed concrete, surrounded 
as it must be by good concrete, was not looked upon as a very serious 
matter. 

A difficulty sometimes met with in using the chute is that when a sud¬ 
den rush of concrete takes place, even if the charge is not entirely lost, the 
concrete within the chute often falls far below the level of the water outside. 
The outside water then, especially if there is a deficiency of sand in the 
concrete, is likely to force its way through the concrete remaining in the 
bottom of the chute, tending to separate the cement from the sand and 
gravel, and making the concrete too wet, and so threatening a complete 
loss of charge. If there are any leaks in the joints of the chute, water 
comes in and tends to cause loss of charge, and this leakage is especially 
troublesome when the concrete in the chute falls below the level of the 
water outside. 

The chute seems to work best when the concrete is mixed not quite 
moist enough to be plastic. If it is mixed too wet the charge is likely to 
be lost; if very dry there is a tendency to choking of the chute. The working 
of the chute is affected also by variations in the proportions of sand and 


DEPOSITING CONCRETE 


3°5 


gravel. With gravel in excess the outside water too readily forces its way 
in at the bottom. With an excess of sand the concrete tends to clog in the 
chute. 

Sometimes when the concrete becomes clogged in the upper part of the 
chute, the concrete below the clogged place continues to flow out, leaving 
a vacant space into which water forces itself through the concrete remaining 
in the bottom of the chute. When the clogged concrete above is loosened, 
it falls into this body of water, which, unable to find exit by the way through 
which it entered, is displaced by the falling concrete, and rises into the 
hopper, sometimes to a level considerably above that of the water outside. 

In the construction of the foundations for the piers for the Cambridge, 
(Mass.) Bridge,* a tube was used in much the same way as that employed 
for the Charlestown Bridge. The concrete was dumped from derrick 
buckets into a hopper, below which was a tube 16 inches in diameter at 
the top and 22 inches in diameter at the bottom, built in’4-foot cylindrical 
sections, which telescoped one another, so that a length varying from 4 to 
40 feet could be obtained. Each layer of concrete was 1 to 2 feet thick. 
The tube was suspended from a traveler running upon a pair of traveling 
trusses which rested at each end upon tracks laid on top of the cofferdam, 
so that concrete could be deposited at any point within the rectangle. 

Depositing Concrete from Buckets. The opinion of engineers is di¬ 
vided as to whether the best method of depositing concrete under water 
is by a chute, as has just been described, or from a bucket. The objection 
to the former is the difficulty in always maintaining a continuous flow, 
while with the latter it is not so easy to place the layers uniformly and to 
prevent the formation of mounds which are more or less washed by the 
water. With careful superintendence, however, either of these methods 
is satisfactory. 

The best results can be attained with buckets so constructed that the 
material flows out through the bottom. A mass of concrete deposited 
under water must be disturbed as little as possible, and in tipping a bucket 
the material is apt to be stirred. Various buckets with bottom doors have 
been devised for opening automatically when the place for depositing is 
reached. In one type, used in 1900 at the Charlestown Navy Yard, the 
slackening of the rope released latches which fastened the trap doors so 
that they opened as soon as the bucket commenced to ascend. Another 
style, designed by Mr. John F. O’Rourke, is shown in Fig. 109. The 
photograph shows the bucket closed. When it reaches the bottom the 

♦See article by Sanford E. Thompson, Engineering News, Oct. 17, 1901, p. 282. 


3°6 


A TREATISE ON CONCRETE 


handle slides down, allowing the doors to swing open and the concrete to 
drop out in a single mass. The bail catches when it has dropped to the 
bottom, so that when hoisting the bucket the doors remain open. Covers 


% 



Fig. 109.—Bucket for Depositing Concrete. (See p. 305.) 


prevent the water from rushing in at the top as the bucket is being lowered, 
and the V-shaped bottom lessens the disturbance of the water. 

Depositing Concrete in Bags. Bags, varying from small paper or mus 


















DEPOSITING CONCRETE 


307 


lin bags to jute sacks containing 100 tons,* have been employed in the 
past for holding concrete together as it passed through the water. In some 
cases the concrete has been placed in the bags dry.f 

Mr. William Dyce Cay in building the breakwater at Aberdeen Harbor 
Eng., employed bags holding from 28 to 50 tons of concrete. A bag 
was placed in the hopper bottom of a barge filled with concrete, and sewed 
up as the barge was being warped to place. When the doors of the hopper 
were released it fell into place. 

John C. Goodridge’s method§ of laying concrete under water, employed 
in 1887, consisted in enclosing the concrete “in paper bags or other soluble 
envelopes, and then lodging the bags or envelopes so filled in the desired 
position under water, in such a manner that the bag or envelope shall not 
be ruptured until after or at the time it and its contents are in place.” 

Molded Blocks. Under some conditions, especially where it is difficult 
to construct a cofferdam and monolithic work is not required, blocks of 

concrete of any desired shapes are 
molded on land and placed after setting. 

On the Buffalo breakwater,|| blocks 
weighing from 15 to 20 tons, one style 
of which is illustrated in Fig. no, were 
employed in parts of the structure. For 
handling them, three iron bolts having 
legs bent to an angle at the ends and of 
unequal length, — one 24 inches long and 
the other 12 inches long, — so that the 
strain would occur in two separate 
planes, were sunk into the top face of 
each block. After placing them in posi¬ 
tion, grooves molded into their adjacent faces were filled with concrete 
so as to dowel them together. 

In the harbor of the Welland Canal, Ontario,^ blocks of somewhat 
smaller size were used just at the water level, with mass concrete placed on 
top of them. For handling these blocks four vertical channels, two on 
each side, were molded into each block, with recesses just below the centra 1 , 
points to catch the four hooks used for moving it. As the hooks passed 

* Proceedings Institution of Civil Engineers, Vol. XXXIX, p. 126, and LXXXVII, pp. 101 
and 126. 

-j-Lt. Col. J. A. Smith, Engineering Record , March 23, 1895. 

§U. S. Patent, No. 358 853. 

l|See article by Major T. W. Symonds, Engineering News, May 29, 1902, p. 420. 

Engineering News, May 15, 1902, p. 382. 



Fig. no.— Face Blocks of Buffalo 
Breakwater. (See p. 307.) 








A TREATISE ON CONCRETE 


308 

down in the channels, they projected so slightly that a block could be set 
close to the last one placed, and the hook removed without disturbing it. 

As early as 1873, concrete blocks ranging in size from 13 to 60 tons in 
weight were used by the Department of Docks in New York City,* and 
in 1900 this method of construction was still in operation in that city. 

In Belgium in 1899, for breakwater construction,! blocks about 25 feet 
square and 82 feet long, weighing 3 000 tons, were formed by building on 
the shore metal caissons of the required size, lining them with concrete, 
then floating to place, and removing plugs in the bottom so as to allow 
them to sink. The remainder of the concrete to fill the caisson was de¬ 
posited in the interior. 

Depositing Dry Concrete under Water. Bv dry concrete is meant in 

this case a mixture of aggregates and cement without water. This method, 
although occasionally practised, is undoubtedly one of the worst to employ 
in laying concrete under water. No matter how carefully the concrete is 
placed, more or less of the cement is carried off by the water. Experiments 
by Mr. B. B. Stoney{ show, as one would expect, that a wall laid in this 
way is honeycombed, and is not nearly so dense as that formed of concrete 
mixed with water in the usual way before placing. 

Plastic Concrete. Plastic or, as it is termed by Mr. Faija, “reset” 
concrete was once employed in England.§ The concrete was mixed on 
land with the smallest possible quantity of water, and allowed to set there 
about three to five hours, or until it attained the consistency of wet clay, 
before being deposited in the water. Mr. Kinniple claimed that setting 
eight hours on land before placing did not reduce the ultimate strength of 
the concrete, and that less of the cement was washed away. 

Concrete in Sea Water. In the United States several instances have been 
noted where concrete has been disintegrated to the depth of 2 or 3 inches 
and sometimes more. The injury in all cases is limited to the space between 
high and low water mark, and frequently appears to be caused in part by 
frost action. Since other concrete close by is often intact, the chief cause 
for the defects seems to be in the character of the concrete. From the many 
cases of structures in good condition after many years, notably the docks 
in New York Harbor, the conclusion is drawn that concrete can be used 
with confidence in sea-water construction provided it is proportioned and 
laid with the best materials so as to form a dense impervious concrete. 
A still further precaution is to keep the concrete from immediate con¬ 
tact with sea-water by leaving the forms in place for several weeks. 

*“Fabrication of Beton Blocks by Manual Labor,” by Schuyler Hamilton,Transactions Amer* 
lean Society of Civil Engineers, Vol. IV, p. 93. 

-j*See paper by L. Vernon Harcourt in Proceedings Institution of Civil Engineers, Vol. CXII, p. 2, 

^Proceedings Institution of Civil Engineers, Vol. LXXXVII, p. 230. 

§W. R. Kinniple, Proceedings Institution of Civil Engineers. Vol. LXXXVII, p. 65. 


EFFECT OF SEA WATER UPON CONCRETE 


309 


CHAPTER XVI 

EFFECT OF SEA WATER UPON CONCRETE 

AND MORTAR* 

By R. Feret, 

Chief of the Laboratory of Bridges and Roads, Boulogne-sur-Mer, France. 

V 

The principal conclusions which have been reached by the author of this 
chapter, as discussed in the following pages, may be summarized as follows: 

(1) No cement or other hydraulic product has yet been found which 
presents absolute security against the decomposing action of sea water. 
(See p. 309.) 

(2) The most injurious compound of sea water is the acid of the dis¬ 
solved sulphates, sulphuric acid being the principal agent in the decompo¬ 
sition of cement. (See p. 310.) 

(3) Portland cement for sea water should be low in aluminum (see p. 
312), and as low as possible in lime. (See p. 311.) 

(4) Puzzolanic material is a valuable addition to cement for sea water 
construction. (See p. 313.) 

(5) As little gypsum as possible should be added, for regulating the time 
of setting, to cements which are to be used in sea water. (See p. 310.) 

(6) Sand containing a large proportion of fine grains must never be used 
in concrete or mortar for sea water construction. (See p. 316.) 

(7) The proportions of the cement and aggregate for sea water con¬ 
struction must be such as will produce a dense and impervious concrete. 
(See p. 316.). 


EXTERNAL PHENOMENA 

At present there is no hydraulic product which is known to be capable 
of resisting absolutely the decomposing influence of sea water. It is true 
that some concrete masonry has remained intact for a very long time in 
salt water, but with our present knowledge it is impossible to say why 
these structures have resisted so well, and there is little doubt that the 
cements from which they were made might have decomposed rapidly if 
they had been used under different conditions. In some cases, on the 
other hand, similar large structures subject to the action of sea water were 

*The authors are indebted to Mr. Feret for this chapter, which has been especially prepared 
by him for this Treatise. 


A TREATISE ON CONCRETE 


3 IG 

ruined in a few years and were torn down and completely rebuilt. Notable 
instances of this kind are the failures which occurred in the ports of Aber¬ 
deen,* Dunkerque, and Ymuiden. 

Such occurrences have aroused great interest in the subject of the action 
of sea water upon mortars, and but few questions have received more 
careful study. In spite of this, however, it cannot be said that any sure 
means of preventing these failures have been found. 

The decomposition manifests itself in various ways: sometimes the 
mortar softens, and little by little becomes disintegrated; sometimes the 
mortar becomes covered with a crust which finally cracks off; more often 
fine white veins develop on the surface of the mortar, these gradually grow 
large and open, the mortar swells, cracks, and falls off in small pieces or 
collapses in a pulp-like mass. Almost always the interior of the decom¬ 
posed mortar is found to contain a soft white material which may be easily 
separated from it. The chemical composition of this substance is not, 
however, constant.f Generally, the more advanced the state of decom¬ 
position, the more readily the white material can be extracted from the 
mortar and the richer it is in magnesia. The proportion of sulphuric acid 
in it also increases with the degree of decomposition, though less uniformly. 

ACTION OF SULPHATE WATERS 

For several years the injurious action of sea water upon hydraulic com¬ 
pounds was attributed chiefly to the magnesia in the water. It is note¬ 
worthy, however, that chloride of magnesia is almost without action, while 
sulphate of magnesia acts very energetically upon cement, and it has now 
been ascertained that magnesia plays only a secondary part, while in fact 
it is the sulphuric acid combined as a soluble sulphate which is the real 
cause of the decomposition. 

This has been confirmed in practise by the destruction of masonry 
washed by water which has traversed earth containing gypsum, or built 
from mortar made with sand which has been extracted from strata con¬ 
taining sulphate of lime.J A consideration of this fact makes it apparent 
how dangerous it is to use, in concrete or masonry subject L o the action of 
sea water, cements to which the gypsum has been added for the purpose of 
regulating the rate of their setting or of increasing their initial strength.§ 

There are numerous instances in which brick masonry has rapidly de- 

*Smith, Proceedings Institution Civil Engineers, Vol. CVII, 1891-92. 

•[•Feret, Annales des Ponts et Chaussees, 1892, II, p. 93. 

jBied, Annales des Ponts et Chaussees, 1902, III, p. 95. 

§Feret, Annales des Ponts et Chaussees, 1890, I, p. 375. 


EFFECT OF SEA WATER UPON CONCRETE 


3 TI 

composed because the bricks, burned with coal, contained alkaline sul¬ 
phates which when drawn out by water attacked the mortar of the joints.* 

These practical observations combined with certain laboratory experi¬ 
ments intelligently conducted have demonstrated that sulphuric acid is the 
principal agent in causing decomposition. 

CHEMICAL PROCESSES OF DECOMPOSITION 

Messrs. Candlot,f Michaelis,J and Deval§ have discovered successively 
by different methods that aluminate of lime Al 2 0 3 3 CaO, which exists in 
cements in company with other calcareous salts, such as silicates, possesses 
the property of combining with sulphate of lime so as to give a double 
salt Al 2 0 3 3 CaO, 3 (SO s CaO) combined with a large quantity of water 
with great increase in volume. This substance, moreover, has no firm 
coherence. It is soluble in pure water, but insoluble in lime water, a fact 
that explains its existence in a solid state in mortars. 

On the other hand, even if the cements do not contain free lime when 
they are anhydrous, their setting under the action of water frees a part of 
the lime which was combined with the acid elements, principally with 
silica. If a soluble sulphate other than sulphate of lime is placed in con¬ 
tact with a hydraulic binding material during hardening or after having 
set, it produces, with the freed lime, sulphate of lime, which in turn com¬ 
bines with the aluminate, giving “sulpho-aluminate,’’ and produces the 
swelling which causes the disintegration of the mortar. The same reac¬ 
tions would be produced, moreover, without the intervention of free lime 
as a result of the reaction of the sulphuric acid of the salt dissolved by the 
water upon a part of the lime of the binding material. 

Although the formation of the sulpho-aluminate of lime seems to be the 
principal cause of the decomposition of cement by sea water and sulphate 
waters, it may not be the only one: the setting and the hardening of the 
cement in contact with water result in the separation of compounds rich in 
lime, in salts less calcareous, and in free lime. According to the nature 
of the medium and the conditions affecting its preservation, this reaction 
may be modified or counteracted in such manner that the hardening cannot 
follow its regular course; likewise, the lime set at liberty may be dissolved 
little by little in the water which penetrates the mortars, and may disappear 
by exosmose, giving place to other more or less injurious compounds. 

*Zamboni, Industria, October 15, 1899. 
fCiments et Chaux Hydrauliques, Paris, 1891, p. 257. 
jDer Cement-Bacillus, Berlin, 1892. 

§Bulletin de la Societe d’Encouragement pour Plndustrie Nationale, 1900, I, p. 49, 


3 12 


A TREATISE ON CONCRETE 


These various phenomena are yet far from being satisfactorily explained; 
nevertheless, it appears that those cements which are richest in lime are 
the most quickly decomposed. 

SEARCH FOR BINDING MATERIALS CAPABLE OF RESISTING THE 

ACTION OF SEA WATER 

For a long time the efforts of experimenters have been directed toward 
finding a cement of such composition that it cannot be decomposed by sea* 
water. Thinking at first that the destructive action of the water resulted 
from the substitution of the magnesia which it contained, for the lime of the 
cement, the idea was conceived of making cement by burning dolomitic 
limestone which consequently was composed largely of salts of magnesia. 
But it was found that the magnesia which this contained, since it was 
burned necessarily at a very high temperature, was slaked with great 
difficulty, and by its tardy hydration caused the mortar to swell. Cements 
were also made experimentally of baryta, a laboratory product whose high 
price does not permit its introduction into regular practice.* 

After the discovery of the sulpho-aluminate of lime, the question changed 
its aspect, and alumina was considered a dangerous element in cement, 
the proportion of which ought to be reduced as much as possible. At 
present the specifications adopted by the Administration of Public Works 
in France limit to 8% the maximum amount of alumina allowed in cement 
intended for use in sea water, and this limit would be placed much lower 
were it not for the fact that in many localities it would be very difficult to 
obtain products containing less alumina. On the other hand, the percen¬ 
tage of alumina cannot be greatly reduced without at the same time ren¬ 
dering more difficult the burning of the cement, in which operation this 
element acts as a flux. Accordingly, it was suggested that the alumina 
be replaced by iron oxide. Cements have been made in the laboratory 
which were absolutely free from alumina and rich in iron, and these re¬ 
sisted sea water very well.f The various hydraulic cements and limes 
produced by the works of Teil, whose reputation is world-wide, contain 
not more than 2% of alumina, and some of them usually last much better 
in sea water than most of the Portland cements which contain between 
7% and 8% of alumina. These too, however, become decomposed under 
certain conditions, but with this peculiarity — that their disintegration is 
not usually accompanied by any increase of volume. 

*Le C'hateli'* 1- , Annales des Mines, May and June, 1887. 

fLe Chatelier, Con^res International des Materiaux de Construction, held at Paris in 1900, Vol 
II, Part 2, p. cr 


I 


EFFECT OF SEA WATER UPON CONCRETE 313 

It has been noted that the cements which are the richest in lime decom¬ 
pose the most quickly in sea water. Based upon this observation, the 
experiment was also tried of making cements for marine use by burning 
mixtures less rich in carbonate of lime than the ordinary Portland cements. 
This diminished the strength of the cement, but the falling off in strength 
was only of secondary importance. The principal difficulty lay in the 
process of manufacture. In burning cements of this class there was pro¬ 
duced in the kilns a considerable quantity of powder possessing only a 
comparatively feeble hydraulic power, which obstructed the draught. 
This difficulty was lessened by mixing ferruginous materials (ore, etc.), 
or even sulphate of lime,* with the raw materials before burning. Also, 
the use of rotary furnaces prevents the choking of the draught. As has 
just been said, cements low in lime do not attain as great strength as the 
ordinary Portland cements, but they generally resist the decomposing 
action of sea water better. 

When the proportion of limestone is small, the burning can be done 
only at a very low temperature, and the cement obtained sets very quickly. 
Some of these low lime cements appear to resist chemical decomposition 
satisfactorily, while others resist no better than most of the Portland ce¬ 
ments, a difference which has not yet been explained. In any case, on 
account of the rapidity of set, this class of cements cannot readily be used 
on large work, and, in fact, their use is mainly limited to special cases. 

Another means of neutralizing the bad effects of the excess of lime liber¬ 
ated by the setting of Portland cement consists in mixing with the latter, 
before using, materials capable of combining with this lime so as to pro¬ 
duce insoluble compounds. Puzzolans have been found to be the most 
useful material for this purpose. Laboratory tests, verified by experiments 
on a larger scale,f have shown that mortars made in this way generally 
resist sea water better than if they had been made from similar cements 
without puzzolanic material. Sometimes, too, their strength is increased 
bv this mixture. It is conceivable, however, that the substances which 
in the Puzzolans appear as acids are less energetic in their action upon the 
lime of the cement than the sulphuric acids of sea water or of water con¬ 
taining gypsum, and that therefore in the end they will be displaced by 
the latter with the consequent decomposition of the mortar. This method 
cannot then be looked upon as giving absolute security against deterio¬ 
ration although it has been proved to be useful. • 

*Candlot, paper delivered at the meeting of the French and Belgian members of the Inter¬ 
national Association of the Materials of Construction, on April 25, 1903. 

fFeret, Annales des Ponts et Chaussees, 1901, IV, p. 191. 


3 i 4 A TREATISE ON CONCRETE 

METHOD OF DETERMINING THE ABILITY OF A BINDING 
MATERIAL TO RESIST THE CHEMICAL ACTION OF 

SULPHATE WATERS 

One method is to gage the cement to be tested with sufficient water to 
obtain a plastic paste, spread this paste on glass plates so as to form cakes 
or pats with thin edges, immerse the pats in sea water, and observe them 
from time to time. But with this method the amount of deformation in 
the pats depends to a large extent upon the hardness of the paste at the 
time of immersion, so that a cement which cracks when immersed before 
setting may stand a long time without showing any trace or alteration if 
the pat is not placed in contact with the water until twenty-four hours after 
gaging. Further, the surface of the pat is quickly covered by a crust more 
or less thick resulting from the partial carbonization of the freed lime, so 
that the substitution of magnesia for a part of this lime and the presence 
of this crust may influence the decomposition of the underlying cement. 

Another and more exact method consists in molding a block of cement 
or of mortar of a sufficient thickness; for example, a briquette such as is used 
for a tensile test. Allow this to harden in the usual way, say for twenty- 
eight days, then cut out from the center of this block a small solid disc with 
sharp edges, and immerse it in sea water or in a sulphate solution (satu¬ 
rated gypsum, sulphate of magnesia, etc.). In order to prevent all new 
superficial carbonization of the specimen, carbonic acid should not be 
allowed to come in contact with or be present in this liquid. When de¬ 
composition occurs in the cement it is indicated by cracks which appear 
at the edge of the disc after a lapse of a variable time. 

As a third test, sea water under pressure can be made to filter contin¬ 
uously through mortars made with fine sand. The author of the present 
chapter uses for this test mortars containing from 250 to 450 kilograms 
(551 to 991 lb.) of cement per cubic meter (35.3 cu. ft.) of sand (corre¬ 
sponding approximately to proportions 1:6 to 1:3 by weight) which he 
gages to a plastic consistency and molds into cubes 50 square centimeters 
(7.74 sq. in.) on a face, with a tube of brass penetrating to the center of 
the block. After a few days the brass tubes are attached with India rubber 
tubes to a vessel containing sea water under a head of 2 meters (6.52 ft.). 
The amount of water which flows through each cube in a given time is 
accurately measured from time to time, the cube being immersed in sea 
water in a glass receptacle, where the state of preservation of the mortar 
can be closely observed. 

Finally, the following quite rapid method is used in the laboratory at 
Boulogne. A mixture is made consisting of 100 parts of cement to be 


3i5 


EFFECT OF SEA 


WATER UPON CONCRETE 


tested and 300 parts marble ground to a fine powder. To this is added 
gypsum in the form of a very fine powder, varying progressively from 
0% to 20% of the weight of the cement. Plastic mortars are then made 
from each of these mixtures, which are molded into prisms 2 by 2 by 12.5 
centimeters (0.8 by 0.8 by 4.9 in.), allowed to harden for seven days in 
moist air, and then immersed in fresh water after the length of each has 
been exactly measured. The water is frequently renewed and at stated 
periods the lengths of the prisms are again measured, at which time their 
state of preservation is also examined. 

The ability of the cement to resist decomposition by sulphates is indi¬ 
cated by the time taken for the prisms to expand abnormally and to develop 
cracks, and also by the quantity of gypsum which the binding material is 
able to bear for a given time without deterioration. 

As a result of a long series of experiments, especially of those made by 
the last two methods, the conclusion has been reached that no binding 
material has as yet been found which will not be decomposed sooner or 
later when subjected to these tests, so that at present no cement can be 
looked upon as absolutely safe from the action of sea water. 


MECHANICAL PROCESSES OF DISINTEGRATION 

It seems possible to divide the phenomena of disintegration into two 
classes according as the destruction of the mortar is produced by a sort of 
progressive dissolution of its elements without appreciable change in 
volume, or as the products of decomposition, collecting in the pores, en¬ 
large them and produce a scaling off and a weakening of the mortar. 
This second class of phenomena is much the more frequent and serious. 

In both cases decomposition may be produced when the mortar is simply 
immersed, because of the penetration of the water into its pores and its 
renewal by the double phenomenon of endosmose and exosmose. But 
when the masonry is subjected to different degrees of pressure upon its 
opposite faces, as is usually the case, this tends to establish a current of 
water through it and the replacement of the dissolving elements goes on 
more actively. However, disintegration may, under these conditions, pro¬ 
ceed more slowly if the current of water is strong enough to carry away the 
solid products of decomposition as they are formed. The writer has cited 
in a former paper* experiments which plainly show the difference between 
these two methods of decomposition: if lean mortars, made with the same 
cement and sands of different granulometric compositions, are kept in abso¬ 
lutely quiet sea water, those which disintegrate most rapidly are the ones 

♦Annates des Ponts et Chaussees, 1892, II, pp. 106 to 116. 


A TREATISE ON CONCRETE 


3 l6 

into whose composition there enters no fine sand, but only medium sand 
or, and above all, coarse sand. These latter are the mortars that contain 
the voids of largest size. On the contrary, if a series of similar mortars are 
subjected to a continuous filtration of sea water, those made from coarse 
sand remain intact, while decomposition is more and more active for mortars 
containing more and more fine sand. In practise this latter is the most 
frequent case, and, in fact, it has been verified that the destruction oj concrete 
or mortar by sea water has in most cases been due to the use oj too fine sands. 

This is a point which cannot be too strongly insisted upon, and experi¬ 
ments show that a rather lean mortar of coarse sand is much preferable to 
a mortar of fine sand, even when a very large quantity of cement is intro¬ 
duced into the latter. Fine sands ought to be banished relentlessly from 
sea water construction even when the cost of coarse sand is very high.* 
When stone is at hand, an excellent sand can be obtained economically 
by crushing it. 

PROPORTIONS FOR MORTARS AND CONCRETES 

From the preceding it is evident that the best means of fighting against 
sea water is to prevent as far as possible its penetration into the mortars 
and concretes, and accordingly to make those of great density. The 
authors of this volume have suggested in a preceding chapter (Chapter IX) 
with what size of sand and what quantity of cement this result can best be 
attained in mortars: the maximum density is obtained with a mortar con¬ 
taining sand composed of material having about two parts of very coarse 
grains to one of fine grains, including cement. Usually, natural sands, 
even the coarsest, contain a proportion of relatively fine sand sufficient to 
make it useless to add more with the cement. If a sand is used from 
which the fine grains have been screened, and this is mixed with about 
one-half of its weight of cement, a mortar is obtained at once very dense 
and of great strength, but whose use would often be too costly. In such 
cases the cement can be replaced by a mixture of sand and cement pre¬ 
pared in advance, such as the product known as “sand-cement,” for the 
making of which a few factories have been built in Europe and also in 
America. It must be borne in mind, however, that this solution, excellent 
for mortars destined to remain in the air or to come in contact only with 
fresh water, would be poor to use in sea water, for very fine sand intimately 
mixed with cement separates its grains and increases the surface of attack, 
and various experiments have shown that this kind of mortar suffers 
severely in sea water. 

*See also, Feret, Baumaterialienkunde, 1896, p. 139, and “Le Ciment,” 1896, p. 212. 


EFFECT OF SEA WATER UPON CONCRETE 317 

For use in sea water, on the contrary, if a good puzzolanic material can 
be procured on favorable terms, it is advantageous to grind this with the 
cement to take the place of the fine sand, so that in the mortar it may play 
both a mechanical and a chemical role, assuring to it a great density, and 
at the same time forming, with the lime freed by the setting, compounds 
which tend to harden the mortar and render it impermeable. 

For concretes the law of greatest density is not the same as for mortars, 
and it has not yet been possible to express a general law. It is necessary 
to see that the concrete does not contain voids, and above all that the cement 
is not diluted by an excess of fine sand, which must always be considered 
as the greatest enemy of masonry in sea water. 

In every case the sea water should be prevented from coming in con¬ 
tact with the work for as long a time as possible, so that the setting of 
the cement may be already considerably advanced. Yet it must not be 
forgotten that when the mortar contains a puzzolanic material its hard¬ 
ening can be properly effected only in the presence of moisture. 


MIXTURES OF PUZZOLAN AND SLAG WITH CEMENTS 

Tests by M. Vetillart and the writer, described in detail in a paper pub¬ 
lished in Annales des Ponts et Chaussees, 1908, I, page 121, indicate that 
Puzzolanic material may be of great value when mixed with Portland cement 
for concrete construction in sea-water, materially increasing the durability 
of the concrete without increasing its cost. 

The conclusions reached in these tests are as follows: 

The use of Puzzolan in hydraulic mortars in combination with the cement 
increases the strength, and in a great many cases appreciably retards disin¬ 
tegration by sea-water. It should be employed then, at least experiment¬ 
ally, in accordance with the following recommendations: 

Grind the Puzzrian to the fineness of Portland cement. 

Mix it mechanically with the cement so as to obtain an absolutely thor¬ 
ough mixture. 

For Portland cement and a good natural Puzzolan, take two parts by 
weight of cement to one part of Puzzolan. 

Select only Puzzolan of known good quality; the use of gaize slightly 
roasted is especially recommended. 

If other kinds of cement or limes are used with Puzzolan, or if the Puz¬ 
zolan is of doubtful quality,—especially if it is obtained from granulated 
slag or a similar industrial by-product,—determine the proportions of the 
mixture by means of preliminary trials based on tests of strength. 

Add to the sand the mixture of cement and Puzzolan as pure cement 
would be added, and in the same proportions; mix and place the mortar in 
the usual manner. 

Always use for comparison with the Puzzolan mortar, specimens of 
mortar, of the same proportions and made under identical conditions, in 


A TREATISE ON CONCRETE 


3 i 8 

which the mixture of cement and Puzzolan is replaced by the same weight 
of pure cement. 

Allow the Puzzolan mortar to harden in the presence of moisture. 

It is as yet impossible to suggest detail rules for the acceptance and con¬ 
trol of Puzzolan cements. The recommendation is made, however, that 
their ability to resist the decomposing action of the salts in sea-water be 
compared to the resistance of pure cements by means of the test with sul¬ 
phate magnesia already referred to.* 

VARIOUS PLASTERS AND COATINGS 

Various methods have been tried to prevent sea water from wetting 
masonry too soon, either by coating the work with materials designed to 
obstruct the pores, or by covering it with a layer more or less thick and 
more or less impermeable, consisting usually of a rich mortar, clay, bitu¬ 
minous materials, etc. 

This method of protecting the work is generally rather costly and is not 
applicable to all kinds of construction. Besides, it presents this disadvan¬ 
tage, that if by accident there is any break in the continuity of the cover¬ 
ing, the sea water finds a passage towards the heart of the masonry and 
creeps in from one place to another, so that often the coating offers only an 
illusory security. 

In certain cases, a coating is formed spontaneously by the carbonization 
of the lime in the parts of the mortar near the free surface, and this action 
is aided by the development of sea organisms such as sea-weed and shell¬ 
fish. This cause, together with the differences in the saltness and the 
temperature of the water, and the course of the ocean currents, is the 
one which is most often called upon to explain why mortars decompose 
more quickly in some regions than in others. 


* See also Annales des Ponts et Chaussees, 1908, I, p. 107- 


LAYING CONCRETE IN FREEZING WEATHER 319 


CHAPTER XVII 

LAYING CONCRETE AND MORTAR IN 
FREEZING WEATHER 

The results of practise and experiment with cements exposed to frost, 
which are discussed more in detail in the following pages, may be summa¬ 
rized as follows: 

(1) Most Natural cements are completely ruined by freezing. (See 
p. 320.) 

(2) The setting and hardening of Portland cement in concrete or mortar 
is retarded, and the strength at short periods is lowered, by freezing, but 
the ultimate strength appears to be but slightly, if at all, affected. (See 
p. 321.) 

(3) A thin scale is apt to crack from the surface of concrete walks or walls 
which have been frozen before the cement in them has hardened. (See 
p. 320.) 

(4) Frost expands Natural cement masonry and settlement results with 
the thawing. (See p. 320.) 

(5) Heating the materials hastens setting and retards the action of frost. 
(See p. 323.) 

(6) Salt lowers the freezing point of water, and in quantities up to 
io% of the weight of the water does not appear to affect the ultimate 
strength of the concrete or mortar. (See p. 324.) 

(7) In practise concrete work should be avoided if possible in freezing 
weather, because of the difficulty and expense of attaining perfect results. 
(See p. 320.) 

EFFECT OF FREEZING 

Numerous experimental tests have been made, chiefly in the United 
States, where the effect of frost is a more serious question than in England, 
France, or Germany, to determine the effect of freezing temperatures upon 
hydraulic cements. Although the conclusions of different experimenters 
are not in perfect accord, it is the generally accepted belief, corroborated 
by tests under the most practical conditions and by the appearance of 
concrete and mortar in masonry construction, that the ultimate effect of 
freezing upon Portland cement concrete and mortar is to produce only 
surface injury. 

In their practise and research the authors have never discovered a case, 


320 


A TREATISE ON CONCRETE 


either in laboratory work or in practical construction, where Portland 
•cement concrete or mortar laid with proper care has suffered more than 
surface disintegration from the action of frost. They do not wish to imply, 
however, that it is always expedient to lay Portland cement masonry in 
freezing weather, for the expense of laying is increased, and it is much more 
difficult to satisfactorily mix and place the materials. Mortar for brick 
and stone masonry freezes in the tubs and in the joints, while in laying 
concrete the surface freezes unless measures are taken to prevent it, and 
any dirt or “laitance” which rises to the surface of wet mixtures is hard to 
remove. It is a well-known fact that a thin crust about T V inch thick is 
apt to scale off from granolithic or concrete pavements which have frozen, 
leaving a rough instead of a troweled wearing surface, and the effect upon 
concrete walls is often similar. It may be stated as a general rule that 
concrete work should, if possible, be avoided in freezing weather, although 
if circumstances warrant the added expense, with proper precaution and 
careful inspection mass concrete may be laid with Portland cement at 
almost any temperature. 

Most Natural cements, on the contrary, are seriously injured by frost 
especially by alternate freezing and thawing, and while occasional cases 
are on record, especially in heavy stone masonry in which the weighted 
joints have thawed slowly, where Natural cement mortar has been laid in 
freezing weather without serious results, numerous examples might be 
cited where even after several years the concrete or mortar was but slightly 
better than sand and gravel. Mr. Thompson has observed this result in 
Natural cement mortar laid during the comparatively warm winter of 
North Carolina on days when the temperature was considerably above 
freezing at the time of laying, and also in the cold climate of Maine where 
the mortar froze as it left the trowel and did not thaw until spring. 

The settlement of the masonry when thawing is often a serious charac¬ 
teristic of Natural cements. Stone masonry walls laid in freezing weather 
in Natural cement mortar may settle as much as ^ inch in the height of a 
window jamb. 

Experiments upon Natural cement mortars have not positively confirmed 
the judgment reached by nearly all engineers experienced in construction 
in freezing weather. Occasional tests are recorded in which such mortars, 
especially when subjected to a uniformly cold temperature and then sud¬ 
denly thawed, have attained full strength, but these are insufficient to 
warrant the use of any except Portland cements when frost is likely to 
occur before the mortar is thoroughly dry. 

The prevention of injury from frost in certain cements may be due, at 


LAYING CONCRETE IN FREEZING WEATHER 321 

least in part, to the internal heat produced when setting. In the interior 
of a large mass, some cements, especially high grade Portlands, attain a 
high temperature. (See p. 130.) 

Freezing Experiments. An extensive series of experiments upon frozen 
mortars has been conducted by Mr. Thomas F. Richardson, at the Wachu- 
sett Dam in Massachusetts. The results of tests extending up to one year 
showed that although briquettes mixed 1 part cement to 3 parts sand had 
less strength at the end of seven days than those which had not been frozen, 
the frozen specimens after longer periods, especially at the end of one year, 
gave as high and often higher strength than those which were kept at 
ordinary temperatures. The conclusion was reached, therefore, that Port¬ 
land cement mortar is not permanently injured by freezing. 

Mr. Richardson’s experiments were conducted in the middle of the 
winter of 1902. He gives the following description* of the tests: 

Two bags of Portland cement were thoroughly mixed together and all 
the briquettes were made from cement from these bags. Masonry work 
on the Wachusett Dam was in progress during the period, and briquettes 
were made each week and submitted to the same conditions as the masonry, 
the molds being filled with mortar and placed out doors in the air, not in 
waFr, immediately after filling. 

Briquettes were made at the same time as the ones exposed to the weather, 
and kept in the laboratory, either in the air or in water, those in the air 
approximating more closely the conditions which obtained on the masonry 
construction at the dam. About \ of the briquettes out doors were exposed 
to temperatures as low as 9 0 above zero in the first 24 hours, and some of 
them to temperatures as low as 12 0 below zero in the first week. Salt was 
used in most of the experiments, the quantity ranging from 4 to 16 pounds 
per barrel of cement, the average being about 6 pounds or about 3% by 
weight of water. Our experiments indicate that 8 pounds of salt per barrel 
of cement is sufficient, even in the coldest weather, and the results from 
4 pounds are very nearly as good; 16 pounds do not seem to give quite as 
good results. 

The following table gives the average results of the experiments: 


Effect of Frost upon Tensile Strength of 1:3 Mortar. (See p. 321.) 
By Thomas F. Richardson. 


Briquettes Kept 

No. of 
Bri¬ 
quettes 

Tensile Strength, lb. per sq. in. 

7 d. 

28 d. 

3 mo. 

6 mo. 

1 yr. 

Water in laboratory. 

20 

268 

3° 4 

359 

37° 

401 

Air in laboratory. 

20 

298 

35 2 

364 

39 2 

50 

Out doors, below freezing. 

80 

139 

238 

344 

435 

627 


♦Kindly furnished by Mr. Richardson for this Treatise. 





















3 22 


A TREATISE ON CONCRETE 


The briquettes were made in sets of 5, consequently 4 experiments are 
shown for water and air in laboratory, and 16 for out doors. 

In France similar results have been reached by Mr. P. Alexandre* as 
to the effect of temperatures slightly above freezing. 

Mr. Charles S. Gowenj* also has concluded from his tests that “there is 
no indication that freezing reduces the ultimate strength of the mortar, 
although it delays the action of setting.” 

The effect of different uniform temperatures upon neat cements and 
mortars is illustrated in Fig. in, which is selected and adapted by the 
authors from a series of experiments by Mr. J. E. HowardJ at the Water- 

town Arsenal. The results with both neat cements and mortars show but 

* 



7000 


6000 


5000 


4000 


3000 


2000 


1000 


0 


•Fig. iii. —Strength of Neat Portland Cement Mortar, 2-inch Cubes, 
Set in Air at Different Temperatures. (See p. 322.) 


slight increase in strength while the specimens are maintained at o° Fahr. 
(—18° Cent.), but a decided increase in strength as soon as they are sub¬ 
jected to a higher temperature. The zero cubes were removed from the 
freezer and allowed to set one day at 70° Fahr. (21 0 Cent.) before break¬ 
ing. 

Cold retards setting. Prof. Tetmajer§ found, for example, that 1: 3 
Portland cement mortar which attains its initial set at 2f hours and its 
final set at 8£ hours when mixed at 65° Fahr. (18 0 Cent.), at a temperature 
of freezing reaches its initial and final set at 21 and 38 hours respectively. 

*Annales des Ponts et Chaussees, 1890, II, pp. 302 and 422. 
fProcec dings American Society for Testing Materials, 1903, p. 393. 
fTests of Metals, U. S. A., 1901, p. 530. 

§Johnson’s Materials of Construction, 1903, p. 616. 


























































































































































































































































































































































































































































































































































































































































































LAYING CONCRETE IN FREEZING WEATHER 323 


METHODS OF CONSTRUCTION IN FREEZING WEATHER 

Certain classes of concrete construction, such as foundations or heavy 
walls, whose face appearance is of no consequence and which will have 
opportunity to thaw and then thoroughly harden before loading, may be 
laid in freezing weather with first-class Portland cement, but it is absolutely 
necessary to thoroughly remove all dirt and frozen “laitance” (see p. 393) 
before placing fresh concrete. This is a much more difficult matter than 
would appear, because frozen dirt has the same appearance as set concrete. 

In the case of structures which must not be permitted to freeze, work 
may often be conducted by maintaining the atmosphere artificially above 
the freezing point. In temperatures only a few degrees below freezing, it 
is a common practise to heat the materials, the heat tending both to accel¬ 
erate the setting of the cement and to lengthen the time before the mixture 
becomes cold enough to freeze. The addition of salt lowers the freezing 
point of the water, and therefore of the concrete or mortar. 

Protection from Frost. The method of maintaining masonry above 
the freezing point depends upon the character of the structure. 

In building construction, the reinforced concrete must be kept from 
freezing and maintained at a fairly high temperature to permit proper 
hardening. A common plan is to cover a floor as soon as laid with clean 
straw, free from manure, to a depth of about 12 inches, and then protect 
the columns and girders underneath by temporary canvas walls surround¬ 
ing the entire building, heating the enclosed space with stoves, t 

A dam was constructed at Chaudiere Falls, P. Q.* when the temperature 
was 20 0 below zero. A house 100 feet long by 24 feet wide was built over 
a portion of the dam in sections about 10 feet square, bolted together, and 
heated by sheet-iron stoves about 18 inches in diameter by 24 inches high, 
burning coke. The concrete was mixed and laid in this house, which, 
when one portion of the dam was completed, was taken down and erected 
in another place. 

Heating the Materials. Where hand-mixing is employed, an arrange¬ 
ment used on the Newton, Mass., sewers is useful. Sand for one or more 
batches is placed in a bottomless box containing a coil of steam pipe, the 
exhaust end of which is then extended to the mixing platform and arranged 
to discharge through the bottom of the platform into the bottomless box 
employed for measuring the stone, so that the latter is heated by the ex¬ 
haust steam. The cement is warmed by piling the bags on top of the sand 
box. 

f Transactions American Society Civil Engineers, Vcl. LX, 190S, p. 453. 

* Engineering News, May 7, 1903, p. 402. 


324 


A TREATISE ON CONCRETE 


An ordinary sand heater, such as is used for asphalt materials, may also 
be employed, and the stone heated by steam from a hose. A modification 
of the sand heater,* arranged to form the combined water, sand, and stone 
heater illustrated in Fig. 112, has been used on the New York Central 
Railroad. 

Experiments by Mr. Thomas F. Richardsonf tend to show that heat¬ 
ing the materials of mortar has but little, if any, permanent effect upon 
its strength. 

Addition of Salt. Because of its cheapness salt is most commonly 
employed to lower the freezing point of water. Other materials, such as 



PLAN 


Fig. i i 2.—Combined Water, Sand, and Stone Heater for Concrete 
Work in Winter. (See p. 324.) 


glycerine, alcohol, and sugar, have been experimentally employed, but these 
appear to have a tendency to lower the strength of the mortar. 

Salt has been more extensively employed in mortars than in concretes. 
Rules have been formulated for varying the percentage of salt with the 
temperature of the atmosphere. Prof. Tetmajer’sJ rule, for example, 
reduced to Fahrenheit units, requires 1% by weight of salt to the weight 
of the water for each degree Fahrenheit below freezing. 

A rule frequently cited in print, which practical tests by the authors 
have proved to be entirely inadequate, is to require one pound of salt to 
18 gallons of water for a temperature of 32 0 Fahr. and an increase of one 

♦George W. Lee in Engineering News., March 19, 1903, p. 246. 

fReporl Metropolitan Water and Sewerage Board, 1904, p. 110. 

J Johnson’s Materials of Construction, 1903, p. 615. 








































































I 


LAYING CONCRETE IN FREEZING WEATHER 325 

ounce for each degree of lower temperature. For 16 0 Fahr. this corre¬ 
sponds to but slightly more than 1% of the weight of the water, an amount 
too small to be effective. Since the temperature of the air usually cannot 
be determined in advance, an arbitrary quantity is as suitable as a variable 
one. In the New York Subway work in 1903, 9% of salt to the weight of 
the water was adopted. On the Wachusett Dam, during the winter of 
1902, 4 pounds of salt were used to each barrel of cement. For 1:3 
mortar this corresponded to about 2% of the weight of the water. 

Experiments show that ordinary “quaking” concrete in proportions 
1: 2\: 5 requires about 130 pounds of water per barrel of Portland cement, 
hence 10% of salt in average concrete is equivalent to 13 pounds per barrel 
of Portland cement. Ordinary 1: 2\ mortar requires about 120 pounds of 
water per barrel of Portland cement, hence 10% of salt in average mortar 
is equivalent to about 12 pounds salt per barrel of Portland cement. SaP 
is sometimes added in sufficient quantity to “float a potato” or an egg. 
According to tests of the authors, about 15% of salt to the weight of the 
water is required to float a potato, and about 11% to float an egg. 

Recent experiments, by Mr. Gowen* and Mr. Richardson,f extending 
up to a period of one year, tend to show that salt in a quantity corre¬ 
sponding to at least 10% of the weight of the water does not lower the 
ultimate strength of ordinary mortar. The time of setting, however, is 
considerably increased and the strength at short periods is lowered. The 
effect, at laboratory temperature, of 10% salt with 1: 3 Portland cement 
mortar is illustrated in the following table: 

Tensile Strength 0 / 1:3 Mortars made with Fresh and Salted Water. 

By- Charles S. Gowen. 



1 week. 

1 mo. 

3 mos. 

6 mos. 

9 mos. 

12 mos 

Fresh water used. 


183 

268 

335 

351 

458 

Salted water used. 

68 

I 3 1 

215 

266 

3 QI 

4 F 3 


In Mr. Richardson’s experiments^; smaller percentages of salt proved 
beneficial. Portland cement mortar in proportions 1: 3, mixed with 4 and 
8 pounds of salt per barrel cement (corresponding respectively to about 
2% and 4% of the weight of the water), gave slightly higher tensile strength 
than the unsalted mortar at all periods from 7 days to one year. 

Experiments by Mr. E. S. Wheeler§ indicate that the use of 10% of salt 
tends to prevent the swelling of briquettes in the molds, even if the speci¬ 
mens freeze. 

^Proceedings American Society for Testing Materials, 1903, p. 393. 

-j-Report Metropolitan Water and Sewerage Board, 1903, p. 112. 
fSee page 321. 

§Report Chief of Engineers, U. S. A., 1895, pp. 2963 to 2971. 




3 2 6 


A TREATISE ON CONCRETE 


Practical Proportion of Salt. Since in practice it is impossible to tell 
how low the temperature will fall before the concrete sets, Mr. Thomp¬ 
son has adopted the arbitrary rule of 2 pounds of salt to each bag of 
cement to be used when the temperature is expected to fall several degrees 
below freezing, and if experience shows that this is not quite sufficient 
to prevent the frost catching the surfaces, 3 pounds of salt per bag of 
cement are to be used instead. 

The salt can be added most conveniently by putting it into the mixing 
water. To determine the amount of salt per barrel or per tankful of 
water, the quantity of water used per bag of cement must be noted and 
from this the amount can be readily figured. 

Calcium Chloride. Experiments indicate that calcium chloride added in 
quantities not exceeding 2% of the weight of the cement is an effective 
agent for lowering the freezing point of the concrete. It should be used 
with caution, however, since a larger quantity than this is likely to so 
hasten the set as to make the concrete difficult to handle. 


FIRE AND RUST PROTECTION 


327 


CHAPTER XVIII 

FIRE AND RUST PROTECTION 

Observations of steel imbedded in concrete which has been exposed to 
fire or to corrosive action, and experimental tests prove conclusively that 
if to 2 inches of dense Portland cement concrete, made in ordinary pro¬ 
portions, with broken stone, gravel, or cinders, of good quality, and mixed 
wet, will effectually resist the most severe fire liable to occur in buildings, 
and will prevent the corrosion of steel even under extraordinary conditions. 
In members of inferior importance or which are only liable to fire of com¬ 
paratively low temperature, a less thickness of concrete, in many cases 
j-inch or even ^-inch, will prove effective. (See p. 333.) 

In buildings concrete has been found a more effective fire-resisting 
material than terra-cotta (see p. 333) and fully equal to first-class brickwork. 
Brickwork cannot exist in a structure except in combination with some 
other material like steel or wood, which is seriously affected by fire, whereas 
concrete reinforced with steel may replace not only the brickwork, but also 
the steel or wood columns and beams. 

PROTECTION OF STEEL BY CONCRETE 

Tests by Prof. Charles L. Norton 

Extended practical tests have been conducted by Prof. Charles L. 
Norton for the Insurance Engineering Station in Boston. As a result of 
experiments made in 1902 upon several hundred specimens, he concludes:* 

(1) Neat Portland cement, even in thin layers, is an effective preventive 
of rusting. 

(2) Concretes, to be effective in preventing rust, must be dense and 
without voids or cracks. They should be mixed quite wet where applied 
to the metal. 

(3) The corrosion found in cinder concrete is mainly due to the iron 
oxide, or rust, in the cinders, and not to the sulphur. 

(4) Cinder concrete, if free from voids and well rammed when wet, is 
about as effective as stone concrete in protecting steel. 

In his first series of experiments, round rods of mild steel, soft shee 
steel, and expanded metal were each imbedded in the center of blocks o* 

*Engineering News, October, 1902, p. 334. 


A TREATISE ON CONCRETE 


3 28 

concrete, 3 by 3 by 8 inches. Neat cement, 1: 3 mortar, and concrete in 
proportions 1 cement : 5 broken stone; 1 cement : 7 cinders; 1 cement: 
2 sand • 5 broken stone; and 1 cement : 2 sand : 5 cinders, were employed 
for imbedding the steel. The stone was chiefly of trap rock. These 
specimens, after setting, were subjected continuously to the action of steam, 
air, and carbon dioxide. Unprotected pieces of steel were also exposed 
to the same test. 

At the end of three weeks the unprotected pieces of steel “were found to 
consist of rather more rust than steel.” The protection of the steel incased 
in neat cement was perfect. The remaining specimens, in mortar and 
concrete, were seriously corroded in spots, but it was observed that the 
“rust spot was invariably coincident with either a void in the concrete or 
a badly rusted cinder. In the more porous mixtures, the steel was spotted 
with alternate bright and badly rusted areas, each clearly defined.” One 
point is exceedingly instructive: 

In both the solid and the porous cinder concretes, many rust spots were 
found, except where the concrete had been mixed very wet , in which case the 
watery cement had coated nearly the whole 0 / the steel , like a paint , and 
protected it. 

Protection of Rusty Steel. In 1903, Prof. Norton made tests to de¬ 
termine the protection afforded ordinary rusty or dirty steel. He found 
that while unprotected steel “vanished into a streak of rust,” if protected 
by an inch or more of sound concrete, not only the sound steel but ordinary 
structural steel of any degree of cleanliness likely to be in use in a building 
is unaffected by such extreme treatment as was accorded it in the tests. 
The conditions of these later experiments were similar to those of the 
previous year. Each piece of steel was stamped, and this removed loose 
scale. Dirt was removed by a soft wire brush. The steel was imbedded 
to a depth of ij inches in all directions in broken stone concrete of pro¬ 
portions i:2j:5 and in cinder concrete of proportions 1:3:6. The 
treatment of the specimens was similar to that of the previous ones. 

A portion of Prof. Norton’s conclusions* are given in the following 
paragraphs: 

Condition of Specimens. After varying lapses of time from one to 
three months for the specimens in the “corroders,” and from one to nine 
months for the others, the specimens were broken out of the briquettes 
cleaned by brushing, and weighed and calipered. Not one specimen had 

*Engineering News , January, 1904, p. 30. 


FIRE AND RUST PROTECTION 


329 


shown any sensible change in weight or dimension, except where the 
concrete had been poorly applied. Some specimens were purposely bedded 
in very dry concrete, and some in concrete partly set, and many of these 
were not well covered and the steel was seriously attacked where there were 
voids or cracks. Of the hundreds of specimens of rusty steel examined, 
not one which had a continuous unbroken coating of concrete gained 
or lost anything in volume or weight by treatment which caused the prac¬ 
tical destruction of some of the unprotected specimens. If loss by cor¬ 
rosion as great as 1-1000 of the loss occurring with the unprotected speci¬ 
mens had been experienced in the case of the protected pieces it would 
have readily been noted. 

Conclusions. It would therefore seem that if we admit that from a 
severe trial of a short duration, we may judge relatively of the effects of 
the less severe but longer test of time, it can not be questioned that struct¬ 
ural steel is safe from corrosion if incased in a sound sheet of good concrete, 
at least for a period of years so long as to make the subject of more interest 
to our great-grandchildren’s children than to us. We know that bare 
steel does not rust and fall down over night, and that much of the steel 
standing has been bare of everything that could protect it, for long years, 
and it seems to me beyond question that steel properly covered in concrete 
may well be expected to last far longer than the changes in our cities will 
allow any building to remain. 

Protection by Cinder Concrete. There is one limitation to the whole 
question, that is the possibility of getting the steel properly incased in 
concrete. Many engineers will have nothing to do with concrete because 
of the difficulty in getting “sound” work. This is especially true of cinder 
concrete, where the porous nature of the cinders has led to much dry 
concrete and many voids, and much corrosion. I feel that nothing in this 
whole subject has been more misunderstood than the action of cinder 
concrete. We usually hear that it contains much sulphur and this causes 
corrosion. Sulphur might, if present, were it not for the presence of the 
strongly alkaline cement; but with that present the corrosion of steel by 
the sulphur of cinders in a sound Portland concrete is the veriest myth, 
and as a matter of fact the ordinary cinders, classed as steam cinders, 
contain only a very small amount of sulphur. There can be no question 
that cinder concrete has rusted great quantities of steel, but not because 
of its sulphur, but because it was mixed too dry, through the action of the 
cinders in absorbing.moisture, and that it contained, therefore, voids; and 
secondly, because in addition the cinders often contain oxide of iron which, 
when not coated over with the cement by thorough wet mixing, causes the 
rusting of any steel which it touches. 

Mix Wet. There is one cure and only one, mix wet* and mix well . 
With this precaution I would trust cinder concrete quite as* quickly as 
stone concrete in the matter of corrosion. 

Rust no Protection for Steel. It has been suggested that steel which 
has been rusted to a slight depth becomes protected by this coating from 
further rusting. Nothing could be further from the truth. A large num* 

*See page 280 for the authors’ definition of a very wet mixture. 


330 


A TREATISE ON CONCRETE 


ber of specimens were rusted by repeated alternate wetting and drying to 
see if they finally reached a constant condition. Instead of doing this, they 
all showed an irregular but persistent loss in weight, on further rusting, 
until some had practically been washed away. 

Small Rods. The increasing use of steel of small dimensions in floors 
and roofs, twisted rods, expanded metal, etc., has caused some question as 
to the advisability of their use in view of the possible great effects of cor¬ 
rosion, as compared with the effects of corrosion on larger members, but 
with sound concrete of a thickness of about in. between the steel and 
the weather I do not question the durability of these lighter members. 

CHEMICAL UNION OF STEEL AND CEMENT 

Experiments of Mr. Breuille* indicate that clean steel may form with 
cement a chemical combination which is soluble in water. This presents 
an additional reason for making concrete in which steel is imbedded as 
impervious as possible, to avoid the penetration of moisture which will 
wash away this chemical compound, if such is found to exist in actual 
structures. Large I-beams imbedded in concrete would be especially 
subject to deterioration from this cause, but as rust rarely forms between 
two plates of steel which are riveted together in a bridge, even although the 
rest of the structure is badly corroded, the danger is probably insignificant. 

Cement Paint for Protecting Steel. The property of neat cement 
which prevents steel from corrosion is taken advantage of in different forms 
of cement coating. Mr. Maximillian Toch in ic)03f made a series of 
experiments upon metal covered with various preparations of cement, and 
drew the following conclusions: 

(1) A proper cement paint can be applied to a surface that has begun 
to oxidize, and further oxidation will be arrested. 

(2) If the cement be absolutely fine and free from iron, calcium sulphate 
and sulphites, and of low specific gravity, it will set on the surface within 
a very short time, and eventually become an integral part of the metal. 

For exposed iron work Mr. Toch recommends a protective coat of cement 
paint followed by a coat of linseed oil paint. To protect from the fumes 
of a factory, he states that after applying three coats of cement paint, an 
alkali-proof, adherent paint may be spread, and an absolute protection 
afforded to the iron. 

Air. J. W. SchaubJ refers to the use of cement mortar in Europe and in 

* J. W. Schaub in Transactions American Society of Civil Engineers, Vol. LI, p. 124. 

fLecture on the Permanent Protection of Iron and Steel, delivered before the New York Sec¬ 
tion of the American Chemical Society, March 6, 190^. 

t-Engineering News , June 16, 1904, p. 561. 


FIRE AND RUST PROTECTION 331 

the United States for coating iron exposed to destructive agencies. He 
says: 

The mortar is usually a mixture of 1 cement and 2 sand, applied with a 
brush as a wash. Five or six coats are applied in this way to give the metal 
a proper coating. This is especially applicable in the case of the iron 
work exposed in roundhouses, where the gases from locomotives are so 
destructive, and where paint is so inefficient. 

FIRE PROTECTION 

Numerous experimental tests* have been made showing the value of 
concrete as a fire-resisting material, but the best proof of its ability to resist 
the heat of a severe fire — such as is liable to occur in an office or factory 
building — lies in the fact that concrete has actually withstood very severe 
fires more successfully than have terra-cotta and various other so-called 
fireproof materials. 

The reinforced concrete factory of the Pacific Coast Borax Co. at Bay¬ 
onne, N. J., passed through a severe fire in 1902. Still more recently, in 
1904, occurred the conflagration at Baltimore in which many building 
materials utterly failed. 

Such practical tests, further confirmed by numerous experiments with 
test buildings of reinforced concrete, have proved that while in a severe 
fire, where the temperature ranges from 1600° to 2000° Fahr., the surface 
of the concrete may be injured to a depth of from ^ to } inch, the body of 
the concrete is unaffected, so that the only repairs required consist of a 
coating of plaster, and even this only in rare instances. 

Tests upon small briquettes of cement placed in a furnace indicate that 
the strength of cement is destroyed by a heat reaching a dull, red color,f 
but as stated below, in an actual fire, the injured material protects the rest 
of the concrete so that the danger is theoretical rather than real. 

Fire in Borax Factory. The fire in the 4-story reinforced concrete 
factory of the Pacific Coast Borax Company, built entirely of concrete 
except the roof, utterly destroyed the contents of the building, the roof, 
and the interior framework, but the walls and floors remained intact 
except in one place where an 18-ton tank fell through the plank roof and 
cracked some of the floor beams, and in one place on the outside of the 
wall where the surface of the concrete was slightly affected. The fire was 
so hot that brass and iron castings were melted to junk. A small annex, 

*See References, Chapter XXIX. 

•{■Digest of Physical Tests, Vol. I, p. 217. 


332 


A TREATISE ON CONCRETE 


built of steel posts and girders, was completely wrecked, and the metal beni 
and twisted into a tangled mass. 

Baltimore Fire. The effect of the fire upon the concrete in various 
buildings located in the center of the burned districts of Baltimore is best 
appreciated by an examination of the reports of experts upon the fire. 
Capt. John S. Sewell, in his report to the Chief of Engineers, U. S. A.,* in 
referring to the fire in one of the buildings built with reinforced concrete 
columns, beams, and arches, writes: 

It was surrounded by non-fireproof buildings, and was subjected to an 
extremely severe test, probably involving as high temperature as any that 
existed anywhere. The concrete was made with broken granite as an 
aggregate. The arches of the roof and the ceiling of the upper story were 
cracked along the crown, but in my judgment very slight repairs would 
have restored any strength lost here. Cutting out a small section — say 
an inch wide — and caulking it full of good strong cement mortar would 
have sufficed. The exposed corners of columns and girders were cracked 
and spalled, showing a tendency to round off to a curve of about 3 in. 
radius. In the upper stories, where the heat was intense, the concrete 
was calcined to a depth of from J to f inch, but it showed no tendency to 
spall, except at exposed corners. On wide, flat surfaces, the calcined 
material was not more than J-inch thick, and showed no disposition to 
come off. In the lower stories, the concrete was absolutely unimpaired, 
though the contents of the building were all burned out. In my judgment, 
the entire concrete structure could have been repaired for not over 20% 
to 25% of its original cost. On March 10, I witnessed a loading test of 
this structure. One bay of the second floor, with a beam in the center, was 
loaded with nearly 300 pounds per sq. ft. superimposed, without a sign of 
distress, and with a deflection not exceeding J-inch. The floor was de¬ 
signed for a total working load of 150 pounds per sq. ft. The sections next 
to the front and rear walls were cantilevers, and one of these was loaded 
with 150 pounds per sq. ft. superimposed, without any sign of distress, or 
undue deflection. 


Captain Sewell concludes as a result of the examination of this and other 
buildings containing reinforced concrete construction: 

As the material is calcined and damaged to some extent by heat, enough 
surplus material should be provided to permit of a loss of say }-inch all 
over exposed surfaces, if the structure is to be exposed to fire; moreover, all 
exposed corners should be rounded to a radius of about 3 inches. This 
latter precaution would add much to the resistance of all materials used in 
masonry — whether bricks, stone, concrete or terra-cotta — if they are to 
be exposed to fire. 


^Engineering News, March 24, 1904, p. 276. 


FIRE AND RUST PROTECTION 


333 


Concrete Versus Terra-Cotta. Prof. Norton, in his report on the Balti¬ 
more fire to the Insurance Engineering Experiment Station,* says: 

Where concrete floor arches and concrete-steel construction received 
the full force of the fire it appears to have stood well, distinctly better than 
the terra-cotta. The reasons I believe are these: First, because the concrete 
and steel expand at sensibly the same rate, and hence when heated do not 
subject one another to stress, but terra-cotta usually expands about twice 
as fast with increase in temperature as steel, and hence the partitions and 
floor arches soon become too large to be contained by the steel members 
which under ordinary temperature properly enclose them. Under this 
condition the partition must buckle and the segmental arches must lift and 
break the bonds, crushing at the same time the lower surface member of 
the tiles. 

When brick or terra-cotta are heated no chemical action occurs, but 
when concrete is carried up to about i ooo° Fahr. its surface becomes 
decomposed, dehydration occurs, and water is driven off. This process 
takes a relatively great amount of heat. It would take about as much heat 
to drive the water out of this outer quarter-inch of the concrete partition as 
it would to raise that quarter-inch to i ooo° Fahr. Now a second action 
begins. After dehydration the concrete is much improved as a non-con¬ 
ductor, and yet through this layer of non-conducting material must pass 
all the heat to dehydrate and raise the temperature of the layers below, a 
process which cannot proceed with great speed. 

Cinder Versus Stone Concrete. Prof. Norton compares the action of 
stone and cinder concrete in the Baltimore fire as follows: 

Tittle difference in the action of the fire on stone concrete and cinder 
concrete could be noted, and as I have earlier pointed out, the burning of 
the bits of coal in poor cinder concrete is often balanced by the splitting of 
the stones in the stone concrete. I have never been able to see that in the 
long run either stood fire better or worse than the other. However, owing 
to its density the stone concrete takes longer to heat through. 

Further experiments are required to determine the relative durability 
under extreme heat of concrete made with different kinds of broken stone. 
It seems probable, from the composition of the rock, that hard trap or 
gravel may be preferable to limestone, slate, or conglomerate as fire- 
resisting material. 

Thickness of Concrete Required to Protect Metal from Fire. The 

conclusion reached by Prof. Nortonf from tests upon concrete arches is 
that two inches of good concrete gives perfect assurance of safety in case of 
fire, even if the steel to be protected is in the form of I-beams. Rods of 

*Engineering News, June 2, 1904, p. 529. 
f Insurance Engineering, Dec., 1901, p. 483. 


334 


A TREATISE ON CONCRETE 


small dimensions can be more effectively coated, and it appears evident 
from the vario.us tests and from practical experience in severe fires that 
inches of concrete around steel rods is sufficient protection. The 
Pacific Borax Company’s fire and other similar tests indicate that in slabs 
of reinforced concrete, \ inch to J inch affords ample protection. Second¬ 
ary members, such as cross girders, or slabs of long span, should have a 
thickness of concrete outside of the steel varying from J inch to inch. 
Although in slabs protected by only \ inch of concrete, the latter may be 
softened by an extreme fire, and the metal exposed when it is struck by 
the stream from a hose, the metal in the majority of cases would still remain 
practically uninjured, and it is questionable economy to put an excess of 
material where there is so little probability of its being needed, and where 
a failure would merely produce local damage. 

THEORY OF FIRE PROTECTION 

Mr. Spencer B. Newberry, in an address delivered before the Associated 
Expanded Metal Companies, Feb. 20, 1902,* gives the following explana¬ 
tion of the fire-proof qualities of Portland cement concrete: 

The two principal sources from which cement concrete derives its 
capacity to resist fire and prevent its transference to steel are its combined 
water and porosity. Portland cement takes up in hardening a variable 
amount of water, depending on surrounding conditions. In a dense 
briquette of neat cement the combined water may reach 12%. A mixture 
of cement with three parts sand will take up water to the amount of about 
18% of the cement contained. This water is chemically combined, and 
not given off at the boiling point. On heating, a part of the water goes 
off at about 5oo°Fahr.,but the dehydration is not complete until 900° Fahr. 
is reached. This vaporization of water absorbs heat, and keeps the mass 
for a long time at comparatively low temperature. A steel beam or column 
embedded in concrete is thus cooled by the volatilization of water in the 
surrounding cement. The principle is the same as in the use of crystallized 
alum in the casings of fireproof safes; natural hydraulic cement is largely 
used in safes for the same purpose. 

The porosity of concrete also offers great resistance to the passage of 
heat. Air is a poor conductor, and it is well known that an air space is a 
most efficient protection against conduction. Porous substances, such as 
asbestos, mineral wool, etc., are always used as heat-insulating material. 
For the same reason cinder concrete, being highly porous, is a much better 
non-conductor than a dense concrete made of sand and gravel or stone, 
and has the added advantage of lightness. In a fire the outside of the 
concrete may reach a high temperature, but the heat only slowly and 
imperfectly penetrates the mass, and reaches the steel so gradually that it 
is carried off by the metal as fast as it is supplied. 

*Cement, May, 1902, p. 95. 


FIRE AND RUST PROTECTION 


335 


TESTS OF FIRE RESISTANCE 

Prof. Ira H. Woolson of Columbia University has made several series 
of tests* to determine the effect of heat upon the strength and elastic proper¬ 
ties of the concrete and upon the thermal conductivity of the concrete and 
the imbedded steel. 

Effect Upon Strength. Tests to determine the effect of heat treatment 
upon the strength and elastic properties of different mixtures showed that 
the trap concrete was least affected. Concrete two months old, in pro¬ 
portions 112:4, the crushing strength of which before heating was about 2500 
pounds per square inch tested in 7-inch cubes, after being subjected to a 
heat of 1500° Fahr. for two hours gave a strength of about 1000 pounds 
per square inch. However, since this reduction in strength was due at 
least in part to the reduction in the effective area because of the surface 
deterioration (if the surface was injured to a depth of i| inches the effec¬ 
tive area would be reduced from 49 sq. in. to 20 sq. in.), it is probable that 
the interior of the blocks was affected very little. The concrete made with 
gravel, which in these tests was nearly pure quartz having a high coeffi¬ 
cient of expansion, was affected to a much greater extent. Cinder con¬ 
crete, which showed a normal crushing strength of about one-half that of 
the trap, after heat treatment gave a corresponding weakening. 

The modulus of elasticity of the concrete was always greatly reduced by 
heat treatment. 

CONDUCTIVITY OF CONCRETE AND IMBEDDED STEEL 

As a result of the conductivity tests, which were made upon specimens of 
trap, gravel and cinder concrete having thermo-couples for measuring heat 
transmission imbedded so as to indicate the temperature at points varying 
from \ inch to 6 inches from the heated face, Prof. Woolson drew the 
following conclusions :j* 

All concretes have a very low thermal conductivity, and herein lies their 
ability to resist fire. 

When the surface of a mass of concrete is exposed for hours to a high 
heat, the temperature of the concrete one inch or less beneath the surface 
will be several hundred degrees below the outside. 

A point 2 inches beneath the surface would stand an outside temperature 
of 1500° Fahrenheit for two hours, with a rise of only 500° to 700°, and 
points with three or more inches of protection would scarcely be heated 
above the boiling point of water. 

* Proceedings of American Society for Testing Materials, Vol. V, 1905, p. 335; VI, 1906, p. 433; 
VII, 1907, p. 404. 

■{•Proceedings American Society for Testing Materials, Vol. VII, 1907. p. 408. 


A TREATISE ON CONCRETE 


336 

The fact that cinder concrete showed a higher thermal conductivity 
than the stone concrete would indicate that its well-known fire-resistive 
qualities are due, in part at least, to the incombustible quality of the cinder 
itself. 

The thermal conductivity of the gravel concrete* was fully as low as 
that of the trap, but the specimens of gravel concrete cracked and crumbled 
in many cases when the trap and cinder specimens under similar treatment 
remained firm and compact. 

In the tests on the conductivity of imbedded steel with the end project¬ 
ing from concrete, Prof. Woolson found practically the same results with 
concrete from all three aggregates. With the temperature of the end sur¬ 
face of the concrete and the projecting end of the bar 1700° Fahrenheit, 
a point in the bar only 2 inches from the heated face of the concrete developed 
a temperature of only iooo° Fahrenheit, while at a point 5 inches in the 
concrete the temperature was only 400° to 500°, and at 8 inches the tem¬ 
perature reached only the heat of boiling water. 

From these results Prof. Woolson concludes that “ where reinforcing 
metal is exposed in the progress of a fire, only so much of the metal as is 
actually bare to the fire is seriously affected by it.” 

Tests by the National Fire Protection Associationj* in 1905 upon beams 
8 inches by 11^ inches by 6 feet long, of different kinds of concrete, showed 
that the strength of rods imbedded 1 inch from the lower surface was 
reduced about 25 per cent after heating to a temperature of 2000° Fahren¬ 
heit for one hour. With rods imbedded 2 inches a similar reduction in 
strength occurred after 2 hours and 20 minutes heating, and the strength 
of the concrete was appreciably reduced to a depth of 4 inches from the 
sides and bottom. 

The hardest and densest mixtures were usually the poorest conductors 
of heat; the cinder concrete gave, however, a slower rise of temperature 
than the others. 

INFLUENCE OF CRACKS IN REINFORCED CONCRETE UPON THE 

CORROSION OF STEEL 

It has been seriously questioned whether the minute cracks which open 
in a concrete beam and slab even under loads which are absolutely safe do 
not permit corrosion of the steel reinforcement. Tests by E. ProbstJ: in 


*As stated in connection with the tests on preceding page, this gravel was nearly pure quartz. 
In other tests, concrete with gravel containing a larger percent of slate or other similar mater al 
has given much better results. 

-j* Cement, January, 1906, p. 273. 

J Report of the Royal Department of Testing Materials in Gross Lichtenfelde, West Prussia. 


FIRE AND RUST PROTECTION 


337 


Germany, in 1907, indicate very conclusively that steel in reinforced beams, 
laid in ordinary wet concrete used in practical construction, is in no danger 
of rusting through the cracks formed in the concrete under tension, until 
nearly the breaking point of the steel. The specimens, 34 beams, which 
contained both plain and deformed bars and rusted and unrusted steel, 
were subjected in loading to the action of a mixture of oxygen, carbon dioxide 
and steam, for a period of from 3 to 12 days. Unprotected steel subjected 
to this mixture was badly rusted in two hours. After breaking up the 
specimens of concrete no rust was found even on steel stressed to its elastic 
limit, although some was discovered on steel stressed nearly to its breaking 
point, which could be attributed to large cracks extending to the metal and 
uncovering it. 


PROTECTING STRUCTURAL STEEL 

In San Francisco at the time of the earthquake and fire, April, 1906, there 
were few concrete structures, but these stood the test of fire and shock on 
the whole better than any other material.* 

Observations after the fire indicate that concrete is also an effective pro¬ 
tection for steel frame construction, but that it preferably should be enclosed 
in a metal basket. 

Captain John S. Sewell, Engineer Corps, U. S. A., in his report to the 
U. S. Governmentf suggests that when such a basket is used the total 
thickness of concrete upon the exposed flanges of girders and floor beams 
should be 2 to 3 inches according to circumstances. For columns incased 
in a metal basket or cage, a thickness of 3 to 4 inches was recommended. 

The structural steel in the Boston subway,{ imbedded for twelve years 
in concrete or protected by the cement mortar joints of brick arches, was 
found upon examination during changes in the structure to be free from 
rust. The only exception to this was under the rather large base plates 
(21 by 24 inches) of columns, where a thin layer of rust frequently was 
found, having tubercles sometimes \ inch thick. This was evidently due 
to che settling of the finer parts of the concrete under the plates. The 
small base-plates were practically free from rust. 


* Transactions American Society Civil Engineers, Vol.' LIX, 1907, p. 208. 
-j-U. S. Geological Survey, Bulletin 324, 1907. 

^Personal correspondence with Mr. Howard A. Carson, Chief Engineer. 


33^ 


A TREATISE ON CONCRETE 


CHAPTER XIX 

WATER-TIGHTNESS 

A wall of concrete may be rendered water-tight in several ways: 

(1) By accurately grading and proportioning the aggregates and the 
cement. (See p. 339.) 

(2) By special treatment of the surface of the concrete. (See p. 341.) 

(3) By the introduction of foreign ingredients into the mixture. (See 
P- 342 .) 

(4) By the application of layers of waterproof material, such as asphalt 
and felt. (See p. 343.) 

It is often advisable to combine two or more of these methods. 

In the succeeding pages directions are given for practically applying 
these methods, and experimental investigation is cited. 

LAYING CONCRETE FOR WATER-TIGHT WORK 

The manner of laying the concrete in walls or floors which are to with¬ 
stand water pressure is as important as the proportioning of its ingredients. 
Approved methods of placing are fully described in Chapter XV. 

The chief points applicable to water-tight work are briefly recapitulated 
as follows: 

(a) Mix concrete of quaking or of wet consistency. (See p. 338.) 

(b) Place concrete carefully so as to leave no visible stone pockets. 

(c) Lay the entire structure, if possible, in one continuous operation, 
working night and day when necessary. 

(d) If joints are unavoidable, clean and roughen the old surface, then 
wet it and coat with a layer of cement or mortar. (See p. 284.) 

( e ) Make suitable provision for contraction by special joints, or by steel 
reinforcement without joints. (See p. 285, also chapter xxi.) 

Effect of Consistency. A series of experiments, conducted by the 
authors, upon several blocks of mortar mixed in the same proportions of 
cement, sand, and stone, but with different proportions of water, indicates 
that the best consistency for concrete designed to withstand water pressure 
is intermediate between a quaking and a mushy mixture, as defined on 
page 280. 

Also, the general conclusion was reached that with the same dry materials 
the consistency producing the greatest density after setting gives the most 


WA TER-TIGHTNESS 


339 


impermeable mortar or concrete up to the point of a very wet consistency, 
when the excess of water affects the chemical composition of the cement, 
forming “laitance” (see p. 302), and thus reduces both the strength and 
the water-tightness of the specimen. After setting, the very wet specimens 
were found to have about the same density as the medium and mushy 
mixtures, because the cement, sand, and stone settled into place and ex¬ 
pelled the surplus water. 

PROPORTIONING WATER-TIGHT CONCRETE 

The proportions* employed to resist the percolation of water usually 
range from 1:1:2 to 1:2^: 4^, the most common mixtures being 1:2:4 
or 1: 2J: 4^. However, with accurate grading by scientific methods, such 
as are described in Chapter XI, water-tight work may be obtained with 
proportions as lean as 1:3: 7. (See p. 183.) Permeability, the quality of 
allowing water to pass through, and porosity, the property of containing 
pores or voids, are not synonymous terms, and the most porous material is 
not necessarily the most permeable, because the dimensions of the voids as 
well as their volume affect by capillarity the passage of water. 

For maximum water-tightness a mortar or concrete may require a 
slightly larger proportion of fine grains in the sand than for maximum 
density or strength, but otherwise the general principles discussed on page 
172 are applicable. A mixed aggregate (such as is shown in Fig. 61, 
p. 173) evidently has fewer channels through which the water can pass 
than an aggregate consisting of coarse stone and sand (such as is shown 
in Fig. 59, p. 172), provided the character and relative proportioning of 
the finest particles are the same in both cases. Recent tests indicate 
that gravel produces more water-tight concrete than broken stone under 
similar conditions. 

Porosity of Concrete. The total voids, air plus water, in first-class 
concrete and mortar of various proportions are shown in column (20) of 
the table of Mr. William B. Fuller’s experiments on pages 376 and. 377. 
The percentage of total voids in the mortars averages about 26%, while in 
the concretes, of proportions commonly employed in practice, the voids 
range from 13% to 17%. 

In neither the concrete nor the mortar do these percentages ever represent 
air alone. A portion of the water, an amount estimated at 8% of the 
weight of the cement,f corresponding to about 2 \% of the volume of 

♦Proportions are based on an assumed unit of ioo lb. cement per cu. ft. or the equivalent of 
3.8 cu. ft. to the barrel. (See p. 217.) 

fAllen Hazen in Transactions American Society of Civil Engineers, Vol. XLII, p. 128. 


340 


A TREATISE ON CONCRETE 


ordinary concrete, combines with the cement, and a still larger portion of 
the water remains in the pores unless dried by artificial heat. 

The porosity of mortars is discussed on page 127. 

Size of Stone. Authorities disagree as to the relative advantages of 
small stone ranging between \ and one inch, and coarse stone, ranging 
from J inch up to, say, 2J inches. The latter is theoretically the better, 
but it is sometimes claimed that the fine material can be placed 
more satisfactorily. This depends upon the workmanship. With 
proper selection of materials and care in laying, the concrete con¬ 
taining the coarse stone produces excellent work, as is illustrated 
by the constructions at Little Falls, N. J. (see Chapter XXVIII), c.nd 
Boonton, N. J. (see Chapter XXVI), where carefully graded stone up to 
2 \ or 3-inch diameter was used. 

If very fine stone, under J-inch, and containing dust, is used for the 
coarser aggregate, the addition of sand may increase the porosity and the 
permeability, because concrete with such small stone is practically a mortar, 
and the finer particles of stone are really sand. A concrete in proportions 
1 part cement : 2 parts sand : 4 parts unscreened stone less than J-inch 
diameter, makes a porous concrete, while a mixture 1 part cement : 2 parts 
sand : 4 parts stone ^-inch to ij-inch diameter, makes a dense one. With 
the small stone, proportions 1:1:2 would be the leanest advisable 
mixture. 

The method of proportioning by mechanical analysis, as described by 
Mr. Fuller in Chapter XI, has been found in practice to produce imper¬ 
meable concrete. 

THICKNESS OF CONCRETE FOR WATER-TIGHT WORK 

It is impossible to specify definite thicknesses of concrete to prevent per¬ 
colation under different heads of water, because of variations in proportions 
and methods of laying. We have known rain water under a head of 2 or 
3 inches to percolate through a 4-foot wall of excellent concrete of dry 
consistency. On the other hand, had the same materials been mixed to a 
wetter consistency and placed with no joints between successive layers, 
concrete but a few inches thick would have withstood a high head. 

The best criterions for thicknesses of walls of first-class concrete are 
obtained from actual examples. Instances are cited in Chapters XXVI 
and XXXVIII of water-tight concrete 4 inches thick sustaining a head 
of 4 feet, concrete 15 inches thick sustaining a head of 40 feet, and con¬ 
crete 5.5 feet thick sustaining a head of 100 feet. 


WA TER-TIGHTNESS 


34i 


SPECIAL TREATMENT OF SURFACE 

Various methods of treating the surface of concrete have been employed 
to increase the water-tightness. 

Plastering. Plastering the surface of concrete with rich Portland cement 
mortar in proportions 1: 1 or 1: is the method which first occurs to one, 
but in temperate or cold climates it is only useful for walls below the surface 
of the ground and therefore not subject to atmospheric changes. In such 
cases it can sometimes be used as a substitute for, or in connection with, 
paper and asphalt. 

In certain sections of the Boston Subway*, a 6 inch wall of concrete was 
iaid up next to the bank of earth and plastered with a layer of 1: 1 mortar 
about ^ inch thick. After spreading the mortar with a plasterer’s ordi¬ 
nary metal float (see Chapter XXIII.) the surface was run over with a 
toothed roller about 12 inches long by 4 inches in diameter, which pressed 
the plaster into any crevices, and left a rough surface. The main wall of 
concrete forming the lining of the Subway was then laid up against this 
plastered surface. 

On the arch of the approaches to the East Boston tunnel, a layer of 
plaster, like that on the walls, was spread before laying the final 6-inch 
thickness of concrete, thus forming a water-tight joint in the interior of 
the arch ring. 

Granolithic Finish. On horizontal or inclined surfaces, a granolithic 
surface of rich mortar of Portland cement and sand, or Portland cement 
and screenings in proportions about 1: 1 may be laid and troweled, as in 
sidewalk construction. (See Chapter XXIII.) The surface finish must be 
placed at the same time as the base, and with the same, that is, Portland 
cement. 

Troweling Surface. The water-tightness of horizontal or inclined layers 
of concrete can be greatly increased by troweling the concrete in the same 
manner that granolithic work is troweled. (See Chapter XXIII.) This 
brings the cement to the surface, and produces a dense, hard surface 
which is nearly equal to a surfacing of rich mortar. This is very effect¬ 
ive for surfacing a structure like the inclined face of the dam shown in 
Chapter XXVI. 

In experimenting upon the permeability of different concretes, the authors 
have noticed that even the very light joggling which is necessary to compact 
a wet concrete, and also the ramming of a stiffer mixture, increases the 
impermeability of the concrete. Even after chipping off the top of the 
specimen for a depth of J or J of an inch, the flow will be several times less 
than when the pressure is directed upon its under surface. 

* In Subway construction since 1902 and in the tunnel built in 1907-9, the trench frequently was 
shored with 2^-inch reinforced concrete sheeting (See Chap. XXV), the surface evened with plaster, 
if necessary, and water-proofing applied. 


342 


A TREATISE ON CONCRETE 


Grout. Portland cement grout is preferable to plaster for coating the 
soffits of arches or for wall surfaces. It is also valuable for coating the in¬ 
terior of cisterns or tanks.* * * § The grout should of course be applied against 
the surface which is to come in contact with the water, and if the wall is to 
be made impervious in both directions, both sides should be washed. 

A specially prepared cement wash has been found effective in preventing 
dampness in masonry.f 

Alum and Lye Waterproof Wash. United States Army Engineers^ 
have satisfactorily employed a wash of alum and concentrated lye mixed 
in proportions one pound lye, 2 to 5 pounds alum, and 2 gallons of water, 
which has been used with good success in several instances. 

Special Coatings. A few patented compounds which have proved suc¬ 
cessful are on the market. These are generally used with neat cement or 
mortar. In many cases it has been found possible to waterproof the face 
of the wall instead of the back upon which the water presses. 

INTRODUCTION OF FOREIGN INGREDIENTS 

The principal advantage of introducing foreign ingredients into a mortar 
or concrete is to permit the use of a lean mixture, the fine particles of 
hydrated lime, or whatever may be used, tending to reduce the volume and 
the dimensions of the voids. Every case must be studied by itself, since 
it is frequently cheaper to obtain the required water-tightness by adding 
cement than by admixtures.. 

Lime and Puzzolan Cement. The effect of the addition of lime in 
small quantities is chiefly mechanical, and the quantity which should be 
employed depends, therefore, upon the fineness of the sand and the pro¬ 
portions of the mixture. 

Although it is impossible to replace the water which separates the grains 
in neat cement paste or rich mortar with a material like lime, a series of 
tests§ made by one of the authors in 1908 indicates that the introduction of 
a small percentage of hydrated lime into the concrete for small structures 
like tanks will render them more watertight, especially at early periods, 
and also that for large masses of concrete the addition of hydrated lime may 
permit the use of leaner proportions. The percentage of hydrated lime to 
use varies with the proportions of concrete and the character of the materials, 


* J. W. Schaub, Transactions American Society of Civil Engineers, Vol. LI, p. 123. 

•j- Oscar Lowinson, Transactions American Society of Civil Engineers, Vol. LI, p. 125. 

j C. B. Hegardt in Report Chief of Engineers, U. S. A., 1902, p. 2482. 

§ “Permeability Tests of Concrete with Addition of Hydrated Lime,” by Sanford E. Thompson, 
American Society for Testing Materials, Vol. VIII, p. <;oo. 


WA TER-TIGHTNESS 


343 


permissible quantities in practice ranging from 5 to 15 per cent of the 
weight of the cement. Results of tests with different proportions are given 
in the paper mentioned.* * * § 

Lime paste made from a given weight of hydrated lime occupies about 
2 \ times the bulk of paste made from the same weight of Portland cement 
and is therefore very efficient in void filling. 

The strength of concrete has been found in some cases to be slightly 
reduced by the addition of hydrated lime, but not in a sufficient degree to 
influence its use in a water-tight wall, where the strength is seldom a deter¬ 
mining quality. 

The effect of the addition of lime upon the strength and density of mortar 
is discussed on page i54d. 

Unslaked lime must not be used under any circumstances. (See p. 156.) 

Puzzolan cement, unlike lime, tends to increase the strength even of neat 
cement and rich mortars,f in many cases 20% by weight of total dry ma¬ 
terials being beneficial if the Puzzolan cement is ground with the Portland. 
Undoubtedly the impermeability is similarly increased, since mixtures of 
Portland and Puzzolan cements have been found to well resist the action 
of sea-water. { 

In Japan in the Nagasaki Dock,§ concrete blocks were made in pro¬ 
portions 0.25 lime; 1 Puzzolana; 1 Portland cement; 4 sand; 8 gravel: 

Clay. Pure clay, finely powdered and free from any trace of vegetable 
matter, has been found to appreciably increase the water-tightness of con¬ 
crete, || especially of lean mixtures. In certain cases 5 per cent of clay 
to the weight of the sand has been found effective. The proportions should 
vary with the character of the aggregates. 

Clay acting as a colloid in combination with an electrolyte such as alum 
sulphate has been suggested by Mr. Richard L Gaines^[ for increasing 
water-tightness. Tests by him show a marked decrease in the flow of water 
due to these materials either added alone or in combination. 

Pulverized Rock. Mortars 1 : 3 and leaner, and concrete made with 
these proportions of cement and sand to the stone, are increased in strength,! 
and probably in impermeability, by the addition of rock pulverized as finely 
as the cement and equal to it in weight, although if the natural sand is very 

* “Permeability Tests of Concrete with Addition of Hydrated Lime,” by Sanford E. Thompson, 
American Society for Testing Materials, Vol. VIII, 1908, p. 500. 

•j-Feret’s Chimie Appliqeue, 1897, pp. 477 and 493. 

|See R. Feret, Chapter XVI. 

§ N. Shirrishi, Transactions American Society of Civil Engineers, Vol. LVI, 1906, p. 76. 

|| See paper on “Waterproofing Cement Structures,” by James L. Davis, Proceedings National 
Association of Cement Users, Vol. IV, 1908, p. 328. 

^ Transactions American Society Civil Engineers, Vol. LIX, 1907, p. 159. 


344 


A TREATISE ON CONCRETE 


fine or contains dust, the addition of tine material is not beneficial. 

Alum and Soap. A soap and alum mixture in various proportions 
sometimes is used to make what is called “waterproof mortar.” The 
Sylvester Process mixture employed in New York Harbor by Major W. L. 
Marshall! was made by “ taking one part cement and 2J parts sand and 
adding thereto f of a pound of pulverized alum (dry) to each cubic foot 
of sand, all of which was first mixed dry, then the proper amount of 
water—in which had been dissolved about f of a pound of soft soap to the 
gallon of water — was added, and the mixing thoroughly completed. The 
mixture is little inferior in strength to ordinary mortar of the same pro¬ 
portions and is impervious to water, and is also useful in preventing 
efflorescence.” 

The effect of alum and soap in diminishing the permeability has been 
experimented upon by Mr. Edward Cunningham§ and Prof. W. K. Hatt,§ 
and found useful for small structures. 

LAYERS OF WATERPROOF MATERIAL 

The use of cement plaster has already been described on page 419. 

Layers of waterproof paper or felt cemented together with asphalt or 
bitumen or tar are extensively used, — and sometimes asphalt alone, — to 
form an impervious layer. A mixture of alum and lye has also been tried. 

Paper or Felt Waterproofing. Layers of paper or felt with tar or asphalt 
between them are employed for a waterproof course in concrete floors, 
roofs, and walls of underground structures of large or long area, like tun¬ 
nels and subways, which require special protection from infiltration of 
water. The materials range from ordinary tarred paper, laid with coal 
tar pitch, to asbestos or asphalted felt, laid in asphalt. Coal tar products 
appear to be satisfactory when made to contain a large percentage of car¬ 
bon, and are being used by manv in preference to asphalt. 

In the New York Subway, portions of which are built below tide-water, 
much of the waterproofing consists of layers of felt laid in asphalt. The 
specifications,**approved by Mr. William Barclay Parsons, Chief Engineer, 
contain the following requirements for the materials: 

The asphalt used shall be the best grade of Bermudez, Alcatraz, or lake 
asphalt, of equal quality, and shall comply with the following requirements: 
The asphalt shall be a natural asphalt or a mixture of natural asphalts, cun- 

X Report Chief of Engineers, U. S. A., 1901,, p. 918. 

§ Transactions American Society of Civil Engineers, Vol. LI, pp. 127 and 128. 

** Contract No. 2, June, 1902, p. 107. 


W A TER-TIGHTNESS 


345 


taining in its refined state not less than ninety-five (95) per cent of natural bitu¬ 
men soluble in rectified carbon bisulphide or in chloroform. The remaining 
ingredients shall be such as not to exert an injurious effect on the work. Not 
less than two-thirds (§) of the total bitumen shall be soluble in petroleum 
naphtha of seventy (70) degrees Baume or in Acetone. The asphalt shall 
not lose more than four (4) per cent of its weight when maintained for ten 
(10) hours at a temperature of three hundred (300) degrees Fahrenheit. 

The use of coal tar, so-called artificial asphalts, or other products sus¬ 
ceptible to injury from the action of water, will not be permitted on any 
portion of the work, or in any mixtures to be used. 

The felt used for waterproofing shall be dipped in asphalt and weigh 
not less than fifteen (15) pounds to the square of one hundred (100) feet. 
All felt shall be subject to the inspection and approval of the engineer. 

With reference to the laying of the water-proofing the contract required:* 

Each layer of asphalt fluxed as directed by the engineer must completely 
and entirely cover the surface on which it is spread without cracks or 
blowholes. 

The felt must be rolled out into the asphalt while the latter is still hot, 
and pressed against it so as to insure its being completely stuck to the 
asphalt over its entire surface, great care being taken that all joints in the 
felt are well broken, and that the ends of the rolls of the bottom layer are 
carried up on the inside of the layers on the sides, and those of the roof 
down on the outside of the layers on the sides so as to secure a full lap of 
at least one (1) foot. Especial care must be taken with this detail. 

None but competent men, especially skilled in work of this kind, shall 
be employed to lay asphalt and felt. 

When the finishing layer of concrete is laid over or next to the water¬ 
proofing material, care must be taken not to break, tear, or injure in any 
way the outer surface of the asphalt. 

Any masonry that is found to leak at any time prior to the completion of 
this work shall be cut out and the leak stopped. 

Method of Laying Paper or Felt. The waterproof layer of a floor may 
be laid directly upon the ground if the soil is fairly dry and firm, but is 
usually spread upon a layer of concrete from 4 to 8 inches thick. In the 
former casef the first layer consists of strips with a 2 to 6-inch lap cemented 
with asphalt, and the remaining layers are mopped on. Upon a concrete 
base it is customary to first spread a layer of asphalt upon the concrete, 
although, if the concrete is damp, the bottom layer of paper or felt may be 
placed dry, as described above. 

The “ply” in waterproofing,—that is, the number of layers which cover 
all parts of the surface,—varies from 2-ply to 10-ply. It is considered better 
practice to “shingle” the strips than to place each ply or layer independently. 

* Contract No. 2, June, 1902, p. 107. 

f This method was followed in portions of the floor in the approaches to the East Boston Tunnel. 


346 


A TREATISE ON CONCRETE 


If the surface to be waterproofed is rough it may be leveled with cement 
mortar. It must be dry before applying the tar or asphalt. The asphalt 
is heated and brought, generally in buckets, to the work. Several rolls of 
paper are started consecutively. Ahead of each roll, as it is unrolled, the 
liquid asphalt is swabbed upon the concrete with a mop, so that the paper 
or felt is spread directly upon the fresh hot stuff. As soon as the first roll 
is started the second is placed to overlap the first, a width depending upon 
the number of ply to be laid. For example, if the felt is 32 inches wide and 
is laid 3-ply, the second roll is lapped upon the first about 22 inches. As 
this is unrolled (in the same general direction as the first roll) the surface 
ahead of it is mopped with asphalt, as described above. A third roll is 
immediately started, lapping both of the two others, and so on for the entire 
width of the surface to be covered. 

A waterproof course of this character always forms a distinct joint in the 
mass, thus destroying its cohesion upon that plane, and the strength of 
the concrete in bending on the two sides of the layer must be considered 
independently. 

Asphalt Waterproofing. Asphalt is sometimes laid as a waterproof 
course in one or more continuous sheets, and is also used for filling con¬ 
traction joints in concrete. 

In the sedimentation basin for the Albany (N. Y.) Filtration Plant* 
16 inches of clay and gravel puddle were covered with 6 inches of concrete 
laid in blocks 7 feet square, with ^-inch asphalt joints 3 inches deep, that 
is, extending halfway through the concrete. This proved to be a successful 
treatment. 

In the Astoria (Ore.) Water Worksf the bottom of the reservoir consisted 
of 6 inches of concrete in approximate proportions, one packed cement : 
0.7 sand : 3.5 fine gravel : 6.5 broken stone, covered with a f-inch finishing 
coat of 1 : 1 mortar, and upon this two layers of Alcatraz brand asphalt. 
The first layer was of natural liquid asphalt, and the second was the prod¬ 
uct of refining natural rock asphalt with about 20% of the liquid as a flux. 
Mr. Adams rfiade the rule that no asphalt should be placed until after 
the concrete had set at least two weeks, and was well dried out. All 
dust was carefully removed from the concrete, and the asphalt was applied 
with twine mops. The slopes of the reservoir were lined with brick laid in 
asphalt upon 6 inches of concrete. Under ordinary conditions such com¬ 
plete measures are unnecessary. 

In the construction of government fortifications by the United States 

♦Alien Hazen in Transactions American Society of Civil Engineers, Vol. XLIII, p. 258. 

■j" Arthur L. Adams in Transactions American Society of Civil Engineers, Vol. XXXVI, p. 29. 


W A TER-TIGHTNESS 


347 


Army Engineers, numerous methods of waterproofing have been used,* * * § in 
some cases an asphalt course being placed between two layers of concrete. 
Asphalt paint has been used for a protective coating where earth is to be 
deposited above or against it.f 

A 4-inch coating of asphalt applied hot with a mop upon a surface already 
covered with grout (see p. 339) has been satisfactorily used by Mr. J. W. 
Schaubf for coating the interior of tanks where the head is greater than 
10 feet. He considers this sufficient to withstand a water pressure of 60 
feet. 

Mr. SchaubJ also suggests the method of building the wall in two parts 
and filling the core or hollow space between with asphalt. 

CONSTRUCTION WITHOUT WATERPROOFING 

New York Subway Practice. Formerly asphalt waterproofing was 
required on the floors, walls and roof of the New York Subway, varying in 
thickness from 3 to 6-ply or else using two layers of waterproofing with 
one or more layers of brick dipped in asphalt. It was found, however, 
that the sections of subway waterproofed in this way were not so cool as 
other sections because the waterproofing prevented radiation of heat. Con¬ 
sequently, it was proposed to use the waterproofing below high water level 
but extending only 2 feet above it, except in special localities. The con¬ 
crete was to be reinforced longitudinally, as well as laterally, using a rich 
mixture, well spaded. This was further protected by a blind drain com¬ 
posed of broken stone 6 inches thick on the top of the subway and hollow 
die built against the walls.§ 

Philadelphia Subway Practice In all of the subway work it is the prac¬ 
tice to rely on the proper placing of the concrete for waterproofing except 
that on the roof a layer of asphalt i-inch thick is used. Longitudinal rein¬ 
forcement, generally to the amount of 0.3 per cent., is introduced to 
prevent cracking of the walls. || 

METHODS OF TESTING PERMEABILITY 

Permeability tests are somewhat difficult to make because of the many 
variables which must be provided for. In all cases it is advisable to meas¬ 
ure the water which has passed through the specimen and not the water 


* Report Chief of Engineers, U. S. A., 1901, pp. 911 to 925, and 1902, pp. 2451 to 2484. 

-j- Report Chief of Engineers, U. S. A., 1902, p. 2473. 

t Transactions American Society of Civil Engineers, Vol. LI, p. 123. 

§ Personal correspondence with Henry B. Seaman, Chief Engineer, 1909. 

|| Personal correspondence with Charles M. Mills, Principal Assistant Engineer, 1909. 


A TREATISE ON CONCRETE 


348 

lowing into it. Results of permeability tests are comparable only among 
the specimens of each individual series. The methods which have been 
successfully employed may be outlined as follows: 

Cementing a pipe upon the top of a block of concrete similar to the plan 
employed by the French Commission for mortar.* 

Incasing a block on all sides except the top and bottom and forcing the 
water through. 

Making thin discs and confining the water pressure to the center by 
means of gaskets. 

These three methods as they have been developed are illustrated in Figs. 
113, 114 and 115. 

In Fig. 113, an apparatus designed by one of the authors,f the pipe is 
enlarged to 4 inches diameter to give a good surface of concrete and permit 


^-20 

CHIPPED SURFACE 




* >r >yO .> v /~) " “ -^'4 v ’ „ ° p ,, • *' * "ry o " o " v ,. 

• .n'UIBDFTi'Sl'lHCira:' • j ‘ 3 REDUCING 


’ ''CHlF»pECi:sClRF/tCE\;>i;*„ , *«"* 0 < J 3 „RE 0 UCING | 

”0 ” “TX- n — , Car | - „ % COUPLING • | 1 ‘ 

mmm 


0 , • *_;«“»» -T •' 

"neATVCEMENT'. «?.•) 



cc 

X 

Ui 

u. 

UJ 

CC 

a. 

a 

< 

-1 z 
=> O 
O CC 

x — 

U »- 
UJ 
UJ UJ 

ai r 

. 7) 


3"hOLE THROUGH Aj|']/ 3 X I REDUCING COUPLING 

BOTTOM OF FORM CONNECTED WITH 

CITY PRESSURE 


O 

z 

o 

z 

CO 

D 



Fig. i i 3. Detail of Specimen for Testing Permeability.* (Sec p. 348.) 


thoroughly chipping it, while at the same time the external pipe connections 
are small, so that tight joints can be made readily. The walls of the mold 
may be coated with neat cement as well as the bottom, if desired, the con¬ 
crete being placed in any case before the neat cement has begun to stiffen. J 
The apparatus used at Jerome Park§ is a still better although some¬ 
what more expensive design which is capable of modification to suit the size 
of the specimen. The concrete specimens, which are described at length in 
the paper referred to, were made first and afterward coated with neat 


* See p. 128. 

J “Permeability Tests of Concrete with Addition of Hydrated Lime,’’ by Sanford E. Thompson, 
American Society for Testing Materials, Vol. VIII, p. 506. 

t For example of the method adopted in earlier experiments, see “Consistency of Concrete,'’ 
by Sanford E. Thompson, Proceedings American Society for Testing Materials, Vol. VI, 1907, 
P ' r4 

§ See “Laws of Proportioning Concrete,’’ by William B. Fuller and Sanford E. Thompson, 
Transactions American Society Civil Engineers, Vol. LIX, 1907, p. 67. 































WA TER- TIGHTNESS 


549 


cement by placing in a mold after thoroughly roughening and wetting the 
surfaces. (See Fig. 114.) 

Molding concrete in iron pipe is not satisfactory because the concrete 
shrinks in setting and there is consequently.danger of leakage. 

The method used in the St. Louis Structural Materials Laboratory* 
is illustrated in Fig. 115. This plan requires expensive castings and great 
care to make a water-tight joint at the rubber washers. 

In tests of permeability the apparatus must be designed so as to make 
all the water pass through the concrete; the surface of the specimen must 
be cut down to the pure interior 
concrete to prevent surface 
effects; the mix must be very 
uniform, the size of the specimen 
being proportioned to the maxi¬ 
mum size of the aggregate; suffi¬ 
cient water must b e used to 
produce uniformity, the consist¬ 
ency depending upon the purpose 
of the tests; a slight excess of 
sand rather than a deficiency 
must be used to prevent large 
voids; if neat cement is used as a 
coating, it must be molded with 
the concrete or else the surface of 
the concrete must be chipped 
rough and soaked with water 
before applying the cement paste, 
and it must be kept wet for some 
time; the specimen should be 
soaked for 24 hours before testing. 

LAWS OF PERMEABILITY 

The following conclusions have been reached with reference to the per¬ 
meability of concrete and mortar: 

(1) The permeability or flow of water through concrete is less as the 
’ percentage of cement is increased, and in very much larger inverse ratio.| 

(2) The permeability is less as the maximum size of the stone is greater. 
Concrete with maximum size stone of 2^-inch diameter is, in general, less 

* Bulletin No. 329, U. S. Geological Survey, 1908, by Richard L. Humphrey. 

-j- See foot-note p. 350. 




























35° 


A TREATISE ON CONCRETE 


permeable than that with i-inch maximum diameter stone, and this is 
less permeable than that with ^-inch stone.* 

(3) Concrete of cement, sand and gravel, is less permeable than concrete 
of cement, screenings and broken stone; that is, for equal permeability, a 
slightly smaller quantity of cement is required with rounded aggregates 
like gravel than with sharp aggregates like broken stone.* 

(4) Concrete of mixed broken stone, sand and cement, is more per¬ 
meable than concrete of gravel, sand and cement, and less permeable than 



Fig. i 15. Permeability Specimen used at St. Louis. {See p. 349.) 

similar concrete of broken stone, screenings and cement; that is, for water¬ 
tightness, less cement is required with rounded sand and gravel than with 
broken stone and screenings.* 

(5) Permeability decreases materially with age.* 

(6) Permeability increases nearly uniformly with the increase in pressure.* 

(7) Permeability increases as the thickness of the concrete decreases, but 
in a much larger inverse ratio.* 

(8) Of mortars containing the same percentage of cement but of variable 
granulometric composition, the most impermeable are those containing 

* “Laws of Proportioning Concrete,’’ by Fuller and Thompson, Transactions American Society 
Civil Engineers, Vol. LIX, 1907, p. 72. 








































































WA TER-TIGHTNESS 


35i 


equal parts of coarse grains, G, and fine grains, F (see p. 142), the latter 
including the cement. * 

(9) Decomposition by the passage of sea-water through mortars mixed 
in equal proportions by weight increases as the sand contains more fine 
grains * 

(10) Medium and fairly wet consistencies produce concrete much more 
water-tight than dry consistencies, and slightly more water-tight than very 
wet consistencies.f 

(11) The surface of concrete as molded is much more water-tight than 
the bottom of a specimen, because of the fine material which rises to the 
top.f 


RESULTS OF TESTS OF PERMEABILITY 

The table which follows gives the comparative permeability of concrete 
specimens 18 inches in length and 6 inches square, made up as shown in 
Fig. 114. The various qualities are referred to in paragraphs which 
follow: 

Effect of Shape of Stone Upon Permeability. In the table it is notice¬ 
able that the most permeable concrete is that composed of broken stone and 
screenings; the next,that containing broken stone and natural sand; and 
the most water-tight of all (comparing similar percentages of cement), the 
concrete of gravel and sand. The rounded gravel stone and sand evidently 
flow better and make a more homogeneous mix. It is noticeable also in 
the Jerome Park permeability tests that the results from the sand and gravel 
specimens were the most uniform. 

Effect of Percentage of Cement Upon Permeability. The table on 
the following page illustrates the very great increase in water-tightness with 
the richness of the mixture. The most extreme differences are noticed in 
the specimens with broken stone and screenings. 

Increase of Permeability With Pressure. A comparison of the columns 
in the table shows that the rate of flow increases nearly uniformly with the 
increase of pressure. 

Effect of Thickness of Concrete Upon Permeability. Other experi¬ 
ments, not here recorded, indicate that the rate of flow increases as the thick¬ 
ness of the concrete decreases, but in a much larger inverse ratio. Speci- 


* R. Feret in Annales de Ponts et Chaussees, 1892, II, p. 109. 

-j-“The Consistency of Concrete,” by Sanford E. Thompson, Proceedings American Society 
for Testing Materials, Vol. VI, 1906, p. 358. 


35 2 


A TREATISE ON CONCRETE 


mens 17 inches in length in proportions 1 : 6.5 by weight were practically 
water-tight, whereas specimens of half that length passed considerable 
water. 

Effect on Permeability of Percentage of Cement, Character of Aggregate and 

Pressure, 

By Fuller and Thompson* (Seep. 351.) 

Thickness of Specimens 18 inches. Area of contract 36 square inches. 
Maximum diameter of stone 2 \ inches. 


1 

1 

1 

O g K 3 
a 5 

KIND OF MATERIAL 

TIME IN 
WHICH 
WATER 
APPEARS 

AFTER 

RATE OF FLOW OF WATER IN 

PROPOR- 

TIONS BY 

Z s 5 Ph 

y a h w 

0 0 0 H 

GRAMS PER MINUTE, AT THE FOL¬ 
LOWING PRESSURES, PER 

• 

WEIGHT 

H V <3 

a 0 0 s 

a H 

Stone 

Sand 

STARTING 

PRESSURE 


bQUAKE INCH 



% 



min. 

20 lb. 

40 lb. 

CO lb. 

SO lb. 

i : ii.5 

8.0 

Crushed 

Screenings 

7 

25 

161 

2 37 

27 3 



stone 







1 : 9 

10.0 

U 

a 

U 

3 

11 

24 

37 

49 

[ : 7 

12.5 

u 

u 

u 

3 

15 

22 

3 ° 

38 

1 : 5.8 

J 5 • 0 

u 

a 

u 

5-5 

5 

8 

10 

12 

1 : 8.8 

10.2 

Crushed 

stone 

Sand 

9 

4 

I I 

T 7 

22 

1 16.9 

12.7 

(i 

U 

U . 

10 

2 

2 

3 

3 

1 : 5-5 

15.6 

u 

u 

u 


0 

0 

0 • 7 

1.4 

1 : 10.8 

8-5 

Gravel 

Sand 

3 

15 

25 

38 

43 

1 : 8.4 

1 10.6 

a 

« 

J 7 

1 

3 

5 

6 

t : 6.5 

13.0 

u 

“ 

100 

0 

O 

0 

o -5 

1 : 5-3 

| i5-9 

“ 

(( 

98 

0 

0 

0 

1.4 


Rate of Flow. The Jerome Park tests indicate that if the surface of 
the concrete is clean and the water pure, the flow is very nearly constant 
for a considerable period. During a four hours’ test there was no appre¬ 
ciable differences in the rate of flow. This result is somewhat contrary 
to other tests, but it is probable that in many cases the apparent plugging 
up of the pores is due to impurities in the water or to the early age of the 
concrete. 

Effect of Size of Stone Upon Permeability. The following table gives 
the comparative permeability of concrete in the same proportions mixed 
with stone of different maximum size. The difference in this case is evi¬ 
dently due to the greater density of the concrete composed of the large stone. 

* Transactions American Society Civil Engineers, Vol. LTX, 1907, p. 132. 




































WA TER-T1GHTNESS 


353 


Effect of Size of Stone on Permeability 
By Fuller and Thompson* ( See p. 352.) 

Thickness of Specimens 18. inches. Area of contact 36 square inches. 
Aggregates, crushed stone and natural sand. 


PROPORTIONS 

BY WEIGHT 

PERCENTAGE OF 
CEMENT TO 
TOTAL DRY 

MATERIAL 

MAXIMUM 
SIZE OF 

STONE 

TIME IN 

WHICH 

WATER 

APPEARS 

RATE OF FLOW OF WATER IN GRAMS 
PER MINUTE AT THE FOLLOWING 
PRESSURES PER SQ. IN. 


% 

in. 

min. 

20 lb. 

40 lb. 

eoib. 

80 lb. 

I : 2.9 : 5.7 

10.2 

2 \ 

7 

I 

4 

8 

1 2 

1 : 2.9 : 5.7 

10.2 

I 

26 

0 

5 

10 

15 

1 : 2.9 : 5.7 

10.2 

1 

2 

29 

0 

10 


20 


Effect of Coarseness of Sand Upon Permeability. As stated, tests by 
Mr. Feret have indicated that for maximum watertightness more fine sand 
is required than for maximum strength. This is borne out by tests by one 
of the authors, the results of which are given in the following table. The 
tests were made in connection with the preparation of specifications for 
the Waltham Reservoir.f 

Tests to determine Relative Permeability of Concrete with Coarse and Fine 

Bank Sand 

By Sanford E. Thompson. (See p. 353.) 

Proportions 1 : 3 : 6 by Volume or 1 : 2.8 : 5.7 by Weight. Age 32 days 


CHARACTER OF SAND 

DENSITY 

c + s + g 

WATER PASSING IN 

GRAMS PER MINUTE 

(1) All coarse. . .. 

0 .853 

14 5 • 1 

(2) coarse, l fine. 

0.846 

10.4 

(3) | coarse, h fine . 

0.843 

43 • 0 

(4) All fine . 

o . 8 1 3 

•30.2 


Analyses of Natural Bank Sand and Screened Gravel used in 7 ests 


SIEVE 

TOTAL PER CENT PASSING SIEVES 

Coarse Sand 

Fine Sand 

Screened Gravel 


% 

% 

% 

i inch.. 



I 00 

b inch. 



5 ° 

\ inch. 

1 00 


0 

No. 5 . 

88 



No. 12 . 

77 

IOO 


No. 40. 

3 2 

96 


No. 200..... 

7 

0 

27 



♦Transactions American Society of Civil Engineers, Vol. LIX, 1907, p. 136. 
jSee p. 701 , 




























































354 


A TREATISE ON CONCRETE 


CHAPTER XX 

STRENGTH OF PLAIN CONCRETE 

The strength of plain concrete, that is, of concrete without steel rein¬ 
forcement, is governed primarily by 

(1) The quality of the cement. 

(2) The texture of the aggregate.* 

(3) The quantity of cement in a unit volume of concrete. 

(4) The densityf of the concrete. 

The percentage of cement and the density of the concrete, which are of 
special importance to the user in determining the proportions of materials, 
may be expressed more explicitly as follows: 

(1) With the same aggregate the strongest concrete is that containing 
the largest percentage of cement in a given volume of concrete, the strength 
varying nearly in proportion to this percentage. 

(2) With the same percentage of cement but different arrangement of 
the aggregates, the strongest concrete is usually that in which the ag¬ 
gregate is proportioned so as to give a concrete of the greatest density, 
that is with the smallest percentage of voids. In many cases relative 
densities nearly correspond to relative weights. 

Although these laws have been long recognized in a general way, having 
been partially proved by experiments of Mr. John Grant as early as 1871, 
but few attempts have been made to apply them practically in the com¬ 
parison of strengths of different mixtures of concrete. 

The authors have evolved a formula (see p. 356) from which, knowing 
the exact quantities of the raw materials entering into a concrete of a 
certain strength, it is possible to estimate the approximate strength of any 
other concrete mixed in different proportions of the same materials, under 
similar conditions of manufacture, storage, age, and methods of testing. 

The compressive fiber strength of concrete, which is an essential factor 
in the design of reinforced concrete, is proportional to the strength of 
concrete in direct compression. 

The table of tests of beams on page 376 covers so wide a range of 
proportions that it may be employed for comparing the transverse 
strength of different mixtures. 

*The word aggregate is defined on page i. 

fThe meaning of density is illustrated on pages 172 and 173. 


STRENGTH OF PLAIN CONCRETE 


355 


further information relating to the strength of concrete made from 
different materials and under various conditions is presented under sep¬ 
arate headings in this chapter. The methods of making concrete speci¬ 
mens for testing are outlined on page 395. 

COMPRESSIVE STRENGTH OF CONCRETE 

The actual strength of concrete in compression, because of the limited 
capacity of testing machines, can be determined only by experiments upon 
comparatively small specimens from 4 to 12 inches square. The results 
from tests of such specimens are probably slightly lower than the actual 
strength of concrete in practice, carefully mixed and laid, because of the 
difficulty in obtaining homogeneous specimens. Experiments by the 
authors show that the strength of the same mixture tends to increase with 
the size of the specimen even if the relative dimensions remain constant. 
Of course carelessness or inexperience will produce irregular work in 
either actual or experimental construction. 

The experimental strength of concrete is not always a criterion for 
fixing the proportions of mixture, in fact most concrete must be made 
stronger than the theoretical loading would require. A lean concrete, for 
example, although it may gain sufficient strength before the load is applied, 
may not be sufficiently strong at a short period to permit the removal of 
the molds or the ordinary wear during building, or for many purposes the 
lean concrete may be too porous. Often a lean Portland cement con¬ 
crete may thus present no special advantage over a richer natural 
cement concrete. (See Chapter IV.) 

Comparative Strength of Concretes of Different Proportions. The 
formula for strength of mortar derived by Mr. R. Feret and presented on 
page 141, as Mr. Feret himself states,* is not applicable to concrete. 
Our formula for concrete mixtures is therefore presented as a practical 
working formula of sufficient accuracy to compare the compressive strength 
of mixtures of the same materials in different proportions. Starting with 
the principles laid down in the two fundamental laws stated at the com¬ 
mencement of the chapter, it is evolved by trial by the method given on 
page 357, to fit the average results of a large number of tests made in this 
country and Europe. 

Let 

P = unit compressive strength of concrete. 
c = absolute volumef of cement in a unit volume of concrete. 

*Chimie Appliquee, p. 522. 

•^Method of determining densities and absolute volumes are described on page 135. 


35 ^ 


A TREATISE ON CONCRETE 


s = absolute volume of sand in a unit volume of concrete. 
g = absolute volume of stone in a unit volume of concrete. 

M = a coefficient, constant for all proportions of the same material mixed 
and stored under similar conditions, but varying with the texture of 
the coarse aggregate and the age of the specimen. 


Then 



(i) 


The absolute volumes, as indicated on page 138, are really ratios of the 
actual volume of the concrete, representing the actual mass or total volume 
of solid particles in a unit volume of concrete. Since ratios are indepen¬ 
dent of the unit selected, the absolute units are the same for any system of 
measurement, and by changing the value of M the formula is adapted to 
English or Metric System. For example, if P expressed in terms of kilos 
grams per square centimeter requires a value of M = 880, P in pounds 
per square inch will require a value of M = 880 X 14.2* =12 500. It 
follows that knowing for a given age the value of M and the strength of a 
concrete composed of known percentages of materials, it is possible to 
estimate the compressive strength at the same age of any other concrete 
of exactly known composition made under like conditions from similar 
materials, but differently proportioned. 

A very slight variation in the values of the terms will so largely influence 
the result that the formula is only useful, on the one hand, where the 
specific gravities of the materials and the weights entering into a unit 
volume of concrete are determined so accurately that the absolute volumes 
can be calculated, and, on the other hand, for comparison of the strength 
of different mixtures of concrete under assumed average conditions. For 
the latter purpose the specific gravity of cement may be taken at 3.1 and 
of sand at 2.65, the weight of a barrel of cement as 376 pounds, the weight 
of the dry sand contained in a cubic foot of moist sand as 89 pounds and 
the percentage of voids in the stone as 46%. In computations, values of 
absolute volumes must be carried to three places of decimals. 

Now let 

P' = compressive strength in pounds per square inch. 
c b = barrels of cement contained in a cubic yard of the concrete. 
s c — cubic yards of sand contained in a cubic yard of concrete. 
g c = cubic yards of stone contained in a cubic yard of concrete. 

M' = a coefficient adapted to pounds per square inch. 



STRENGTH OF PLAIN CONCRETE 


35 7 


Then assuming solid cement with no voids to weigh 193 lb. per cu. ft. 
and the solid particles of sand 165 lb. per cu. ft. formula (1) becomes, 


P' = M' 


37 ^ 

I 93 


376 

27+ —‘ft — 27 

l 9 3 




8 _9 

65 


+ ° 54g, 


) 


O.I 


P f = M' 


13-85 + c t — 7.48 (s c + g e ) 


O.I 



This formula, as stated above, is only adapted for average comparative 
determinations, or where the conditions exactly correspond to those as¬ 
sumed. It may be adapted to other sand and stone by altering the co¬ 
efficients of s c and g c . The table on page 360 is based upon these 
formulas (1) and (2). 

Formula (1) on page 356 is based upon the actual strength of concrete, 
as determined bv tests of Mr. E. Candlot in France and those of several 

j 

other authorities at the Watertown Arsenal, U. S. A. To illustrate its 



Fig. 116.— Comparison of Authors’ Formula with Tests of E. Candlot. (See p. 358.] 































































































































































































































































































































358 


A TREATISE ON CONCRETE 


agreement with actual experiments, tests of Mr. Candlot upon broken 
stone and gravel concrete 28 days old, quoted in full on page 367, are 
plotted on the diagram, Fig.116, page 357, and Mr. George A. Kimball’s 
tests made at the Watertown Arsenal on specimens 6 months old in 

Fig.ii7- 

The accuracy of the formula is shown by the nearness of the points on 



Fig. i i 7. —Comparison of Authors’ Formula with Tests of George A. Kimball. 

(See £.358.) 


each diagram to straight lines starting from the origin. The abscissa of 
each point is determined by calculation of the term in brackets in formula 
(1), and the ordinate is the actual breaking strength of the specimen at the 
given period. The value of M in each case is the tangent of the straight 
line drawn through the points. If Mr. Candlot’s tests are plotted on 
cross-section paper and smooth curves of growth in strength drawn througn 






























































































































































































































































































































































































































































































STRENGTH OF PLAIN CONCRETE 


359 


them, it will be found that the new values taken from such curves, which 
partially eliminate inequalities in the breaking, approach even more nearly 
to the straight lines. 

After a study of the strength of concrete at different periods, the authors 
suggest the following values for M at different ages. The values for 
broken stone concrete are based upon stone ranging in size from 2 to 2\ 
inch down to J to J inch. For broken stone of finer size the values will 
be slightly lower. The composition of the concrete does not affect the 
value of M, since the term of the formula in large brackets is itself 
dependent upon the proportions of the mixture and the density of the 
concrete. The values of M are directly proportional to relative strengths 
at different ages. 

Value of Coefficient M for Compressive Strength in Pounds per Square Inch. 

Coefficient M Ratio of growth 


for broken based on age 

Age. stone concrete at one month 

7 days. 9 5 00 0.76 

1 month . 12 500 1.00 

3 months ... 15600 1.25 

6 months . 16900 1.35 

1 year. 18 000 1.44 


The ratios, which are taken from the curve on page 375, are based on 
the assumption that growth in strength of concrete, mixed under similar 
conditions and of similar consistency, is the same for all proportions of 
like materials. This, as stated on page 374, is not strictly true, but is 
sufficiently accurate for practical purposes. 

Table of Compressive Strength. The strength of concrete mixed in 
various proportions, given in the table on page 360, is based upon a strength 
with proportions 1:3:6, that is, one barrel cement to 11.4 cubic feet sand 
to 22.8 cubic feet stone, of 1950 lb. per square inch at the age of one month, 
this value being selected as the average of tests by different experimenters. 
It corresponds to a value of M of 12 500. Using 1950 lb. per square inch 
for 1:3:6 as the starting point, the strengths for other mixtures are cal¬ 
culated from formula (1) page 356, the absolute units for the different 
proportions being deduced from the average quantities of cement, sand, 

and stone, contained in a unit volume of concrete. The values em¬ 
ployed are similar to those in the table on page 231, except that it was 

necessary to carry them to three places of decimals. The strength at 

the age of six months is based on the growth in strength given on the 
curve on page 375. The assumption, which corresponds to average con¬ 
ditions, is made that a cubic foot of moist bank sand contains 89 lb. of 







A TREATISE ON CONCRETE 


360 

dry grains having a specific gravity of 2.65, and that the specific gravity of 
the cement is 3.1. The stone is assumed equal in quality to sound, hard 
limestone, ranging in size from £ inch to 2 inches. Stone of ^ inch maxi¬ 
mum size may give strength about 20% lower. Specimens mixed of very 
wet consistency show lower strength especially at early periods. Cold 
weather retards strength. Prisms test lower than cubes. 

The values in the table may be readily transformed to safe working 
strength by dividing by the proper factor of safety. 


Relative Compressive Strength of Portland Cement Concrete of Different Pro- 

% portions. 

Based on Cube Specimens and Medium Consistency. 

(See important foot-notes, also p. 359.) 


Proportions. 


Age, one month. 


Age, six months. 


Voids in Broken Stone or Gravel. 


Voids in Broken Stone or Gravel. 





*50 % 

t 45 % 

t40% 

§30% 

§20% 

*50% 

145 % 

t40% 

§30% 

§20% 

<v 

*■6 

q3 

lb. per 

lb. per 

lb. per 

lb. per 

lb. per 

lb. per 

lb per 

lb. per 

lb. per 

lb. per 

c 

<D 

c 

0 

sq. in. 

sq. in. 

sq. in. 

sq. in. 

sq. in. 

sq. in. 

sq. in. 

sq. in. 

sq. in. 

sq. in 

U 

CO 

CO 











1 

1 ft 

2 

2880 

2860 

2840 

2800 

2760 

3890 

3870 

I 

3 8 40 

3780 

3730 

1 

I* * 

3 

2780 

2750 

2720 

2670 

2610 

3750 

3710 

3680 

3600 

3530 

1 

i£ 

4 

2680 

2650 

2610 

2540 

2460 

3620 

3570 

3520 

343 ° 

333 ° 

I 

2 

3 

2560 

2540 

2510 

2460 

2410 

3460 

3420 

3390 

3320 

3250 

1 

2 

4 

2480 

2440 

2410 

235 ° 

2290 

3340 

3300 

3 2 5 ° 

3 I 7 ° 

3090 

1 

2 

5 

24OC 

2350 

2310 

2230 

2170 

3230 

3180 

3120 

3 OI ° 

2930 

1 

2 

6 

2320 

2260 

2230 

2140 

2060 

3130 

3060 

3 OI ° 

2890 

2780 

1 

2 i 

3 

2370 

2340 

2320 

2270 

2230 

3200 

3160 

3130 

3 ° 7 ° 

3020 

1 

4 

4 

2290 

2260 

2230 

2180 

2IIO 

3090 

3050 

3 OI ° 

2940 

2850 

1 

2 \ 

5 

2210 

2180 

213° 

2070 

2000 

2980 

2940 

2880 

2790 

2700 

1 

2 h 

6 

2140 

2100 

2060 

1980 

I9IO 

2890 

2830 

O 

00 

C 4 

2670 

2570 

1 

3 

4 

2120 

2090 

2060 

2020 

1970 

2860 

2830 

O 

OO 

C 4 

2720 

2660 

1 

3 

5 

2060 

2030 

1990 

T 93 ° 

1870 

2780 

2740 

2690 

2610 

2 53 ° 

1 

3 

6 

I99O 

1950 

1910 

1840 

1770 

2680 

2630 

2580 

2480 

2390 

1 

3 

8 

i860 

1810 

1770 

1680 

1600 

2510 

2440 

2390 

2280 

2160 

1 

4 

6 

I7TO 

1680 

1650 

1590 

1530 

2310 

2270 

2220 

2140 

2070 

1 

4 

7 

1 660 

1620 

1590 

I 53 ° 

1460 

2240 

2190 

2150 

2060 

1980 

1 

4 

8 

l6lO 

1570 

1530 

1460 

1400 

2170 

2120 

2070 

1970 

1880 

1 

4 

10 

1510 

1460 

1420 

1340 

12 60 

2040 

1980 

1920 

1810 

1700 

1 

5 

10 

131° 

1270 

1230 

1160 

IO9O 

1770 

1720 

1660 

1570 

1470 

1 

6 

12 

1060 

1020 

980 

910 

840 

1430 

1380 

1320 

1230 

1140 


Note.— Proportions are based on a barrel of 3.8 cu. ft. Values are for average ultimate strength 
which must be divided by a factor of safety for working loads. Quality of materials and methods of 
mixing may affect the strength by 25% in either direction, while the relative values for different propor¬ 
tions are not materially changed. 

*Use 50% columns for broken stone screened to uniform size. 

tUse 45% columns for average conditions and for broken stone with dust screened out. 

tUse 40% columns for gravel or mixed stone and gravel. 

§Use these columns for graded mixtures. 


\ 











































STRENGTH OF PLAIN CONCRETE 


361 


In the table the stone with the smaller percentage of voids gives the lower 
strength. This is due to the proportioning by volume. To illustrate, a 
cubic foot of stone measured loose with 40% voids contains more solid 
material than stone with 50% voids, and hence makes a greater bulk 
of concrete with the same proportions by volume. This is further illus¬ 
trated in the table on page 234. Consequently, there is less cement in a 
unit volume of the concrete when the stone has 40 per cent voids; and while 
the density is slightly greater, it is not enough greater to counterbalance 
the decrease in the percentage of cement. If the proportions had been 
altered so as to use less sand with the stone having 40 per cent voids, the 
concrete would have been stronger, with the same amount of cement per 
cubic yard of concrete, because of the greater density. 

From this it must not be inferred that the aggregate with the largest 
percentage of voids is best to use. As indicated above, it requires more 
cement to a given volume of concrete, and the concrete is apt to be slightly 
less dense than with an aggregate having fewer voids, so that the latter is 
usually the more economical even although it is sometimes slightly inferior 
in strength. In the example in the preceding paragraph, with Portland 
cement at $2 per barrel, the concrete with stone having 50% voids would 
require o. 11 bbl. more cement per cubic yard than the concrete with stone hav¬ 
ing 40' 7 0 voids, and would therefore cost 22 cents higher per cubic yard. 

The following table is presented to indicate in round numbers the probable 


Approximate Average Crushing Strength of Concrete 



MEDIUM CONSISTENCY. 

WET CONSISTENCY. 


Cubes. 

Cubes. 

8 by 16 inch Cylinders 

PROPORTIONS 







BY VOLUME. 




• 




30 days. 

6 mos. 

30 days. 

6 mos. 

30 days. 

6 mos. 


lb. per sq. 

lb. per sq. 

lb. persq. 

lb. per sq. 

lb. persq. 

lb. per sq. 


in. 

in. 

in. 

in. 

in. 

in. 

i : 14.'3 

2800 

3700 

2600 

4100 

2300 

3600 

1:2 : 4 

2 300 

3300 

1900 

3 1 00 

1700 

2700 

1 : 2 A : 5 

2200 

2900 

1700 

2700 

I 5 °° 

2400 

1:3 : 6 

1900 

2600 

1500 

2400 

1300 

2 100 

1:4 : 8 

1500 

2IOO 

IOOO 

1600 

900 

1400 


Proportions are based on the unit measure of one barrel (4 bags) cement assumed as 3.8cu.ft. 
The first column of strength values is taken from the table on the opposite page; the cylinders 
at one month are arranged as averages of a large number of tests in various laboratories made 
during the years 1904 to 1908; the ratio of strength of cubes to cylinders is based upon the St. 
Louis tests (p. 370) and the growth of strength of wet consistency upon tests by the authors (p. 
384). The ultimate strength of long columns is probably from 90 to 95 per cent of the strength 
of cylinders (p. 370.) 























3 62 


A TREATISE ON CONCRETE 


strength of different mixtures of concrete under working conditions. As 
stated on the opposite page, so many conditions affect the strength that 
such data can be presented only as extremely rough approximations. 

Variation in Weight of Concrete of Different Proportions. The weights 
of specimens of similar concrete are of interest in comparing the relative 
strength of different mixtures or of different specimens of the same mixture. 
Of twelve pairs of duplicate cubes which the authors had tested in 1903 
at the Watertown Arsenal and the Massachusetts Institute of Technology, 
the heavier specimen, except in one case, was found to be the stronger. 

The following table of tests selected from tests of concrete and mortar 
cubes made by Mr. James E. Howard* at the Watertown Arsenal illus- 


Weights of Portland Cement Concrete of Different Proportions. 


Age four months. Watertown Arsenal. . {See p. 362.) 


s 

<v 

HH 

PROPORTIONS BY 
VOLUME 

Weight 
per 
cu. ft. 

lb. 

Compressive 
strength 
per sq. in. 

lb. 

s 

0) 

hH 

PROPORTIONS BY 

VOLUME 

Weight 
per 
cu. ft. 

lb. 

Compressive 
strength 
per sq. in. 

lb. 

g 

<D 

S 

a> 

CJ 

T3 

g 

cj 

in 

d d— 

8 g 

0 2 

4 -> 

G 
a j 

B 

q; 

O 

G 

<5 

in 

£2 

33 CO 

1 

1 

1 

0 

136.5 

437° 

11 

1 

5 

IO 

140.2 

797 

2 

1 

2 

0 

134.2 

2506 

12 

1 

6 

12 

1 3 8 " 2 

73 8 

3 

1 

3 

0 

I33- 8 

1812 







4 

1 

4 

0 

120.9 

830 

x 3 

1 

2 

2 

140.3 

1768 

5 

1 

5 

0 

II9-3 

532 

14 

1 

2 

3 

145.2 

1911 

6 

t 

6 

0 

116.9 

169 

i5 

1 

2 

4 

149.1 

2147 

7 

1 

7 

0 

ni-5 

118 

16 

1 

2 

5 

150.9 

2452 







17 

1 

2 

6 

I 5 I .2 

2124 

8 

1 

2 

4 

150.7 

2178 

18 

1 

2 

7 

146.4 

1650 

9 

1 

3 

6 

146.9 

1815 

19 

1 

2 

8 

142.4 

I2 95 

10 

T 

4 

8 

. 143-2 

ii 35 








trates the comparative variation in weight and strength of concrete mixed 
in varying proportions: 

Compressive Tests of Plain Concrete. The tests on pages 363, 367, 
and 366 (Fig.119), are selected from among the best series of concrete 
experiments on record in America and Europe, so that the reader may 
form a general idea of the results obtained by expert experimenters. For 
practical comparisons of strength of different mixtures, reference should 
be made to the more complete table on page 360. The variation in 
strength of concretes mixed in the same proportions is due not only to the 
difference in the materials, but also to the different methods of making 
the tests, and to the fact that in many cases the unit of measurement 

*Tests of Metals, U. S. A., 1899, pp. 788-795. 

("Items (8) to (12), 2^ inch screened broken trap, and items (15) to (19), ij inch screened 
broken trap. 











































Strength oj Concrete in Compression from Various Authorities. Age, one month. 

In pounds per square inch. (See p. 362) 


21:9:1 


H 

s 

o 

a 

H 

L> 

< 


363 


8 

8 . 

nU 

■V* 

v. 

fti 


C c — 

O- cD 

c /5 ti d 

'“'kt ^ 
^ c bL lt. 

■s'sl^g 

^ C c O c >, 2 rt 

3 o >» • rtK?> 

rHcicon'ioot'-ooc'-'—■ 


X 

& 

I- 

i 4 
>» , 


<L> 


>. o Jr; 


g 


r **»» 
V^J <0 

o s: 

co 

« 

£ 


c 

o 

in 

=y 

o 

X 


"8 -vj 
$ 8 
« 5 £ 
£ 5 

(jl 

a 

"8 £ 
CJ 


ra 

C 

9 S 

H 

< 


o'» 
t, >' 

<U-ft 
ti 13 

CD fli 
CO ^ 


01: S: 1 

• • 1 

• « • 

O • • • 
to • • • 

• 1 • 1 


-i—7— 


• • * 

co • • • 

• • • • 




• « • 

Mill 

• • • • 




• O • 

0 • • • 




g: r:i 

. 10 • 

Mill 




• n • 

fs • • • 

• ••• 




• rt i 

Mill 

• • • 1 



S:^: 1 

• • • 

• • • 

• O • 

• • O' • 

• ♦ • • 


; • 


• « « 

* • CN • 

• It! 





• . M . 

• ♦ I I 



£:t-: 1 


• O • • 

• IO • • 

• • 1 ♦ 

• ♦ I 1 





• CO • • 

• •• 

• • I • 

• • I I 



\L\ f: 1 


• ••• 

• • • • 

• • 1 • 

C' 

“~o ~~ 

• 10 





O' 

• 

9: C: 1 

LT. O O 

O • TT 

• . co 



CN 0 « 

Ov * • O 

• • • \£< 




^ OvO 

On • • n 

• • • fs 


• to 


M M H 

n • » CN 

• • . M 


S:£:i 

* • • 

• • • 

• . 0 • 

• • \£j • 

• CO CN • 

• CN Tf . 




• 1 • 

• • O * 

. \Q 0 • 





• • .-1 • 

• i-i CN • 



r ; r:i 

• • • 

• t « 

• O • • 

• CN • • 

• • ♦ • 




• • • 

• O' • • 

• ♦ • ♦ 

♦ ♦ • • 



£:f:i 


• 0 • • 

• CN • 1 

• ♦ • ♦ 

♦ • • 1 




r 1 1 

• rj- . • 

• ♦ • ♦ 




< • • 

• M • • 

• • • • 



zS-. 1 

• » • 

• • • 

• O • • 

• fs • • 

• • • • 

• • • • 


—J~ 


* • « 

• to • • 

• • • ♦ 




• • • 

• Mil 

♦ • • ♦ 



S:f s: 1 

• • 1 

• 1 * 

• • • • 

• • • • 

to • • • 

to » • • 




• • • 

• • • 1 

CN • • • 


/ • 

_ 

• • • 

• ••• 

CO • • 



L:z: 1 

• it 

• • • • 

• • • 1 

• • • • 

• ♦ ♦ § 





• ill 

• ••• 


: : 


• O • 

• • O • 

• • • • 


O' 0 

b'.Z'.l 

• O • 

• • <0 • 

• ♦ • • 


vO to 


• XT' • 

• • *3" • 

• • ♦ • 


r- 


• C'J • 

• • CN • 

♦ ••• 




• O • 

O • • On 

• •• 


Tf O 

f: z: 1 

• O • 

0 ■ ■ O' 

« • • • 


O O 


• QG • 

to • • CO 

• • ♦ ♦ 


0 0 


• CN • 

CN • • CN 

••♦• 


H 



• O O • 

• I 1 1 


OO • 

i.: 2:1 


• O • 

• ♦ I • 


O • 


• •• 

• toco • 

• I I i 


0 ■ 


• • 1 

• H CN • 

• t • • 


1-. • 


• • • 

• O 

• • • I 

• 


2: 1 

• • • 

• vO • • 


• 



• • • 

• O • • 


• 


_ 

• • • 

• CN • • 


t 


1:1 

• • 1 

• • • 

• • • • 

• • • • 


O' 



• • • • 


TT 



• • • 

• • • • 

• • i • 

»-l 


£llll 

• • • 


• • t>. . 


vO • 

• • • 

• • • • 

1 1 H 1 


vO • 


• • • 

• • • • 

• • O' • 


• 


• • • 

• • • • 

♦ • • 


w • 

S : 0: i 

• • • 

• • O • 

• • O • 

till 

1 I 1 I 





• • O • 

♦ III 





i . I-H . 

i • • • 





• • • vO 




2 : 0:1 


• • • Tj- 





• • • 

• • • CO 



• • 


• • « 

• • • co 



• • 


• • • 

• 0 • • 



• • 

t 7 :1 


• CO • • 





• • • 

• vO • • 


• 



• •• 

• M • • 


• 



• • • 

• O • • 

♦ t • • 

• 


£ :i 


• \C • • 

• • I • 

• 





1 • I • 

• 




• CN • • 

• • I I 

• 



• • • 

• O • • 

• 1 • • 

• 


z : 1 

• • • 

• • 

• O • • 

• CN • • 


• 

• 

• • 

• • 



♦ co * • 


• 

• • 


• • • 

♦ O • • 

t I 0 • 

• 


1:1 

• • • 

• \0 • • 

♦ • 0 • 

• 



• • • 

• 10 • • 

• ♦ tJ" • 

• 



• • • 

♦ CO • • 

• ♦ Tj- • 




• • • 

♦ O'* 

♦ »o* 



0:1 

• • • 

• to t t 

• co • • 

• •O' 

. .10 • 

• 

• 




• Tj’ 1 • 

• • to • 

• 



. * 

• M • 

• • ♦ • 

• • • • 

• 

• 

• 

6 

• M , 


• • • • 

• 

• »H 

«-M OJ 

. * . 

• ■ 1 • 

• • • • 


' X 

0 s 


• • • • 

• • • « 



4) • PC 

* HCN * 




* h|CN 

SJ 0 

• CO • 




• CO 

• —4 d2 

m 0. 

; * ; 

ill' 

♦ • • • 


• 

; x 

m 

^ ^ ^ 

, *. J. ^ 

i i ^ 


^ v. 

vO COO 

• CO ’-f <N 

CN CN CN vO 

<N 

<N rt|N 



M 

M M M 

w 

w co 


O 
»o 

VO M 

• 1—( 

• • rv COO 

foo ^ o 

o a - a 

O'GO CO M 

I-I M O 

co r 

—I —I M G 
Cj cD c 
CC rg 
<u <u r 

C n Jj < r~* . 

in >h . <* 


to 


o 

a 


& 

<u 

in 

c/T 

_0 j 

o 

O' o 

"S-w 

• M 

ft a -S 

^ - t-. 

-00 OJ 

M Q\ O 

O 00 c 

-Tt 


~0 

a 

c 

<u 

<u 


cD 

J-. 

-*—• 

C 

OJ 

2, - 


ft£ 

S o 

Jb’o 

c 


cc 

tic. 


:y 


o 

O - <L> . ’ft 

EJS’O of w rt 
O iSiS'rt mo 


cD cD 


<u _3 

—< 

< Pi 


D o S 


cD cD O cD Q o 1 

w w (/) t/) w w 

-*-• w -*->-*_»-*-> -*-» 

C/0 C/0 t/i C/3 C/0 C/5 

OJ GJ OJ OJ OJ OJ 

hhHhHh 1 

CO 05 O f-i CN CO ■ 


<u 

0 

O 

4-J 

co 

OJ 

-+-* 

cD 

u 

<u 

s 

o 


Mil 

m gr 

Sc 3 m 

c O 
c . w 

^ % 


VO 

10 


tOH-1 

*tP 

M > 

80 

s> 

c/T 

r t-< 

4-» cu 

a v 
o c 
^•bi 
. ‘n’rS 

tA„« W 

to. op 

ft oO 
o* bo 0 

g.s h 1 

m fe.i 

- d> o 

a o. 

<u*Sb^t 

gec 

^ cD 
CJ 


.2 

*3 




n Q 

C c. 


OJ 

fee o 

OJ jD 

*H L> 

OJ ^ 
_ > OJ 

S§^s 


c 

o 


o 

■'fr 


M 6 §J 


' • w 

, ft ft 

_l c c< 


- C‘C 
®o» 
^'"6 

O V) 
tuO C/2 CJ 

c ^ o 

"C ■> ’w 

O_. cj 

rt 

.£ c 2 

m £ § 

fi 5 ^ 

W^H 

rt N CO 


c 0; 4; 

-'pace 


-CO 


C P C t/) 

0 0 4 )—; 

x £ E 5 

OJ OJ OJ ^ 

H-iNNlg 

aiTtun 
')_ C C O 
K-J2J2 oi 

OJ t >-< C/) 

O o c <*■> 
h-JPnPuH 
»r 0 (D N 











































































































































.364 


A TREATISE ON CONCRETE 


used in proportioning is indefinite, and, as discussed on page 218, similar 
nominal proportions may apply to quite different actual mixtures. Not¬ 
withstanding these opportunities for variation, however, it is noticeable 
that the results reached by different parties really show less percentage 



Fig.i 18. Twelve-inch Concrete Cube after Crushing in Emery Testing Machine at 

Watertown Arsenal. (See p. 3 6c;.) 


variation than is expected in the tensile tests of neat cements and sand 
mortars in different laboratories even with the same brand of cement. 

In the table on page 363 of data from various authorities, only tests at 
the age of one month are recorded. Strength of the specimens at longer 



STRENGTH OF PLAIN CONCRETE 365 

and shorter periods may be estimated by referring to the curve in Fig. 122, 
Page 375- 

The appearance of a concrete cube after crushing showing the manner 
in which the sides flake off, leaving a double pyramid, and the shearing 
of the particles of stone, is illustrated in Fig.118. The specimen is one 
of a series tested for the authors at the Watertown Arsenal, U. S. A. 

Kimball’s Tests. A series of experiments upon 12-inch cubes made by 
Mr. George A. Kimball,* Chief Engineer of the Boston Elevated Railway 
Company, and tested at the Watertown Arsenal, although included in the 
above table, covers so wide a range in time and proportions that more 
complete values are worth quoting and are presented in the curves on 
page 366. Mr. Kimball also determined the elastic properties of these 
specimens, and tested some of the specimens with a concentrated load, 
as referred to on page 368. He states that the stone used was conglom¬ 
erate from Roxbury, Mass., containing 49.5 per cent, voids. Its analysis 
was as follows: 


Passing 2^-inch ring . 100.0% 

“ 2-inch “ . 95.2% 

“ 1-inch “ . 18.5% 

“ 2-inch “ 0.5% 


The sand and cement were made into a mortar of about the consistency 
of damp sand, and then spread upon the stone, which previously had been 
drenched with water. After ramming with iron rammers and tamping 
bars, the water barely flushed to the surface of the 1:0: 2 and 1:2:4 mix¬ 
ture, while the surface of the 1:3:6 and the 1: 6: 12 mixtures appeared 
merely moist, so that the concrete was what ordinarily would be termed 
dry. The average quantity of water used with the different mixtures in 
addition to the water for wetting the stone is expressed in percentages of 
the weight of the cement and of the cement plus sand as follows: 

Percentages of Water Employed in Kimball’s Tests. 




In terms of weight 

In terms of weight 



of cement. 

of cement plus sand 

Mixture 

I ! O! 2........... 

20.9% 

20.9% 

<< 

1:2:4. 

3 °- 3 % 

10 . 7 % 

C( 

i: 3 : 6 . 

39 - 3 % 

10.5% 

u 

1:6: 12. 

7 I - I % 

8.6% 


These percentages do not include the water used in wetting the stone. 

The specimens were made in cold weather, and therefore set slowly. 


*Tests of Metals, U. S. A., 1899, p. 717. 
-j-Approximate. 








ULTIMATE COMPRESSIVE STRENGTH IN POUNDS PER. SQ. IN. 


/ 


366 A TREATISE ON CONCRETE 

They remained from two to seven days (most of them three to four days) 
in the molds, and were then placed, until tested, in wet ground. Mr. Kim- 
* ball’s remarks with .reference to the leanest mixtures are of interest as 
illustrating the frequent necessity ot using richer proportions than the 
actual loading requires. 

The 1:6:12 blocks were in poor ujndition. This was due to the 
difficulty of getting so lean a mixture well rammed into the corners of 
molds so small as 12-inch, and to the fact that the concrete had not at¬ 
tained sufficient strength, even though handled with care, to hold together 
well in the process of removal front the molds. The cubes of this mixture 
should have had a longer time to set before taking them out of the forms. 
In our foundation work we have used this mixture only as a filling with 
which to replace soft ground and on which to build the foundations proper. 

The diagram in Fig. 119 shows Mr. Kimball’s resultant curves* for the 



{See p. 365.) 

♦From data presented to the authors by Mr. Kimball. 
















































































































































































































































































STRENGTH OF PLAIN CONCRETE 


367 

different proportions based on an assumed weight of cement of 100 lb. per 
one cubic foot at the various ages. The results from individual brands 
of cements are shown by separate points. 

Candlot’s Tests. The table below, giving results of tests by Mr. 
E. Candlot,* of France, converted into English units, is of special 
value because of the accuracy in recording the data, the extreme varia¬ 
tion in proportions and the number of periods at which specimens were 

Tests 0} Strength of Concrete made with Different Proportions. 


By E. Candlot. (See p. 367.) 


PROPORTIONS BASED ON 
PACKED CEMENTf 

- 1 

Volume of mortar in terms of 
0 pe r centage of volume of stone 

ACTUAL QUANTITY 
OF 

MATERIALS 


GRAVEL 

CONCRETE 


BROKEN STONE CONCRETE 

0 

Volume of Concrete 

— Cement in 1 cu. ft. 

T of concrete 

^ Weight per cu. ft. of 
• concrete after setting 

Ultimate Com¬ 
pressive strength in 
lb. per sq. in. 

1 0 

E Volume of Concrete 

r ; 

— Cement in 1 cu. ft. 

of concrete 

^ Weight per cu ft of 

• concrete after setting 

Ultimate Com¬ 
pressive strength in 
lb. per sq. in. 

4-> 

a 

6 

OJ 

0 

lb. 

g 

a 
c n 

cuft 

G 

0 
-+-» 
c n 

cu.ft. 

U 

<D 

a 

£ 

cu.ft. 

7 

C/J 

>* 

d 

Q 

28 

C/3 

d 

Q 

Months 0 

I 

cj 

CD 

Days 

28 

(/) 

D*> 

d 

Q 

Months 0 

1 

1 

u 

d 

V 

i: 6.4: 8.2 

67 

5Si 

35-3 

45-o 

. 6.36 

58.3 

9-5 

144.8 

1031 

1387 

1280 

1292 

54-8 

10.1 

142.3 

1316 

1600 

1636 

194.1 

1: 3.6: 4.7 

67 

992 

35-3 

46.6 

7.42 

6l.I 

16.2 

147-3 

1458 

2454 

2583 

3225 

56.9 

17.4 

147.9 

2240 

2845 

3319 

3508 

1: 2.5: 3.6 

67 

1433 

35-3 

50.9 

8.55 

65.0 

2 2.0 

150.4 

2312 

3094 

3485 

4385 

61.1 

23-4 

149.8 

2845 

3485 

4883 

5026 

1: 1.6: 2.8 

67 

2205 

35-3 

62.0 

10.77 

78.0 

28.0 

149.8 

2632 

34i4 

3579 

5500 

72.0 

30.6 

151.6 

3985 

4303 

4623 

5972 

1:6.4:10.9 

5° 

55i 

35-3 

60.1 

6.36 

67.8 

8.1 

142.3 

747 

924 

1031 

1707 

63.6 

8-7 

142.3 

1316 

1387 

1494 

1683 

1: 3.6: 6.3 

50 

992 

35-3 

62.2 

7.42 

70.6 

I4.O 

145-4 

1743 

1991 

2536 

2964 

67.1 

14.7 

146.6 

2098 

2241 

2845 

3201 

i: 2.5: 4.7 

5° 

M 33 

35-3 

67.8 

8.55 

73-8 

19.4 

149.1 

2169 

3058 

3532 

4505 

70.6 

20.3 

148.5 

2276 

34i4 

3627 

5262 

1: 1.6: 3.7 

50 

2205 

35-3 

82.6 

10.77 

91.1 

24.2 

150.4 

2952 

3592 

4054 

5050 

86.2 

25-5 

151-0 

3556 

3982 

4338 

5572 

1: 6.4:13.6 

40 

551 

35-3 

75-o 

6.36 

79-5 

6.9 

141.0 

676 

924 

1078 

1375 

70.6 

7-8 

143-5 

1280 

1316 

1138 

1778 

1: 3.6: 7.8 

40 

992 

35-3 

77-7 

7.42 

84.8 

11.7 

142.3 

.1031 

1494 

1518 

2608 

78.8 

12.6 

142.3 

1494 

1778 

2347 

2822 

1:2.5: 5.9 

40 

1433 

35-3 

84.8 

8.55 

90.4 

15-9 

145-4 

1245 

1992 

2654 

3247 

85-5 

16.7 

146.0 

2205 

2525 

2963 

3201 

1:1.6: 4.7 

40 

2205 

35-3 

103.3 

10.77 

106.7 

20.7 

149.2 

2454 

2560 

3319 

4503 

102.4 

21.5 

146.6 

2560 

3200 

3532 

3936 


Note. — The gravel weighed 96.8 lb. per cu. ft. and contained 40% voids. The broken stone weighed 85.5 lb. per 
tu. ft. and contained 47.4% voids. Both the gravel and broken stone had been passed through a screen havinjr 
ineshes of r|" diameter. The sand weighed 81.2 lb. per cu. ft., thus containing 50.4% voids, and had been passec 
through a No. 12 sieve. The cubes were 10 centimeters (4 in.) on an edge. 


crushed. The application of these tests to the authors’ formula for strength 
is discussed on page 357. 

The Effect of Concentrated Loading. In concrete foundations for 
piers and in concrete footings it is customary to load an area smaller than 
that of the surface of the concrete. The question at once arises whether 
the stress shall be based upon the load divided by the total area of the 
concrete footing or by the area of contact. Experiments made upon con¬ 
crete and other materials show that neither of these methods is correct, 
but that an intermediate area should be selected for computation. 

*Candlot’s Ciments et Chaux Hydrauliques, 1898, pp. 446, 447. 

•f-Assuming 3.8 cu. ft. in 1 bbl of 376 lb. 





















































RATIO OF STRENGTH OTTOEH CONCENTRATED PRESSURE TO 
STRENGTH UNDER DISTRIBUTED PRESSURE 


368 


A TREATISE ON CONCRETE 


In connection with the designing of concrete footings for the Boston 
Elevated Railway, 12-inch cubes were crushed by concentrating the load 
upon plates 10 by 10 inches and 8 by 8J inches.* At Lehigh Lniversity 
in 1908 a set of experiments was made upon the strength of 6 by 6 inch 
cubes of 112:4 proportions where the compressed area varied from the entire 
area of the specimen down to 1.21 square inches. 

In the diagram, Fig. 120, both sets of valuesf are plotted. The two sets 
agree where they overlap, and also are similar in general direction, and, in 
fact, in actual values of the ordinates, to curves drawn by Prof. J.B. John¬ 
son! illustrating Bauschinger’s tests upon other materials than concrete. 



O TESTS BY GEO. A.-KIMBALL 
Q TESTS BY PROF. F; P. MC KIBBEN 


0.7 0.0 0.5 0.4 0.3 

RATIO OF AREA OF COMPRESSED SURFACE TO TOTAL AREA OF CONCRETE 


Fig. 120. Concentrated vs. Distributed Loading. (See p. 368.) 


In considering the smaller areas, as indicated by the smaller ratios of 
area, the fact must be considered that the compressed surface deforms^ 
that is, actually compresses under the load, and the amount of deforma¬ 
tion, which may be approximately estimated from the modulus of elas¬ 
ticity, may sometimes be the limiting consideration. Also, in the small 
areas the possibility of punching through must be considered. 

The method of using the curve shown in Fig. 120 is best illustrated in 
the following examples: 

/ * Tests of Metals, U. S. A., 1899, p. 740. 

f From data presented to the authors by Mr. George A. Kimball and by Prof. Frank P. McKibben. 

J Johnson’s Materials of Construction, p. 33. 






























































































































































































































































































































































































































































































































































































STRENGTH OF PLAIN CONCRETE 


369 


Examp 1 e 1.—What dimensions of pedestal would be required to safely sup¬ 
port a load of 40 tons concentrated upon a plate 1 o inches square, assuming an 
allowable distributed stress upon the concrete of 650 lb. per square inch ? 

Solution .—Forty tons or 80 000 pounds on 100 square inches represents 
800 lb. per square inch, and the ratio of pressure required under the con- 


800 

centrated load to the allowable pressure is therefore _ = 1.23; hence 

650 

from the curve, the total area of concrete necessary is 100 sc b iru = x 8 2 

°-55 

square inches. 

Example 2.—The breaking strength of a 12-inch cube of 1 12:4 concrete 
having chamfered edges, so that the area of contact of the load is reduced to 
9 by 9 inches, or 81 square inches, is 324 000 pounds. What may be con¬ 
sidered as the ultimate strength of the concrete when loaded over its full 
area? 

Solution .—The strength per square inch of the cube figured on its cham¬ 


fered surface is 4 °- - -° 

81 


= 4 000 lb. per square inch. 


The ratio of the 


compressed surface to the total area is 


81 

144 


0.56, and from the diagram we 


find the ratio of strength to be 1.22. Dividing 4 000 pounds, the unit 
strength on the concentrated surface by this gives as the probable ultimate 
of the concrete when loaded over its full area, 3 280 lb. per square inch. 

The Strength of Short Prisms. The theoretical angle of rupture in 
crushing is about 6o° with the horizontal, and, as a matter of fact, cubes 
or prisms of concrete will leave, after crushing, pyramids whose surfaces 
are at an angle of about 6o° with the base. To develop simply the normal 
compressive strength, the height of a specimen should be at least ij times, 
and preferably 5 times, its least lateral dimension. 

The following formula evolved by Prof. Johnson* by plotting results of 
experiments by Prof. Bauschinger with sandstone prisms, and by Mr. 
Charles Bouton with cast-iron prisms, may be used for comparing approxi¬ 
mately the strength of prisms and cubes. Prof. Johnson states that the 
law holds between ratios of height to breadth of 0.4 to 5.0, the limits of 
the observations. 


strength of prism 0 . b 

-°- L —— = 0.778 + 0.222- . 

strength of cube h 

where b = least lateral dimension of specimen, 
and h = height of specimen. 

♦Materials of Construction, 1903, p. 31. 








37 o 


A TREATISE ON CONCRETE 


Although we have not sufficient data to prove that this formula is exactly 
applicable to concrete, a study by the authors of tests at the Watertown 
Arsenal* tends to show that, considering the variability, of the material, 
it is probably sufficiently accurate for practical use. In the Arsenal 
experiments square prisms were employed, varying in cross-section from 
4 by 4 inches to 12 by 12 inches and ranging in height from 1 to 2 inches 
up to that of a cube. In every case the shorter prisms gave much higher 
strength than the cubes. 

Example .—If the compressive strength per square inch of a 12-inch 
cube is 4 000 lb., what strength may be expected from a prism 12 inches 
square and 18 inches high? 

Solution.—Substituting in formula (3), we have 

X 

- = 0.778 + 0.222yf 

4000 

X = 3704 

Theoretically, specimens of the same shape, as, for example, all sizes of 
cubes, should have the same strength per unit of area. In practice, large 
concrete cubes are apt to show higher unit strength than smaller ones; 
experiments by the authors, for example, giving in every case higher unit 
strength for 12-inch than for similar 8-inch cubes. However, the average 
unit weight of the 8-inch cubes was much lower than that of the 12-inch 
cubes made from the same batches of materials, indicating the difference 
in strength to be due to the fact that the materials can be more compactly 
placed in a large than in a small mold. 

The standard compression specimen adopted by the Joint Committee on 
Concrete and Reinforced Concrete is a cylinder 8 inches in diameter by 
6 inches long. 

Strength of Cubes vs. Cylinders vs. Columns. Computations from 
the United States Government tests at St. Louisf comparing the strength 
of 6 inch cubes and standard cylinders 8 inches diameter by 16 inches long 
gives a ratio of strength of cylinders to cubes at ages of thirteen and twenty- 
six weeks as 0.88. This coincides almost exactly with the above formula. 

But few comparative tests of cylinders and columns are available, but 
these indicate that the above formula is fairly correct and on the safe side 
when comparing the probable strength of a column with the given strength 
of a cylinder. 

* Quoted and tabulated by Committee on Compressive Strength of Cements of the American 
Society of Civil Engineers in Transactions, Vcl. XVIII, p. 264. - . . 

f U. S. Geological Survey, Bulletin 344, 1908. , ; • 



STRENGTH OF PLAIN CONCRETE 


37 i 


Plain Concrete Columns. There are few comparative records of the 
strength of concrete columns of different heights, but both theory and 
experiments tend to show that there is no appreciable difference in the 
compressive strength of columns of heights differing within ordinary limits, 
ranging, say, from a height of 3 to 14 times the least lateral dimension, 
provided the loading is exactly central. Prussian regulations,* 1904, 
require that computation shall be made for flexure, if the height exceeds 
18 times the least diameter. 

In 1897 tests were made at the Watertown Arsenalf on 12 by 12 inch 
columns of plain concrete, built by the Aberthaw Construction Company, 


Compressive Strength of Mortar and Concrete Columns. 
Length of Columns 8 feet. 

Watertown Arsenal {See p. 371.) 





Composition. 

Age. 

+-> 

d 

CO 








C*-. 


03 2 








~*z d 



Nominal size of 







, 

be ST 
£ w 


column. 

£ 


6 

0 




S 5 

V u 

S-h fl) 

o)*ti 
a o 


c* 

G 

<D 

G 

Kind of stone. 

c 

0 

rf7 

G 

£ a 

22 

CO ^ 

22 

oj<£ ® 

■e gj to 

G m 


0 

co 

CO 


s • 

P 



P Eh 

10" Diameter 

neat 

0 

0 

None 

10 

2 5 

I 29 

a 7000 

I907 
p. l86 

10" Diameter 

12" X 12" 

I 

1 

0 

None 

6 

11 

132 

4320 

I906 
P- 473 

I 

2 

0 

None 

j" to p' trap 

6 

0 

130 

3 ° 7 ° 

1905 
P- 379 


12" X 12" 

I 

1 

I 

7 

10 

142 

3522 

I 9°7 
p. 182 

p' to ip' trap 

12" x 12" 

1 

1 

2 

5 

7 

!54 

3900 

i 9°5 
P- 33 1 

§" to ip' trap 

20" Diameter 

1 


O 

0 

10 

2 3 

152 

357 6 

1 9°7 
p. 192 

p' to ip' trap 

12" X 12" 

I 

2 

4 

6 

5 

i 5 ° 

1990 

I 9°5 
P- 334 

p' to ip' trap 

12" Diameter 

I 

3 

6 

5 

5 

146 

b 1446 

1906 
P- 535 


12" Diameter 

I 

3 

6 

Cinders 

5 

0 

IOI 

698 

1906 










P- 537 


a Maximum load applied; column not ruptured. 

b A similar column failed at 750 lb. per. sq. in. but the lower end of this column was less sound 
than the upper part because of leakage of the mold. 


ranging from 2 to 14 feet in length. The results of these tests concur with 
the theory of columns in showing that up to at least 14 diameters there is 
but little decrease in strength as the length of the column increases. 

The table presented above gives results selected from tests made by Mr. 

* See Engineering Record , July 2, 1904, p. 25. 
f Tests of Metals, U. S. A., 1897, p. 383. 




























37 2 


A TREATISE ON CONCRETE 


Howard at the Watertown Arsenal* in 1905, 1906 and 1907, on con¬ 
crete and mortar columns. Generally the first sign of failure in the columns 
appeared in the form of oblique and longitudinal cracks, occurring usually 
from o to 3 feet distant from one end, although sometimes extending the 
entire length. 

A comparison of the strength of plain and reinforced columns is presented 
in the next chapter. 

Strength of Machine vs. Hand Mixed Concrete. Mixing in a well 
designed machine produces a more homogeneous concrete than is possible 
by hand except with excessive labor. The relative strength of the concrete 
of course varies with the conditions, but tests indicate that ordinarily 10 
to 20 per cent greater strength may be expected in a first-class, machine 
mixed concrete, properly handled. It is probable that this more thorough 
mixing at least balances the extra care given to laboratory specimens, so 
that in ordinary practice, strength as great, if not greater, than in the labor¬ 
atory, may be expected. 

Eccentric Loading. The effect of eccentric loading, that is, of having 
the center of gravity of the load one side of the center of the column, is 
to lessen its compressive strength. A similar effect is produced by loading 
a column already bent, or by constructing it of unsymmetrical shape, as 
by bulging one side. 

Most columns in actual structures are loaded more or less eccentrically, 
and this is especially the case with wall columns, which have all the floor 
loading upon one side. This must be allowed for in designing the columns. 

The ordinary formula for the compressive fiber stress due to eccentric 
loading upon solid rectangular columns, as illustrated in Fig. 121,is as 


follows: 


Let 

P = total load. 

A = area of columns. 
e = eccentricity. 
b — breadth of column. 

/ = average unit pressure. 

/' = total unit pressure on outer fiber nearest to line of vertical pressure 


Then 



(4) 


The use of the formula is illustrated by the following example. 


♦Tests of Metals, U. S. A., 1905, 1906, 1907. 



STRENGTH OF PLAIN CONCRETE 


373 


e!» 


Example. — What will be the increase in pressure in a column 
2 feet square due to placing the loading 6 inches off center? 

p 

Solution. — With central loading the pressure is, / = — 


hence 


t) 


Fig. 121. 
Eccentric 
Column 
Loading. 

(See p. 
372 .) 


Substituting the values e = 0.5 and b = 2 

r = 2if 

that is, the pressure on outer fibre is increased 2\ times. 

Concrete vs. Brick Columns. The compressive strength of 
brick piers is of interest to the concrete engineer for comparing 
brick and concrete columns. Tests made at the Watertown 
Arsenal and quoted by the Committee of the American Society of Civil 
Engineers on the Compressive Strength of Cement* give the ultimate 
strength of common brick piers about eighteen months old as ranging 
from 800 to 2 400 pounds per square inch, the results for brick laid with 
lime mortar averaging nearer the lower figure, and those for 1: 2 Portland 
cement mortar nearer the higher figure. 

Prof. William H. Burr,I after discussing the strength of brick piers 
under various conditions, states that 


The results of all the experimental investigations available in connec¬ 
tion with brick masonry and experiences in the best class of engineering 
work indicate that masonry laid up of good hard-burnt common brick may 
safely carry a working load of 15 to 20 tons per square foot or 210 to 280 
pounds per square inch. In the construction of this class of masonry 
where the duties are to be severe it is of the utmost importance that the 
best class of Portland cement mortar be employed, as the carrying capacity 
of brick masonry depends largely, if not chiefly, upon the character of the 
mortar. 

These working stresses are about one-half those recommended for good 
1:2:4 concrete in the chapter which follows. 

More recent tests by Professors Talbot and AbramsJ indicate that the 
strength of the brick column varies with the quality of the brick, the quality 
of the mortar and the care in laying. 


SAFE STRENGTH OF CONCRETE 

The working strength to be used for concrete is fully discussed in the 

* Transactions American Society of Civil Engineers, Vol. XV, p. 717, and Vol. XVIII, p. 264. 
•j- Burr’s Materials ji Engineering, 1903, p. 428. 
j University of Uluiois, Bulletin No. 27, Sept. 1908. 










374 


A TREATISE ON CONCRETE 


chapter which follows. For proportions and conditions differing from 
those presented there, reference may be made to the relative strengths dis¬ 
cussed in the preceding pages. 

In many structures the actual strength of the concrete does not enter 
into the calculation. The dimensions of a concrete foundation, for ex¬ 
ample, are often determined by the area of the superimposed structure, 
or else, on the other hand, by the bearing power of the soil. In such cases 
it often would be theoretically possible to come nearer to the working 
strength of the concrete by using very lean proportions, were it not pro¬ 
hibited by the porosity of the mass or its low strength at short periods. 
However, by grading the materials so as to reduce the voids, a lean mixture 
is often economical. 

The unit pressure to be selected depends not only upon the strength of the 
concrete as determined by its proportions, the character of the raw materials, 
and the methods of mixing, but also upon the character and importance 
of the structure, the nature of the pressure,—whether by direct compression 
or bending, whether from a live or dead load, or whether acting directly 
or through a cushion of inert material,—and the time of setting before 
placing the load. 

GROWTH IN STRENGTH OF CONCRETE 

Records from various tests made upon similar specimens of concrete at 
different periods are plotted in the diagram, Fig. 122. The curve illustrates 
the growth in strength which may be expected in ordinary average concrete 
made with first-class materials. The ordinates on the diagram represent 
ratios of the strength at various periods to the strength at the age of one 
month, in order that the curve may be of general application to various 
mixtures. If, for example, the strength of any concrete at one month is 
found to be 2 000 pounds per square inch, the strength of the same concrete 
at the age of six months may be assumed to be 2 000 multiplied by 1.35, 
the ordinate at six months, or 2 700 pounds per square inch. 

The curve does not allow for the fact that the growth in strength varies 
to a certain extent with different materials, with different proportions, and 
with different percentages of water employed in mixing. As stated on 
page 386, with age, the strength of gravel concrete appears to gain on the 
strength of broken stone concrete. The growth, too, at periods beyond, 
say three months, is undoubtedly affected by the hardness or strength of 
the particles of the coarse aggregate, since a concrete of poor material will 
reach its ultimate strength earlier than one of good material. The tests 
of Mr. Kimball (see page 366) tend to show that the increase with age 


Fier 122 — Growth in Compressive Strength of Portland Cement Concrete. (See p. 374.' 


375 


RATIO OF COMPRESSIVE STRENGTH,TO STRENGTH AT ONE MONTH 



2.00 












































































































































































































Data Concerning Composition and Transverse Strength of Concrete Beams Tested at Little Falls, N. Jby Wm. B. Fuller, C. £. 

During the year 1901. Beams, 6x6x72 inches. Spans, 30 and 60 inches. Atlas Portland Cement, River Silica Sand. 

Crusher Run Trap Rock, | to 3 inches nominal diameter. (See p. 378.) 


c 3 

u 

p 

-*-» 

a 

p 

Pi 


C/5 

J 3 

"3 

-d 

o 

2 


• 3 SBJ 3 AB 
JO JOIJ 3 3 [qB 

-qojd JU 3 D I 3 J 

/-N 

vO 

cq 

O cq "T- 
m cq ci 

qf cooo 
cq cq co 

vq 0 co 
m co cq 

OwO Ov 
H M O 

Q 

cq h 0 

q Cl to 
co cq On 

sq. in. 

• 33 BJ 3 Ay 

to 

cq 

no cq h 

O R co 
O' r* t>» 

cq h t 
cq rf co 
no cq r 

00 O to 

O m to 
I^nO 

\0 't'O 
00 O M 
•rt m\o 

cooo m 

cq cq R 
to to rf 

O' O On 
CO00 m 

rf co co 

J-H 

O 

A 
c n 
"O 

•uinui 

-juijY 

’T 

cq 

N—✓ 

NO 00 OC 
too NO 
00 NO NO 

O NO 00 
00 co cq 
to cq no 

QvVO <*> 

■>t 3- t'- 

oc 

VO M W 
•^•00 O' 

Tf TJ- 10 

O' to 
tooo 

rf rf 

O O' rf 

O rf co 
co co cq 

a 

3 

0 

Ot 

•uinui 

-ixbjy 

/^S 

CO 

cq 

00 cq cq 
nO RO 

O'CO 00 

T h 'O 
cq tovO 
cq 00 

00 ci 

rf O' co 

r>. 

cq cq O 

H T T 
to tovO 

cq cq 
to 
to to 

0 fo 0 

00 H H 
■'t 't Tt 

•S 3 {U 3 Jg 
jo asquint 

/■N 

cq 

cq 

VO 'O VO 

KO CO'O 

vO 'O *0 

vO vO 'O 

vO NO H 

NO NO »0 




I* 

•s 3 

c a 

I ° 

o 

> 


T*»°.L 


•sjugsiSSy 


•JU31U33 


u 

<v 

-*—> • 

m <v 


• C/5 

p S 

“s 

, 5 m 

aJ'o 

I- 


d 

u 

u 


•pv>i 




•Xjq psjoj. 


* 0 UO)g pUl 3 
pUUg p*10£ 


• 9 UO)g 


•puug 


*^U91U93 


d 

cj 

0) 

c 

o 


P 0) 

33 

*o a 

«« f> 

"Ojq 


P ' 
3 
O 
Ph 


.£f 

*3 

is 


C/5 

o 

H 


uinui 

-IXBjy 


•uinui 

-IUIJY 


•pjxtJY 

sy 


uajEAV 


•XT R 

I C J°JL 


• 3 uojg 


PUBS 


UU 3 UI 33 


•} 1 { 3 i 3 av 
Aq suop 
-jodoij 


O 

in 

O 


•ui^i 


N M fO 
CO CO fO 


o 

cq 


O' 


>OCN D 
M R O 
't M (S 


OCO T 
O m cq 
OOO 


rf rf rf 
CO CO co 


Tf lO H 

0 \ r r 
h cq cq 


rf rf co 
10 co 
O M o 


rf ro rf CO rf co co co CO 

co co co <OCOCO cococo 


O' ’TOO 

H00 

eq m w 


to cq C50 
*0 T T 
m m cq 


R M \0 
cq o to 
cq cq m 


roO 00 
rf rro 
OOO 


O On 00 
vO tooO 
OOO 


cq no co 
O On NO 
MOO 


CO CO to 
CO CO co 


to H to 

CO CO CO 


CO 00 w 
IOIOIN 
OOO 


CO 


to rf CO 

W to 00 
rf cq H 

O M 00 

rf 0 co 
m m cq 

cq no O 

R CO H 

M M M 

>0 ro O 
O>00 vO 

0 0 « 

to to co 
cq 0 O 

M M 0 

cq CO rf 

00 R-vO 
OOO 

M to O 
t>. 0 

O O' O 

NO 0 rf 

O0O0 R 
OcO O 

00 m to 

1^00 0 

O' O O' 

O co O 

0 00 to 
OOO 

O R co 
00 00 NO 
OOO 

rf 00 VO 

00 00 0 

OOO 

w 



M 



NO R R 
00 rf O 
co cq cq 

0 1010 

00 Tf 

W M N 

R to CO 
OnO 

M W M 

to to R 
to cq O 
m m cq 

t^oo 0 
oco H 
cq h m 

O' O M 

M l-t CO 

M M M 

to 00 CO 
00 cq O' 

NO R R 

NO to O' 

O cq cq 

00 R R 

m no cq 

00 H cq 
R’CO 00 

to 00 cq 
rf tO to 
00 00 R 

Ov Tf 

r^oO 

to O to 

NO VO VO 

00 00 00 

O rf 

co 
CO to 

O to CO 
000 0 
vO to co 

R- CO O 

co cq O 
too O 

m >—1 
w rf cq 

R- R~ lO 

O M CO 
O to H 

tovO R* 

O'vO rf 
rf nO R' 


o -t 
r co 
co 10 


tOOO On 

00 to to 
to co cq 


°0 cq no 

00 to cq 
co to no 


On to 
O 00 
NO to 


cq co co rf 
to On 00 to o 

M CO t tovO 


cq to nO 
00 O O 

h COT 


00 n cq 
r cq no 

Tf tO lO 


co to to co R R R rf no R W O' cq 

On CO cq co to CO cq h TO ncOh 

co cq cq h m m to rf co co cq cq cq 


R <n no 
O' ’f CO 
M M CO 


rf COO 
T O' >0 
cq m m 


T N to 

co h cq 
m m cq 


ROO m 
N T CO 
M M M 


O co M 
M o On 
M M O 


O O R 

00 COOO 

W M O 

R co NO 

co O O 

CO rf nO 

3- O M 

to R to 

O to M 

TfvO VO 

VO IO Tj- 

tONO vO 

O'O "<f 

to too 

vO vO vO 

M M M 

M M M 

M M M 

M M M 

M M M 


O' 


O R R 

M CO CO 

cq T to 


00 o o 

T O' to 

to co co 


O'00 M 
T h ro 
rf to lO 


to o O' 


R O 

too 


cq 


O' 


cq 


, ’tO 
O' to co 06 O' O' 
<0 rf to to to to 


00 


q no no 
R co cq 
co tOO 


O to M 

COO to 

O T T 


M M M (H 


T M to 
co O' M 

to too 


Oco T to co 00 cq 00 


too 

o o 


On rf O' 
rf to tO 


CO to to 
OOO 


H TON 

rf to cq 
cq m m 


cq r co 
m O' to 


co cooo 

ci 6 6 

H M M 


R00 O' O' R rf rf rf cq 

d R cq w h r roO 


o 


ONCj ts cq 00 00 HO0R T cq T tooO On ’TOO O 


cq 00 O' 
h co T 


M o On 
to CO cq 


M 00 O 
T T to 


tooo O 
to to co 


O cq m 
co rf to 


NO RR 
to to to 



h oq 

O' O' 
NO O 

00 rt 

co d 

M 0 

M M 

H T T 

R 4 6 
rf R On 

1 

103.6 

113.0 

M M O 
rf R.NO 

co to R 

f in m 

O'06 in 

00 0 0 



On 

O cq cq 

OnnO O' 

CO H O 

R to O 



rf 

R R 6 

to cq no 

OO N O 

•rf o> In 



NO 

rf CO CO 

cq cq 00 

'O >n in 

rf CO CO 

O' 

m O' 

O ■rf O' 

O CN| M 

0"0 >0 

« 

cooo to 

<q 

d d 

06 r' vr 

R R 6 

to cq co 

3-06 in 

cq d R 

M NO T 

H 

co cq no 

rf CO co 

cq cq rf 

co cq cq 

cq m m 

0 

w cq 

CO rf O 

m cq co 

rt in O 

\2 

3 

rf to no 

0 

0 0 

O 0 H 1 

M M M 

m m cq 

^ « Cl 

cq cq cq 

H 

M M 

H H M 

W W M 

M M M 

W H M 

W M M 


^^^co rx p O m cq co rj* to 'no'^ROo' 






























































































377 


so* cj cn es 

N « |f)H 

>—' 

<OH t 

CO oj 10 

O' ci cq 

CN 00 M 

w°o n 
co M v6 

W 

co q 

4 6 cn 

00 q q 

OHO 

q q vq 

6 CO CN 

^ 0 
(N O O 

« 88 

h88 

3 JS * 

-—\ 00 O »o 

H \0 lO 

w rf CO to 

ICO O' 

00 01 CO 

01 01 01 

00 »o O' 

O* Tf 

M M CN 

0 O' O' 
m O rf 

CN CN M 

m rf 

00 VO CN 

M M M 

CN CO H 

CO vo 

M M M 

M O' O' 
vo CN 0 

M M M 

VO CO CN 

HH O' O 

HH HH 

CO 00 rf 

HH X^OO 

HH 

O' VO H 

00 O' rf 

p 4 c£ O 

^^11 

3 -m O' 

/—v cn rt 00 
rf O' !"■* fO 

M fOW n 

01 co O 

VO H W 

W N 0» 

O' CO CN 

VO CN vO 

M M CN 

00 CN rf 

O' O m 

M CN HH 

O vO O 

I''* VO CN 

M M M 

0 O O' 

CO rf 

M M M 

O' co 10 

VO CN O 

M M M 

CO CN CN 

H O' 0 

HH HH 

HH 

HH 

HH 

00 

u O 
* hO 

•s* . 

/*—S N N O' 
co co O'O 

CN rf CO CO 

N-/ 

00O N 

O rf 10 
co 01 0* 

CN VC ^ 

O' O' 

M M CN 

VO O' rf 
co HCO 

CN CN H 

O CO N 

O' VO CN 

M M M 

CO 0 co 
COOO vo 

M M M 

CO rf CO 
vO co m 

M M M 

O rf cn 

CN O' O 

HH hH 

VO 

HH 

HH 

HH 

O' 

;s 1 ^ 

& i 0 

c n 

>1 - 

'cn'vO 'OVO 

CN 

v-' 

co VO CN 

r CO'O 

CO CN 

CN CN CN 

CN rf CN 

CN CN CN 

CN CN CN 

CN M M 

CN H H 

O' fl 0 

CN 










S'g « 

/*N 

M VO lo CO 

CN CO CO CO 

CO CO CO 
CO co co 

CO co CO 

CO co co 

rf rf rt 

CO CO CO 

*cf rf 

co CO CO 

rf CO rf 

CO co CO 

rf rf co 

CO co co 

CO co co 

CO co co 

CO co co 

CO CO co 

co CO co 
co co co 

O .M N 

tt? m w<a 

rti 0 

vO 0> O 

M-v P)(OH 

O m m f'. 

M CN M M 

N Cl W 

vO vo co 

HH H HH 

CN rf VO 

CO co vo 

M M CN 

O O' 
rf O'vO 

CN M M 

CO vo 0 

vo VO rf 

M M hH 

r - '* ■t'"* w 

M VO O 

M CN CN 

VO co O' 
vO rf O 

M M M 

O 00 O 

CN X^* rf 
hh CN CN 

X^ CN vo 
x^ x^ co 

HH HH HH 

VO X''* vO 
m 10 rf 
hh CN CN 

’ W-H M 

t 3 • <u 

C O' fl 
rt S, O 

/—v'O <N rf 
O' CO H O 

Hi M HH O 

VO O O' 

O O'N 
MOO 

Vt O « 
00 0"0 

0 0 « 

M M 
rf m 

tO ft O' 

O H O' 

H M O 

CO 0 rf 
X-CO rf 

O H W 

vO O O 
►H O 

HH M O 

'O tN 
00 M 00 

O tt H 

O' H 0 \ 

N tO O 
MHO 

HH O VO 

00 O O' 

0 CN M 

g'R- 

2 cd tn^j 
tn-o 0 0 
p 0 

(18) 

.117 

.IOI 

.077 

HVO CO 
vO vo vo 
OOO 

00 "t CO 
•T -t O' 
OOO 

O '00 0 
vO vo vo 
OOO 

N CO H 

■Cf ”Cf ^f 
OOO 

O' X^ 

CO X^ vo 

000 

O CO O' 
rf rf co 
OOO 

H - tt to 
tovo m 

0 0 0 

00 W 

t t n 
OOO 

rf N H 

CO VO VO 
OOO 

^ 00 n M-« 

C CN O 

O (J 

1 Sgs? 

0 co O 0 

rO O N 

rr o VO 

I s * o o o 

M Tf O 
vo 00 01 

O' O' 0 

M 

co 0 *o 

00 N CN 

O' O' O' 

vo CN CO 
VO N O' 
O' O' O' 

OOO 

OOO 

000 

M M M 

0 M CN 

0 10 x^ 

0 0 O' 

M 

CO 0 0 
OOO 

O' 0 0 

HH M 

O co O' 

O rf 10 

0 O' 0 

HH 

VO 00 O 

a>00 0 

O' O' 0 

HH 

0 00 00 

O rf ro 

O O' O' 

4 “ \2 M 

ro mi ” a) 

M T 3 P 

- . 0 w 

tl ft u M 
-*-• , _Q 

a« mO 

*J fi Ci ? 

^s\0 vooO 
\C O'NCO 

M M M M 

00 VO 01 

01 CO CO 

M M M 

vo rf m 

H OOO 

10 M O 

0 t^vO 

CN M M 

co vo O 

IO VO rf 

x^oo CO 

M O 

M CN M 

CO CO O' 
vO rf O 

HH HH HH 

0 M O' 

CN CN O' 

M CN HH 

CO O O 
X^vO co 

HH HH HH 

VO 10 rf 

H OX 

HH CN HH 

^ x^ o 

VO rfOO CN 

m r^oo 

V_^ • 

COCO 00 

CO ^t \0 

co CO 00 

00 O r 
00 tf 
oO 00 

O M CO 
vO O CO 

x^oo 00 

IT) O 
tf to 

00 00 00 

CO CO O' 

00 ^ O' 

00 ^ N 

VON H 

CO vo O' 
00 00 00 

O CN O 

00 CN vO 

X N N 

COOO rf 

CN CN VO 

CO 00 00 

vo CO rf 

CO rf vo 

X N N 

^ J • - s 
E-S'g § 

0 4 P E 
>> cn O 

>-> ir> O 
'Zf.OO Tt- CN 

J «OVO t-» 

V_x 

O' 

nO O' 
t--. f'- r-~ 

O co co 

O O « 

00 00 vO 

CN O' CO 

VO H O 

vo NN 

H rf CN 

00 00 O 
r^oo 

00 vo O' 

CN CO H 
OOvO 

\0 lO lO 

vo O' to 

r~ t' OO 

Cl CN rf 

CO co 00 

00 vO vO 

vo O m 

VON H 

X"* r^oo 

N CN h 

COVO 00 

00 vO vO 

.ti >h ^ cj 

rt c 

S-H , OrH 

/-s O N 

CO rf CO 

HH M CO 

V-/ • • 

in h 10 
Vt & to 
Nf H" m 

M CO 

VO 00 

10 10 

CO vo 

O co CO 

CN CO ’t 

tot 
f>0 O 
tj- in m 

O O 

x^ rr 

10 CN 

O' 0 co 

VO rf h 

CO rf IO 

O' VO 
rf vo 

VO HH 

O M 00 
OO'O CO 
cn co rf 

00 

O' 

rf 

o~ 3 
- •- 

•cc'ga 

O OJ P M 
ft g ° g 

CN O n g 

O m ^ 

^ M o CO 

CN 00 O'CO 

H to rf CO 
V-/ • • 

01 00 O' 

0 N>0 
co 01 01 

O' O co 
CO CN h 

CN CN vO 

O' CN 00 
vooo CN 
rf CO CO 

00 

0 00 vO 

CO CN CN 

00 10 0 

VO co Xn 

CN VO rf 

X^»vO co 

0 VO CN 

rf co co 

CO CN 00 

00 CO CN 

CN vo vo 

VO O' co 
x^ 0 x-> 
rf rf to 

O' CN HH 

COVO 00 
cOvO vO 

/-^\0 CN O' 

1- VO "'t O 

M HH M HH 
V-/ * * * 

0 0"t 

CO 

OOO 

00 CO H 
'O'O CO 

O O M 

00 CN O 
OOO 

0 0 0 

VO H O 0 
O'O VO 
OOO 

VOOO O 

VO o x 

O M O 

O' HH VO 
vO vO vo 
OOO 

X O'O 
rf O' N 
OOO 

00 00 co 
vo vo vo 
OOO 

00 m co 
rj CO C' 
OOO 

0 | O 0 

C D ^ 0 

• 24 o^ 

(xo) 

143.6 

150.4 

158.0 

m vo co 

6 oi 10 

OvO O 

HH HH HH 

°o O'rf 

VO IO CN 
vO vO rf 

HH HH M 

vo covO 

^4 6* 

rf vo VO 

M H M 

rf q q 

M M CO 
vO vo vo 

M M M 

q vq q 

N H (N 
vO rf vo 

M M M 

qoo q 

X^* HH vo 

vovo vO 

H M HH 

w q q 

vO O' vo 
vO co rf 

HH HH HH 

oq q q 

4 vo ci 

VO vovo 

HH HH HH 

x^oo oq 
vo 6 M 

VO rf rf 

9 C/} Q O 

HH C O' M 
r-1 . TJ 

Tt co q 
^600 

O co CO 't 

N -^ M M M 

q co cs 

M 4 oO 

VO VO VO 

M H M 

vq vo rf 

00 00 00 

VO VO CN 

H H M 

q cn co 

4 co 6 

co 'f vo 

M M M 

O' O' HH 

CN CN VO 

10 VO VO 

M W M 

1C co N 

6 NO 
vo CN rf 

M M M 

qcq q 

co 4 6 

rf VOO 

HH HH M 

cq hh q 

O' CO HH 

10 CN CO 

HH HH HH 

CO HH VO 

4 x- 4 

rf rf vo 

HH HH HH 

cn 0 q 

O'O x^ 

VO CN CN 

HH HH HH 

fiH m C 
cd . P 

” r 0 o» 
o' M - • 

r & 

C ti h 

q q 0 

^ 6 06 10 
OC rf -* VO 

^ HH HH HH 

qq co 
OH 10 
vovo vo 

HH HH HH 

oq q q 

4 4 4 

vo vo co 

HH HH HH 

COVO CN 

VO CN O' 
rf vo vo 

M M M 

rf q q 

m m ro 
'OO'O 

M M H 

q vq co 

x-^oo 6 

vO co vo 

M W M 

oq oo q 

X^- In vo 
VOVO vO 

M HH HH 

HH IO HH 

vO vo co 

vO co rf 

H HH HH 

q CN CN 

4 VO CN 

10 vovO 

M H HH 

X"VO O 

4 N N 
vO co CO 

HH HH HH 

( 7 ) 

12.2 

10.9 

8.6 

O »0 <N 

00 CO 00 

CN VO fO 

X^vO M 

M 

GO q- q 

CN O O 

M M M 

von r> 

O' O'co 

co q cq 

X^ CO 6 

H M 

cn qoo 

6 06 vo 

M 

qq rf 

X''* CO CN 

HH HH 

cq q q 

6 6 06 

HH H 

cn oq vo 
n ci 4 

HH H 

1 

00 M CO 

^ 

'O w CO i- 
'—' HH HH HH 

X^ HH M 

O' co 

rf 10 vo 

H HH HH 

vq vo 

4 t^vo 

vo VO CN 

M H M 

vo O' CN 

CN H O' 
CO Nf rf 

M M M 

q 0 cn 

W CN VO 

vo vo vo 

- M M W 

qq 10 

O' vo Oi 
VO CN CO 

H M M 

q qoo 

N Cl O' 
rf 10 10 

HH HH HH 

O NN 

06 M 6 

10 CN CO 

HH HH HH 

00 CN q 
COVO co 
rf rf vo 

HH H HH 

VOOO rf 

06 4 vo 

vo CN CN 

H HH HH 

rrj O ’4 ^ 

•3 cn P 0 

S ft.Eu 

rf HH 

/ lO CO 

y_X CN VO 

01 O' 0 
CO M 0 

00 O' 0 

M 

q w 
vo O' 

0 0 

H H 

q M rf 

co h 
COVO 00 

vo vooo 

00 co O' 
00 O' O' 

VO VO 

vO vo 

O 

M 

h co q 

X^ CN VO 
vO 00 O' 

VO Hi 

CN O' 

0 CN 

HH 

cq vo 0 

CN X^ CN 

vovo 00 

CN 

CO 

O 

S’S c + 

^ 5 vo 

. 03 

^ ^ ,.4 

,-vOO cn <N 
to 

w O>00 vO 

O' O'cq 

O VO CN 

rfr rf rfr 

VO CO H 

O'VO M 

CO co O 

M 

O cn 

VO 4 4 

f'-'O »o 

vq 00 co 

6 vo 4 

vo rf rf 

O N VC 

01 4 N 

rf O N 

hh cq co 

X^-00 CO 
VO vo vo 

t. ft) H 

« tt. 

t 0 00 

rf vq vq 
X N H 

X^vo vo 

0 w r 

IO O' P» 
in 0 m 

• ~ <v _P 

0 0 -mCJ 
0 0 e II 

H « 6 II 

d -M cd O 

O rt 0 

* 7 o N H 

W CO 01 01 

vq co co 

vO 4 4 

H HH M 

M HH CO 

CO CN vo 
M H CN 

qcq 0 

CO 4 co 

H H H 

r-> i-h 

CN M M 

H H M 

vq O' vo 

6 6 4 

H CN M 

rf oq q 

CO M 6 

H H HH 

to *t in 

O' 4 4 

H H 

M CN CN 

CO M 6 

H HH H 

coq q 

6 4 4 

HH HH 

U Cd M 

ft <u ^3 . 

3 i -2 

0 H cn 

vovO 

00 O' 0 

N tt-vO 

t^oo O' 

2 0 to 

VON O' 

m 0 r» 

•f m3 GO 

2 0 0 

ul « , 
cnr-g^^ 0 
2 * 2'o 
3 §-icj 

04 + 

> rt 00 

-- 0 
M O 0 

C t^^to 

co CO CO 

CO CO H - 

*t Tf tt 

ttt 


vo VO VO 

485 8? 

OCvO 

vo 

M H H 

w M M M 

H M iH 

H HH HH 

M H M 

H H H 

H - M 

H H W 

h - M 

Hi H HH 







_ ____ 

__ 

_ 


h N 0) 

01 CN CN 
—''—/ 

vovO N 

Cl Cl CN 

00 O' 0 

N ft to 

M CN CO 
CO CO CO 

rf vovC 

<0 CO CO 

X"» 00 0 
CO co co 

0 M CN 
rf rf rf 

co rf vo 
rf rf rf 

vO X^ OO 

rf rf rf 




































































A TREATISE ON CONCRETE 


37 8 

is greater with rich than with lean concrete, but on the other hand, tests 
of specimens made at the Watertown Arsenal indicate the reverse. The 
difference is slight in both cases, however, and it may be assumed for 
practical purposes that the rate of growth is approximately the same what¬ 
ever the proportions. A wet consistency of the concrete produces lower 
strength, especially at early periods, and a larger percentage of growth 
than is indicated in the diagram. (See page 383.) 

The curve does not apply to concretes of Natural cement mortar. 12-inch 
cubes of concrete in various proportions made from Akron Star cement 
tested at the Watertown Arsenal for William Wirt Clarke & Son* show an 
average ratio of increase in strength between one month and one year of 
1.96. With this series of specimens the average strength at the age of one 
year was no greater than at seven months, but this is probably an excep¬ 
tional case, since, for instance, tests by Capt. William M. Black on 
Natural cement concrete show a slower and continual growth, with an 
equally large ultimate strength. 

TRANSVERSE STRENGTH OF CONCRETE 

The strength of a beam of plain concrete is limited by the tensile strength 
of the concrete at the place of greatest strain, which, with vertical loading, 
is its lowest surface. The value of this transverse “fiber” strength or 
modulus of rupture is of less importance than the crushing strength, be¬ 
cause, on account of the brittleness of concrete in tension, that is, its 
liability to crack from shrinkage or sudden loading, it is seldom safe, and 
usually is not economical, to construct beams or girders without metal 
reinforcement. Most formulas for reinforced design disregard the tensile 
strength of the concrete. In certain computations, however, the tensile 
strength must be considered. Since concrete beams can be broken with 
less powerful and less expensive apparatus than crushing specimens, this 
form of specimen is often convenient for comparing the relative strength 
of different mixtures or different materials, and while the ratios thus ob¬ 
tained will not exactly coincide with those for crushing strength, they will 
be sufficiently close for many purposes. 

Fuller’s Beam Tests. The tablef on page 376 gives the results of a 
comprehensive series of tests of 6 by 6 by 72-inch beams made by Mr. 
William B. Fuller at Little Falls, N. J. Although different materials 
than those used by Mr. Fuller will of course show slightly different 
strength, the table is sufficiently representative of average conditions to 
permit its use for comparisons of different proportions, and, with a proper 

*Tests of Metals, U. S. A., 1901, p. 609. 

f Especially prepared for this treatise by Mr. Fuller. 


STRENGTH OF PLAIN CONCRETE 


3 79 


factor of safety, as a working guide to the safe transverse strength of con¬ 
crete. 

The proportions are given by weight but can be transformed to 
volume measure by referring to the footnote. The various columns 
present valuable data on weights and volumes and voids. 

The curves in Fig. 123 are plotted from the results in the table, and 
illustrate also the proportions corresponding to maximum strength for a 
given per cent, of cement. 

Tests by other authorities are mentioned under Strength of Beams in 
References, Chapter XXXI. 



Fig. 123. Curves showing strength of beams in pounds per square inch for various 
proportions by weight of sand and stone to one part Portland cement. Age 34 days 


Formula for Transverse or Bending Stress in Plain Concrete. The 

common formulas for representing the longitudinal forces of compression 
and tension upon a beam are usually expressed with the following notation: 


/ 

M 

I 


y 

b 

h 


Let 

= intensity of stress at any point in the beam. 

= bending moment. 

= moment of inertia about its neutral axis of section containing the 
point under consideration. 

= distance of the point from the neutral axis. 

= breadth of beam. 

= height of beam. 

Then , My , v , ,, // 


My 

f- ~ 


(5) 


also, M = 


( 6 ) 

























































38 ° 


A TREATISE ON CONCRETE 


For rectangular sections, / = —- and up to the elastic limit for beams 

12 

of homogeneous material (but not for reinforced beams), y = \h. 

Hence for rectangular beams of homogeneous material, 


6 M 
~bh? 



also, M - — / b h 2 (8) 

o 


In considering the strength of a beam, since the stress is greatest at one 
or the other of the surfaces, y is generally understood to represent the dis¬ 
tance of the most strained fiber from the neutral axis, and / the intensity of 
stress upon this fiber. 

The neutral axis —• which is the line formed by the intersection of any 
cross section with the neutral plane, the plane upon which there is no 
longitudinal stress of either tension or compression — in a beam of homo¬ 
geneous material passes through the center of gravity of the cross section. 
This is true for mortar and concrete which contain no reinforcement in the 
earlier stages of loading. Since, however, the neutral axis passes through 
the center of gravity of the beam only within the elastic limit,* the fiber 
stress, /, at the breaking point, as obtained by the common formula, does 
not represent the actual tensile stress upon the material. The comparative 
relations between different results, however, are unaffected by this limita¬ 
tion of the law, and the formula can therefore be used for comparing the 
strength of beams composed of similar material. For example, while 
the stresses at the instant of breaking, that is, the moduli of rupture, as 
figured by the formula, are not strictly correct either for 8 or io inch 
beams, they are nearly proportional to the actual stresses, so that the 
strength of plain concrete beams of different dimensions may be com¬ 
pared by means of the formula without appreciable error. 

For convenience in designing, a table is given in Chapter XXI for 
bending moments caused by uniformly distributed loads and for loads 
concentrated at different points. Also, in the same chapter, the moments 
of inertia, I, for various sections are tabulated. These tables are applic¬ 
able for the most part to both plain and reinforced beams. 

* Although concrete and mortar have no true elastic limit the general principles apply to 
beams of these materials. 




STRENGTH OF PLAIN CONCRETE 


3 Si 

Relation of Transverse to Compressive Strength of Concrete. There 
is no fixed relation between the tensile fiber stress of concrete beams and 
the crushing strength of specimens made from the same material under 
identical conditions. The growth of strength is different in the two classes 
of tests, and although the general laws of increase in strength due to in¬ 
creasing the percentage of cement and the density appear to hold in both 
cases, the authors’ formula given on page 356 for compressive strength is 
not applicable to transverse tests. 

Experiments by the authors comparing 8-inch cubes and 8-inch beams 
of 1: 2J: 5 concrete give a ratio of crushing strength to modulus of rupture 
at one and two months of 6: 1. 

Mr. A. Fairlie Brucej* states from his experiments on the strength of 
concrete bars and arch ribs that he found the ratio between the crushing 
strength of the arch and the modulus of rupture of the bars to be about 
6: 1 for concrete two to four weeks old, then increasing to about 10: 1 at 
the age of six months. 



NUMBER OF REPETITIONS PRODUCING FAILURE. 

Fig. 124.— Fatigue of Neat Cement under Compression. {See p. 381.) 

THE FATIGUE OF CEMENT 

The action of cement under repeated stresses has been slightly investi¬ 
gated by Prof. J. L. Van Ornum* at Washington University. The ex¬ 
periments were made upon 2-inch neat Portland cement cubes four weeks 
old. The results of tests on 92 blocks are shown in the diagram in Fig. 124. 
The effect upon concrete of repeated applications of a load is discussed 
in the following chapter. 

Engineering Record , Oct.31, 1903, p. 533. 

* Transactions American Society of Civil Engineers, Vol. LI, p. 443. 





































































































































3 8 2 


A TREA VISE ON CONCRETE 


STRENGTH OF CONCRETE IN SHEAR 

The actual strength of concrete* in direct shear is much greater than 
was formerly supposed because in many of the earlier tests this was con¬ 
fused with diagonal tension which, as indicated in the following chapter, 
may be dangerous in a beam even when the vertical shear is small. Owing 
to the difficulty in eliminating in experiments the effect of bearing action, 
diagonal tension and beam stresses in general, it is not easy to devise a form 
of test specimen and a manner of testing which will determine satisfactorily 
the resistance of concrete to direct shear. In tests made at the Massa¬ 
chusetts Institute of Technology under the direction of Prof. Charles M. 
Spofford in 1904 and 1905, the final failure of the specimens appeared to 
be by true shear. These tests gave a shearing strength ranging in general 


Shearing Strength of Concrete 
By Prof. Charles M. Spofford. 

Massachusetts Institute of Technology. (See p. 382 ) 
Age of Concrete 24 to 32 days. 


Mixture. 

Method of 
Storing. 

Shearing Strength lb. per sq. inch. 

Average 
Compressive 
Strength in 
lb. per sq. 
inch. 

Ratio of 
Compression 
to Shear. 

Maximum. 

Minimum. 

Average. 

1 : 2 

: 4 

Air 

1630 

960 

1310 

2070 

0.63 

i : 2 

: 4 

W ater 

2090 

1180 

1650 

2620 

0.63 

1 •• 3 

• 5 

Air 

1590 

890 

1240 

1310 

0 • 95 

1 •' 3 

•' 5 

W ater 

1380 

840 

1120 

1360 

0.82 

1 : 3 

: 6 

Air 

145 ° 

950 

n8o 

950 

1 . 24 

1 : 3 

: 6 

W ater 

1200 

I 040 

1120 

1270 

0.88 

Average 

Ratio for 1:2: 

4 and 1:3:5 Concrete 


0.76 


from 60 to 80 per cent of the compressive strength of the concrete, which 
agrees substantially with experiments made by Prof. Arthur N. Talbotf 
in 1906. 

This direct shear must not be confounded with shear in a beam involv¬ 
ing diagonal tension where the concrete may break with a shearing 
stress 10% of the crushing strength. 

At the Institute three grades of concrete were used, and the specimens 
were stored both in air and water. The test specimens were cylinders 5 
inches in diameter by 18 inches long, and in testing, the end thirds of the 

* Shearing tests of mortar, by Mr. Feret, are recorded on page 136. 

f University of Illinois, Bulletin No. 8, 1906. 























STRENGTH OF PLAIN CONCRETE 


383 


cylinders were held rigidly by cast iron yokes, the pressure being applied 
through a cast iron half cylinder bearing, fitting between the two yokes, 
so as to shear the concrete across two planes. To compare the compressive 
strength of the concrete with the shearing strength, six extra cylinders of 
the same dimensions were crushed. The following table gives the relation 
between the shearing and crushing tests. 

From the experiments made at the University of Illinois, referred to, the 
conclusion was drawn that the resistance to shear is dependent upon the 
strength of the stone as well as upon the strength of the mortar, and for 
the richer mixture the strength of the stone probably exerts the greater 
influence. 

EFFECT OF THE CONSISTENCY UPON THE STRENGTH 

The general result of experiments and practice tends to show that the 
strongest concrete can be secured with a mixture containing only sufficient 
water to produce a film of mortar upon the surface after very hard ramming 
in thin layers, but with a wetter “quaking” mixture the ultimate strength 
will be nearly as high as with the dry mixture, and because of the greater 
ease in laying and obtaining a homogeneous mass, it is generally to be 
preferred. An excess of water injures the cement by decomposing parts 
of it before it has had opportunity to set. The actual strength of concrete 
is often of less importance than other consideiations. If, as in many classes 
of structures, there is an excess of strength, cheapness in placing, the ap¬ 
pearance of the surface, or the proper imbedding of reinforcing metal, 
may be of primary importance. In such cases the quantity of water must 
be suited to the attendant conditions. 

The curves in Fig. 125 are plotted from experiments by the authors* upon 
the strength, densityf, and permeability of the concrete mixed with different 
percentages of water. In the three curves the points of maximum density, 
strength and water-tightness all lie not far from the medium quaking con¬ 
sistency, although for maximum water-tightness a still softer consistency 
appears to be slightly more efficient. 

These tests further indicate that (1) the consistency which will pro¬ 
duce the densest concrete will result in the greatest ultimate strength pro¬ 
vided an excess of water is not employed; (2)dry mixtures attain highest 
strength at short periods, but mixtures of quaking consistency approach 
the dryer specimens after longer setting; (3) very wet mixtures, especially 
of lean proportions, may be chemically injured, by the excess of water. 

* Proceedings of American Society for Testing Materials, "Sol. VI, 1906, p. 35 ^’ 

•J- See p. 1 for definition and p. 138 for method of determining density. 


3 8 4 


A TREATISE ON CONCRETE 


Effect of “Laitance.” Whenever concrete is laid under water, the 
water is likely to be clouded by what appear to be particles of cement 
floating up from the mass which is being laid. This whitish substance is 
generally termed “laitance.” A similar formation occurs on the surface 



Fig. 125.—Comparative Permeability, Strength and Density of 1 : 2 A : 4 i 
Concrete, mixed with Different Percentages of Water, 

By Taylor and Thompson. (See p. 383.) 


of concrete laid with a large excess of water. In certain cases, we have 
found as much as J inch rising from a layer of 1 : 2^ : 5 concrete less than 
five inches thick. 


















































































































































































































































































































































































































































































































































































































































































































































































































































































































































STRENGTH OF PLAIN CONCRETE 


385 


Chemical and microscopical analyses, which Mr. Clifford Richardson 
has very kindly made for us, show that this laitance has nearly the same 
chemical composition,* except for a large loss on ignition, as normal Port¬ 
land cements, but consists largely of amorphous material of an isotropic 
nature,—that is to say, it does not affect polarized light, and has almost 
no setting properties. 

It is evident, therefore, that when concrete or mortar is laid under water, 
or with a large excess of water, a portion of the cement is rendered incapable 
of setting, and the strength of the mass is consequently reduced in propor¬ 
tion to this loss. The conclusion is naturally reached that for concrete 
laid under water, or in locations where a large excess of water is required 
in mixing, a higher percentage of cement than usual, about one-sixth 
more, should be employed. 

A lean mixture has been found to be more seriously injured by an excess 
of water than a rich one, probably because the water has a greater oppor¬ 
tunity to penetrate the mass, and therefore to dissolve the cement. 

GRAVEL VS. BROKEN STONE CONCRETE 

Comparative tests of broken stone and gravel concretes, in the same 
proportions by volume, show almost invariably that concrete made from 
hard broken stone, such as trap, or hard limestone, gives higher compressive 
strength than concrete made from gravel. This appears to be the rule 
not only when the materials are mixed by measured volumes, regardless of 
the percentages of voids, but also when the broken stone and gravel are 
each screened to substantially the same sizes. 

The relative values of gravel and broken stone concrete in the table 
which follows are based on the comprehensive series of a comparative test 
made by Mr. Candlot in France and tabulated on page 367. 

/ 

Comparative Strength of Broken Stone and Gravel Concrete. 

From Candlot’s Experiments 

Ratio of strength of broken stone concrete to gravel concrete. 


Broken stone 47.4% voids. 

Age. With equal voids Gravel, 40% voids. 

7 days . 1.30 1.33 

1 month . 1.26 1.19 

6 “ . 1.18 1.20 

1 year . 1.12 1.09 


Each ratio gives the extra strength of broken stone over gravel con¬ 
crete of similar age. For example, if a concrete containing gravel having 


* See page 302 * 






386 


A TREATISE ON CONCRETE 


40 % voids tests 2 000 lb. per sq. inch at the age of six months, a concrete 
in similar proportions by volume containing broken stone with 47.4% 
voids should, according to Candlot’s experiments, test 1.20 times greater 
or 2 400 lb. per sq. inch. 

The last column is averaged directly from Candlot’s table, and may be 
taken as applicable to average conditions. It is noticeable that the gravel 
concrete approaches the broken stone concrete as its age increases. Since 
in many cases the ultimate strength of concrete is determined by the strength 
of its coarse aggregate, it follows that at, say, the age of a few months 
a gravel concrete may reach or surpass the strength of a broken stone 
concrete having a coarse aggregate of soft stone of low strength. 

Although the claim is frequently made that gravel concrete is stronger 
than broken stone concrete, the authors have failed to find substantial 
proof of this. On the other hand, various records, among them a number 
of tests at the Watertown Arsenal,* as well as the tests tabulated on page 
388, tend to show the probable accuracy of Candlot’s tests. 

Another argument in favor of broken stone concrete lies in the fact that 
gravel is often covered with a film of dirt, difficult to remove, which lowers 
the strength. In experiments for the East Boston Tunnelf by Mr. Howard 
A. Carson, Chief Engineer, concrete beams made with washed gravel were 
about one-third stronger than beams made with gravel coated with a thin 
film of dirt. 

Advocates of gravel concrete, among them Mr. R. Feret,J assert that 
as the rounded stones slip more readily into place, it is easier to make 
with them a compact mass. Loose rounded stones also contain a smaller 
percentage of voids than angular, but this is at least partly offset by the 
fact shown by the experiments of the authors, tabulated on page 171, that 
broken stone compresses more on ramming. 

Although the weight of evidence apparently favors broken stone concrete, 
it by no means follows that broken stone always should be used to the 
exclusion of gravel. In many instances, the ultimate strength of the con¬ 
crete is of minor importance because the proportions of the concrete are 
determined by other considerations. Often, where strength is the cri¬ 
terion, but gravel is cheaper than broken stone, an additional percentage 
of cement may be economical. Moreover, the ultimate strength of gravel 
concrete is undoubtedly greater than that of concrete made with a poor 
quality of broken stone. With fixed proportions, as discussed on page 15, 

♦Tests of Metals, U. S. A., 1898, pp. 649 to 654. 
f Boston Transit Commission, 7th Annual Report, 1901, p. 39. 
t Chimie Appliquee, p. 533. 


STRENGTH OF PLAIN CONCRETE 387 

gravel is cheaper for the contractor than broken stone, because a given 
loose volume makes a larger quantity of concrete. 

As indicated on page 388, in mixtures of like proportions by volume, 
the gravel concrete will have less cement in a cubic yard of concrete than 
a broken stone concrete unless the stone is well graded. Under ordinary 
conditions to attain concretes of nearly equal strength, with gravel and 
with broken stone, the sand should be proportioned in each according to 
the volume and dimensions of the voids in the stone,* * * § and the quantity 
of cement per unit volume of compacted concrete should be the same in 
each. The gravel concrete thus will be apt to be the denser, and this 
will tend to overcome the slight difference in strength due to the varying 
character of the surfaces of the particles of the gravel and broken stone. 

Sometimes it is advantageous to mix a small percentage of gravel with 
broken stone. 

In comprehensive tests at the U. S. Government Laboratories, St. Louis,f 
upon concrete beams, cylinders and cubes of different aggregates, a granite 
concrete was about 10 per cent stronger than a gravel concrete made of 
exceptionally clean hard gravel pebbles, while the gravel concrete showed 
a strength about 10 per cent greater than that attained by a limestone 
concrete. 

Tests made by Messrs. William B. Fuller and Sanford E. Thompson^ 
at Jerome Park Reservoir, New York City, in 1905, upon the density and 
strength of concrete with different aggregates are illustrated in the curves 
in Fig. i26.§ Because of the greater density, the proportions by volume 
being the same, the specimens made with gravel and sand contained, in the 
set concrete, a slightly larger percentage of cement, so that the strength of 
the gravel concrete is slightly higher than if allowance had been made for 
this. The relatively low strength of the concrete with broken stone and 
screenings may be due in part to the character of the screenings, since tests 
by other experimenters have sometimes given exceptionally high strength 
when screenings were used. 

The following conclusion was drawn with reference to the relative strength 
of broken stone and gravel concrete. 

A concrete with an angular coarse aggregate, such as broken stone, is 
stronger than one with a rounded coarse aggregate, like gravel, and the 

* This can be better accomplished by trial mixtures, thoroughly compacted, of the dry aggregate, 
or, still better, of small batches of concrete, than by water measurements of the voids. The propor¬ 
tions of the aggregates giving the smallest bulk of concrete to a given weight of the mixture of aggre¬ 
gates will be the best. Also, see Chapter XI on Proportioning. 

•j- U. S. Geological Survey, Bulletin No. 344, 1908. 

J Transactions American Society of Civil Engineers, Vol, LIX, p. 67, 1907 

§ Engineering News, May 30, 1907, p. 599. 


3 88 


A TREATISE ON CONCRETE 


same sand and cement—although the rounded aggregate produces greater 
density—thus indicating a stronger adhesion of cement to broken stone 
than to gravel. However, if the sand is also angular, like screenings, but 


BROKEN STONE BROKEN STONE 

AND SCREENINGS GRAVEL AND SAND AND SAND 




average transverse strength 


>- 

h 

CO 

z 

UJ 

a 


.850 


.300 


.750 


< 

10 GRADED_' 

-——— TTTi 

cm;— —— 







BROKEN STONE GRAVEL AND SAND BROKEN STONE 

AND SCREENINGS AND SAND 


AVERAGE DENSITY 


Fig. 126 . —Comparative Density and Strength of Concrete made with 
Different Aggregates. By Fuller and Thompson. (See p. 387) 


with its grains of the same sizes as the sand, the concrete with rounded 
coarse and fine aggregate is the stronger, probably because of its greater 
density. 








































STRENGTH OF PLAIN CONCRETE 389 

EFFECT OF THE SIZE OF STONE OR GRAVEL UPON THE STRENGTH 

OF CONCRETE 


The dimensions of the largest particles of stone and gravel which may 
be used in a concrete are often limited by practical considerations of mixing 
and placing. For ordinary work it is often specified that the stone shall 
pass through a 2-inch, or, more often, through a 2^-inch ring. For ordinary 
mass concrete of wet consistency the limit may be placed as high as 3 



.850 

H 

« .800 
in 

D .750 


Fig. 127. —Comparative Density and Strength of Concrete made from 
Broken Stone of Different Maximum Sizes. Proportions 113 :6. 

Age, 140 Days. (See p. 390.) 

inches. In some cases, however, the stone must be small enough to pack 
readily around reinforcing metal, while in walls whose surface is to be 
picked or washed as described on page 289, a better appearance will result 
with stones under, say, one inch diameter, although the strength of con¬ 
crete appears generally to increase with the size of the largest particles of 
stone in the mixture. This is illustrated with the gravel and the finer trap 
in experiments by Mr. Howard* at the Watertown Arsenal upon 12-inch 

*Test on Metals, U, S. A., 189S, p, 65"4< 


































390 


A TREATISE ON CONCRETE 


cubes of i : i : 3 concrete made with uniform stone of different sizes. The 
weights of the specimens indicate that the increase of strength is due pri¬ 
marily to the density. The higher the limit of size the greater the variation 
in the sizes of material and therefore the greater the density of the mixture. 

John Kyle* nearly doubled the strength of i : 2 : 6 concrete made with 
ij-inch stone by substituting 4 parts of 3j-inch stone for a like portion of 
the i^-inch. 

Tests by Messrs. Fuller and Thompsonf showing the effect of aggre¬ 
gates of different maximum size are illustrated in the curves in Fig. 127. 

From these tests the following conclusions were drawn: 

1. —Stone of the largest size makes the strongest concrete under both 
compression and transverse loading, i.e., a graded aggregate in which the 
maximum size of the stone is 2J in. in diameter gives stronger concrete than 
a graded aggregate with i-in. maximum size, and the i-in. stone gives a 
stronger concrete than ^-in. stone. A concrete in which the graded aggre¬ 
gate runs to 1 in. in maximum size will require for equal strength about 
one-sixth more cement, and with an aggreate running to ^-in. maximum 
size, about one-third more cement than concrete with an aggregate in which 
the maximum size is 2J in. 

2. —The largest stone makes the densest concrete. Concrete made with 
graded stone having a maximum diameter of 2J in. is noticeably denser 
than that with i-in. stone, and this is denser than that with ^-in. stone. 

EFFECT OF THE QUALITY OF THE STONE UPON THE STRENGTH 

OF CONCRETE 

The ultimate strength of concrete is often limited by the texture or 
strength of the coarse aggregate. This is evidently the case with cinder 
concrete. . Experiments by Mr. Geo. W. RafterJ gave the strength of con¬ 
crete made with hard broken sandstone and various proportions of mortar 
from 1.5 to 2.4 times the strength of similar mixtures of broken shale and 
mortar, and this discovery led to the rejection of the latter as a material 
for concrete. 

Tests of the authors upon 12-inch cubes broken at the Watertown 
Arsenal lead them to believe that at least in certain cases the ultimate 
strength of a concrete is actually fixed by the shearing strength of the 
particles of stone which make up the aggregate. Cubes in proportions 
1 : 2J : 4§,—based on a cement barrel of 3.8 cubic feet,—attained an ulti¬ 
mate strength of 5000 to 5500 pounds per square inch. On account of 


♦Proceedings Institution of Civil Engineers, Vol. LXXXVII, p. 88. 

-j- Transactions American Society of Civil Engineers, Vol. LIX, p. 67, 1907. 
t Second Report on the Genesee River Storage Project, New York, 1894. 


STRENGTH OF PLAIN CONCRETE 


39i 


differences in the methods of mixing and ramming, some of the speci¬ 
mens reached this limit at the age of two months while others did not 
attain it for six months; but it was noticeable that at whatever period the 
ultimate strength was reached the planes of fracture were smooth, break¬ 
ing through each piece of stone, whereas before the ultimate strength was 
reached many of the stones pulled out from the concrete, leaving jagged 
instead of smooth surfaces on the pyramids remaining after the cubes 
were broken to destruction. The stone employed for these specimens was 
a hard, dense trap. If a weaker stone had been used, it is probable that 
the pieces would have sheared at a much earlier period and the ultimate 
strength would have been lower. 

Tests at the United States Government Laboratories at St. Louis § upon 
6-inch cubes of exceptionally good 1:2:4 concrete 26 weeks old, made with 
different coarse aggregates, show the following average ultimate strengths: 

Granite concrete, 4750 pounds per square inch. 

Gravel concrete (quartz pebbles), 3810 pounds per square inch. 

Limestone concrete, 3460 pounds per square inch. 

Cinder concrete, 2320 pounds per square inch. 

If concrete is mixed in such proportions or by such methods that the ulti¬ 
mate strength is reached before the stones shear, the strength of the particles 
Of stone is a much smaller factor in the result. 

Tests of crushing strength of building stone made by Mr. Richard L. 
Humphrey * give the relative strength of specimens of several kinds of 
stone: 

The average of a large number of tests of 2-inch cubes, part on edge 
and part on bed, by Gen. Q. A. Gillmore, and quoted in Burr’s “ Materials 
of Engineering, ”f shows average results for granite and sandstone almost 
identical with the average of Humphrey’s tests on these materials, while 
the average strength of specimens of limestone and marble was about 
13 000 lb. per square inch. Tests at the Watertown ArsenalJ give the 
crushing strength of 4-inch cubes of sound trap rock as 33 300 lb. per 
square inch, and of seamy trap as 19 400 lb. 

The table giving results of Mr. Humphrey’s test is especially interesting 
as showing in a general way that the heaviest rock is apt to have the highest 
strength. Of the 8-inch cubes tested on their bed, so as partially to elimi¬ 
nate the effect of cleavage planes, the specimen of quartzite is the only one 
which does not follow this rule. In Gillmore’s tests mentioned above, the 


§ U. S. Geological Survey Bulletin, No. 344, 1908. 

* As tabulated by Edwin C. Eckel in Engineering and Mining Journal , June 20, 1902, D. 921- 
J Edition of 1903, p. 433. 

| Tests of Metals, U. S. A., 1898, p. 577. 


39 2 


A TREATISE ON CONCRETE 


variation in the same kind of stone from different localities is large, but in 
each kind the heavier rocks usually give the higher resistances. We may 
state, therefore, as a general rule in comparing rocks of the same kind, that 
those of the highest specific gravity are apt to be the strongest, and this rule 
may be extended in many cases to the comparison of different kinds of rock, 


Crushing Tests of Cubes of Stone. 

By Richard L. Humphrey. ( See p. 391.) 


Location. 

Kind of Stone. 

cr Weight per cubic foot. 

Specific Gravity. 

Absorption. 

Average Crus 

2-inch cube. 

ling Strength. 

8 -inch cube. 

Bed. 

fc d 
cv" 

a % 

Edge. 

a 

Bed. 

<D d 

a ^ 

Edge. 

b d 

a & 

Chester, Pa. 

Gneiss 

165.71 

2.69 

0-385 

6 097 

5 446 

9 5°5 

6 426 

Germantown, Pa. 

Gneiss 

176.23 

2.825 

0.135 

19 891 

*5 555 

11 636 

13 984 

French Creek, Pa. 

Granite 

190.46 

3 - 0 8 5 

o.i 55 

19 997 

14 348 

17 274 

7 9 IQ 

Conshohocken, Pa.... 

Mica schist 

177.76 

2.91 

o.i 55 

20 038 

15 680 

10 417 

7 532 

Curwensville, Pa. 

Sandstone 

146.00 

2.40 

2-335 

10 218 

8 013 

7 513 

4 463 

Lumberville, Pa. 

Quartzite 

158.19 

2.63 

0.998 

no test 

no test 

14 841 

8 637 


EFFECT OF PERCENTAGE OF CEMENT UPON THE STRENGTH 

OF CONCRETE. 

The strength of concretes of the same density made with similar mate¬ 
rials varies approximately with the percentage of cement, so that the com¬ 
parative strength of concrete in different proportions sometimes may be 
estimated sufficiently close for practical purposes. The following table 
gives the results of certain of the Jerome Park tests* by Messrs. Fuller and 
Thompson, where the density of the concrete was maintained nearly 
constant. 


DESTRUCTIVE AGENCIES 

The effect of sea water, frost, fire, and rust, are treated in Chapters XVI, 
XVII and XVIII. 

Effects of Acids. Experience shows that after concrete has thoroughly 
hardened, it resists the attack of diluted acids, such as are found in sewage, 
and that it is only seriously affected by strong acids which injure nearly all 
other materials. Concrete has proved to be the most successful lining for 
digesters in pulp mills, where sulphurous acid is present under high heat 
pressure. 


* Transactions American Society of Civil Engineers, Vol. LIX, p. 67, 1907. 






























STRENGTH OF PLAIN CONCRETE 


393 


Effect of Manure. Concrete of good quality after hardening is not 
affected by manure, although it may be injurious to green concrete.* * * § 

Effect of Oils. Testsf indicate that mineral oils do not injure concrete 
even if applied to it when only a week or two old. Animal fat and vegetable 
oils tend to disintegrate it if applied when the concrete is green, but these 
appear to be successfully resisted if the concrete has thoroughly hardened. 
Hardened concrete may be affected by the vapor from the melting of animal 
fat, probably because of the acid which it contains. Mr. Tochj: states that 


Comparative Density and Strength of Similar Concrete with Different Percen+~ 
of Cement and 2\-inch Stone Graded as an Elli se and Straight Lin' 

By Fuller and Thompson. {See p. 392.) 


ft 

Materials. 

Density with Different 
Percentages of Cement* 

Modulus of 
Rupture at 90 
Days, Different 
Percentages of 
Cement.* 

Compressive Strength 
at 140 Days, Dif¬ 
ferent Percentage^ 
of Cement. 

Stone. 

Sand. 

8% 

10 % 

12*% 

15 % 

8% 

10% 

124 

i 5 % 

8% 

10% 

I2i% 

i 5 % 

Crushed 

Screenings 

0.829 




18L 




980 




u 

0.846 



25o 



I 129 



a 

U 


0.832 



245 



I /* s 


u 

U 



0.839 



326 




1 634 

u 

ft 

0.871 



163 



990 

. 


Gravel 

Sand 

o .855 



245 



1 7 i 5 



U 

U 


0 .865 



307 



I 890 


u 

u 



0.867 



339 



2 04c. 












Averages 


0.8S0 

0. 85 o 

0. 848 

0.853 

176 

248 

276 

332 

985 

1 428 

1 654 

1 837 


Strength computed as proportional to the 
centage of cement, based on strength 
8% cement. 

per- 

with 

176 

220 

275 

330 

9 85 

12 30 

1 540 

1 85 . 


* In gravel and sand mixtures the percentage by weight of cement was increased in each case 
to balance the difference in specific gravity between this and the crushed material. 


«• 

the action of fat or vegetable oil is due to expansion caused by the formation 
of crystals of stearate and oleate of lime. Light oils, like kerosene or 
naphtha, penetrate any substance very readily, so that if concrete tanks are 
used for their storage, special precautions must be taken in their construc¬ 
tion. 

Effect of Electrolytic Action. Tests§ and experience indicate that con¬ 
crete is injured by electrolysis. However, there is less danger for plain con¬ 
crete or for reinforced concrete than for structural steel even if the latter 
is incased in concrete or other masonry. 

* See “Investigation of Collapse of Filter Roof during Construction at Lawrence, Mass.,’’ by 
Sanford E. Thompson, Journal New England Water Works Association, Vol. XXII, No. 2. 

■j- James C. Hain in Engineering News, Apr. 20, 1905, p. 279. 
j Engineering News, Apr. 20, 1905, p. 419. 

§ By A. A. Knudsen, American Institute Electrical Engineers, Vol. 26, p. 133, by Maximilian 
Toch, Engineering Record, June 30, 1906, p. 794, and by N. J. Nicholas, Engineering News, Dec. 
14, 1908, p. 710. 






























































n 394 


A TREATISE ON CONCRETE 


STRENGTH AND ELASTICITY OF CINDER CONCRETE 

Tests at the Watertown Arsenal* on t 2-inch cubes of cinder concrete 
mixed in different proportions gives results arranged in the following tables: 

Compressive Strength of 12-incli cubes of Cinder Concrete. 

Watertown Arsenal. (See p. 394.) 


Cement. 

Proportions 

Cement. Sand. Cinder. 

Age, 1 

month. 

Age, 3 

months. 

Mean weight 

lb. per cu. ft. 

Compressive 

strength lb. 

per sq. in. 

I 

Mean weight 

lb. per cu. ft. 

Compressive 

strength lb. 

per sq. in. 

German Portland. 

I 

I 

3 

112.1 

I 466 

110.4 

2 OOI 

- 

I 

2 

3 

115.2 

I 098 

112.8 

I.634 


I 

2 

4 

III .2 

9°4 

io 7-9 

I 325 


I 

2 

5 

108.8 

769 

io 5-3 

I 084 


I 

3 

6 

IO7.6 

529 

io 3*5 

788 

Ameiican Portland. 

I 

I 

3 

II7.2 

1 9 6 5 

115.2 

2 624 


I 

2 

5 

111 -3 

818 

110.0 

I 412 


Note: Each value for German cement is an average of three 12-inch cubes. Each 
value for American cement is an average of six 12-inch cubes made from two brands of 
first-class Portland cement. The exact age of the German cement specimens was 
38 and 99 days, and of the American cement specimens 31 and 90 days. 


Elastic Properties of Cinder Concrete, 12-inch cubes at three months. 
Watertown Arsenal. {See p. 394.) 


American Poriland 
Cement. 

Proportions. 

Age when Tested. 

Modulus of Elasticity 
between loads per sq. in. 

Permanent sets after loads 
per sq. in. of 

Com pressive 
strength lb. per sq. in. 

r 5 

<L> 

s 

0 

O 

a 

in 

C 

0 

C 

U 

100 and 
600 lb. 

0 

0 0 

0 0 

M .H 

1000 and 
2000 lb. 

Q 

O 

O 

VO 

A 

0 

0 

0 

£ 

O 

O 

O 

CS 


1 

1 

3 

90 

2 500 OOO 

2 500 OOO 

I 429 OOO 

0. 

.0001 

.0006 

2 780 

A 

1 

2 

5 

90 

I 087 OOO 

957 000 


.0008 

.0028 


I 402 


1 

2 

5 

90 

I 471 OOO 

I 286 OOO 


.0002 

.0010 


1 715 


1 

1 

3 

90 

4 167 OOO 

3 214 000 

I 190 OOO 

0. 

.0001 

.0014 

2 368 

B 

1 

1 

3 

90 

2 083 OOO 

I 875 OOO 

I 351 OOO 

.000 r 

.0002 

.0017 

2 580 


1 

2 

5 

90 

I 190 OOO 

849 OOO 


.0009 

.0066 


I 200 


1 

2 

5 

90 

I 087 OOO 

865 OOO 


.0024 

.0089 


I 265 


♦Tests of Metals, U. S. A., 1898, pp. 561 and 573. 





























































STRENGTH OF PLAIN CONCRETE 


395 


MAKING CONCRETE SPECIMENS FOR TESTING 

Complete and careful records must be made of the methods employed 
and the materials used in making concrete specimens for testing, in order 
to reach results of value for comparison with those of other experimenters. 
The lack of this care and accuracy has rendered the larger number of tests 
on concrete of only local significance. 

The practical relation of the density of a concrete to its strength, as 
discussed in the preceding pages, indicates that it is not merely necessary 
to measure roughly the materials entering into the composition, but that 
the exact amount of solid matter, the coarseness of the particles, the char¬ 
acter of the surfaces of the grains, the moisture in the materials, and the 
additional quantities of water used, must be very carefully recorded. 

The cost of making and testing concrete specimens is so great, that the 
additional time required for entering notes full enough to produce results 
of scientific value is insignificant. The blank form with the values in an 
actual test filled out is presented on page 396 for recording data relating 
to the making of concrete specimens. On the same form may be added 
places for recording the results of the tests. In most cases it is advisable 
for greater exactness to make separate batches for each specimen. 

In addition to the information outlined, mechanical analyses should be 
made of the aggregates as a part of the permanent records, and for the com¬ 
putations in the form, it is also necessary to determine the specific gravities 
of the materials. 

The specific gravity of Portland cement in most cases may be assumed 
as 3.1, and, in fact, the specific gravity of the sand may also be assumed 
without appreciable error as 2.65. For the specific gravity of other aggre¬ 
gates special tests are necessary. 

Concrete for experimental specimens should be mixed by experienced 
men. There is a certain knack in properly turning the materials so as to 
mix them thoroughly which can be acquired only by practice, and the 
amount and manner of ramming or puddling is so important that specimens 
may be rendered worthless by improper manipulation. 

The molds for specimens should be made of metal or of good quality 
lumber, preferably white pine, so that it will not twist or get out of shape, 
and the surface next to the concrete should be planed, and all joints made 
water-tight. The mold should be wet or greased before placing the con¬ 
crete. If metal, the grease or oil must cover every part of the surface. 
A wooden mold for two cubes is shown in Fig. 128. 

Dimensions of Specimens. Compression specimens are limited in size 


39^ 


Item. 

1 

2 

3 

4 

5 

6 

7 

8 

9 
i o 
11 

1 2 

*3 

14 

15 

16 

17 

18 

19 

20 

2 I 
22 

23 

24 

2 .S 

26 

27 

28 

29 

32 

33 

34 


Expt. No. _ 

File Waltham Reservoir. 
Date 2/9/061. 

Form for Recording Data on Concrete Specimens 
(Figures in ( ) refer to Item Numbers.) 

Nominal Proportions... 1 : 1.8 : 4.1 

Car No. 00 

Kind of Cement . Atlas 

Kind of Sand ... | u.c. {G 

Analysis No. 320 and 321 

Kind of Coarse Aggregate . W. Gravel 

Analysis No. 4.22 

Weight of Cement Used . 3.12 

Weight of Sand Used. 5.72 

Weight of Coarse Aggregate Used. 12.83 

Weight of Water Used. 1.77 

Per Cent Water to Weight of Cement plus Sand. 20% 

Temperature of Water. 6o° F. 

Temperature of Laboratory. 70° F. 

Total Weight of Material (8) + (9) + (10) + (n). 2 3-4-6 

Weight of Mold Empty . 500 

Weight of Mold Filled. 26.^0 

Weight of Concrete Net. 23.30 

Weight of Concrete Left Over. 0.00 

Weight Unaccounted for—Assumed as Solid Material*. 0.16 

Weight Unaccounted for—Assumed as Water. ■ 0.00 

Volume of Fresh Specimen (cu. ft.).• -0.1327 

Weight of Specimen—Mold Removed. 22.7 

Method of Storage . Air 

Weight of Specimen Before Testing. 22.3 

Measurements of Specimen Before Testing. .. .7.99" X 8.02" X 3.12" 

Date and Hour Specimen Made. 2/9—3 p.m. 

Date Tested. .. 3/9-10 a.m. 

Specific Gravitv Cement. . . .3.15 30. Sand. . . .2.65 31. Stone. ...27s 

(18") 

Weight of Cement in Fresh Concrete (8) X ;—v-;—r ? on 

& (18) + (19) + (20) " ’ ' J' u y 

(l8) 

Weight of Sand in Fresh Concrete (9) X 

Weight of Coarse Aggregate in Fresh Concrete 

(18) 

(10) X 


(18) -f (19) + (20) •* ‘ '5-68 


35 - 

3 6 - 

37 - 

38 . 

39 - 

40. 

41. 

42. 


(18) + (19) + (20) 

Weight of Water in Fresh Concrete (11) X 


12.76 


_(18)_ 

(18) -f- (19) + (20) 

Absolute Volume Cement in Fresh Concrete (assume 1 cu.ft.water, 62.4 lb.) 

_( 3 D)_ 

(22) X 62.4 X (29).. 

Absolute Volume Sand in Fresh Concrete 

( 33 ) _ 

(22) X 62.4 X (30). 

Absolute Volume Coarse Aggregate in Fresh Concrete 

( 34 ) 


.1.76 


0.103 


0.223 


( 35 ) 


(22) X 62.4 X (31) . 

Absolute Volume Water in Fresh Concrete 7- . 

(22) X (62.4) '' ’ 

Total Absolute Volume Materials (36) + (37) + (38) + (39) 

Density (36) +(37) + (38).'. 

Remarks . 


0.387 

0.183 


0.999 

0.815 


Computed by G. B. 
Checked by S. E. T. 

♦Adhering to Tools and Trays. Divide the Total Loss, (15) — [(18) + ( 19 )], by Estimation 
into Items (20) and (21). 













































397 


STRENGTH OF PLAIN CONCRETE 

by the capacity of the testing machine. The Emery Machine at the 
Watertown Arsenal, one of the largest in the world, has a capacity of 
800000 pounds, and the authors have had 12-inch concrete cubes tested 
there which reached this limit, so that 12 inches on a side may be fixed in 
general as the maximum size for specimens. For a lower limit it is doubtful 
if specimens less than 6 inches square can be made to give accurate results. 
A series of comparative tests by the authors upon 8-inch and 12-inch cubes 
gave much higher breaking strength per square inch for the larger size 



Fig. 128. -Mold for Concrete Cubes. (See p. 395.) 

specimens. It was evident from the lower unit weight of the smaller 
specimens, that the difference was due, at least in part, to variation in 
homogeneity. 

Cubes have been the common form of compression specimens and are 
suitable for comparative tests of ultimate breaking strength, but for study¬ 
ing the real value of concrete in compression, or for determination of 
elastic properties, long prisms are preferable. 

For column tests, the length of a specimen should be at least five times 
the largest lateral dimension. Both theory and practice show that beyond 
this point there is but little variation in the strength per square inch, pro¬ 
viding the loading is central. See p. 369. 
























39^ 


A TREATISE ON CONCRETE 


The specimen recommended for crushing tests by the Joint Committee 
on Concrete and Reinforced Concrete, and used at the U. S. Government 
Laboratories at St. Louis, is a cylinder 8 inches diameter by 16 inches long. 

For reinforced concrete beams the Committee recommended 8 by n 
inches by 13 feet long, testing this on a 12-foot span. 

Beams for testing the transverse strength of concrete are usually made 
from 6 to 12 inches square. The smaller size is satisfactory provided the 
mixture is a fairly wet one so that the corners and surfaces of the molds 
can be filled. For specimens 6 inches square a convenient length is 6 
feet, to be broken on a 60-inch span. The halves of the specimens may 
be afterwards broken to average with the full beam test or to compare the 
strength at different periods. Experiments prove that the ultimate fiber 
stress in the half beams will be practically, as well as theoretically, the same 
as that in the whole beams. 

Specimens for crushing must be faced with some material which will 
transmit the strain to all points in the surfaces. At the Watertown Arsenal 
plaster of Paris or neat cement is employed. After spreading the surface 
with a coat of plaster or cement, a block of polished steel is placed upon 
it, and it is allowed to set. Before crushing, the surface is tested with a 
straight-edge, and any irregularities are smoothed off with its sharp edge. 

Specimens for Rough Tests. If the quality of sand is questioned and a 
laboratory is not available, a rough test may be made by mixing up a block 
of mortar or concrete, using the same aggregates mixed in the same propor¬ 
tion and to the same consistency that is to be employed in the work and 
examining the specimens from day to day. If kept in a warm room under 
a moist cloth, the mortar or concrete should harden after 24 hours so as to 
resist the pressure of the thumb and at the end of a week in the air it should 
be hard and sound. 

Method of Quartering. To obtain an average sample from a pile of 
sand, gravel, or stone, the method of quartering is useful. Shovelfuls of 
the material are taken from the various parts of the pile, mixed together 
and spread in a circle. The circle is quartered, as one would quarter a 
pie, two of the opposite quarters are shoveled away from the rest, thor¬ 
oughly mixed, spread, and quartered as before. The operation is re¬ 
peated until the quantity is reduced to that required for the sample. 


REINFORCED CONCRETE DESIGN 


399 


CHAPTER XXI 

REINFORCED CONCRETE DESIGN 

Reinforced concrete is concrete in which steel or other metal is imbedded 
to increase its strength. Although it has been employed generally as a 
building material for only a few years, the laws governing the effective 
combination of concrete and steel are now sufficiently well established to 
enable the engineer to design a structure with assurance of permanent 
strength and durability. 

Occasional failures have occurred in reinforced concrete construction 
through neglect of essential principles. The causes have been (i) poor 
design, particularly in the details which do not occur in steel design; (2) 
poor materials, especially poor sand; (3) misplacement of reinforcement; 
and (4) too early removal of forms. These are all readily preventable 
causes under careful engineering and superintendence. Some of the more 
important points to guard against are outlined in Chapter II, page 28a. 

Until recently there has been considerable divergence in the theory of beam 
design and of column design. Authoritative reports were brought out iti 
Europe in 1907 and 1908. In America, the Joint Committee on Concrete 
and Reinforced Concrete presented its first Progress Report early in 1909. 
This Joint Committee U composed of members selected from the American 
Society of Cb il Engineers, the American Society for Testing Materials, the 
American Railway Engineering and Maintenance of Way Association, and 
the Association of American Portland Cement Manufacturers, and there¬ 
fore represents the highest authority in the United States. Its recommen¬ 
dations have tended to standardize general practice. 

In this chapter the recommendations on design of this American Joint 
Committee have been followed, not only because of their general acceptance 
as a standard, but because they agree with the views of the authors and 
represent the most satisfactory rules thus far formulated. This has necessi¬ 
tated no changes in the methods of analysis given in the first edition, since 
the theory of stress there presented has since been generally adopted. 

Results of recent tests have made possible a more complete treatment of 
the details of design, and extensive study and investigation have led to the 
addition of simple working formulas and practical recommendations. 

In general, only brief discussions together with the rules and principal 
formulas for design are given in the text, the analytical treatment of each 


A TREATISE ON CONCRETE 


^oo 


subject being transferred to the Appendix or printed in footnotes for the 
use of readers interested in the theory. 

In the following pages, then, are discussed: 


Fundamental principles of the combination of steel and concrete. 
General principles of design and formulas for rectangular beams 

and slabs. 

Simple formulas for T-beams. 

Design of the ends of continuous beams next to the supports. 

Reinforcement for diagonal tension and shear . 

Bond of steel to concrete. 

Details of beam design. 

An example of floor design. 

Theory of the design of flat slabs. 

Bending moments and shears from an elementary standpoint. . . . 

Distribution of loads. 

Tables and curves for beam and slab design. 

Tests of reinforced beams. 

Columns of plain concrete, vertically reinforced, and hooped. 

Reinforcement for temperature contraction. 

Types of reinforcement. 

Analyses for the derivation of beam formulas, including: 

Simple rectangular beams. 

T-beams. 

Beams with steel in both tension and compression. 

Beams with concrete bearing tension. 

Simple beams treated by the parabolic theory. 


400 to 416 


416 to 422 
423 to 426 
427 to 430 
441 to 456 
456 to 461 
441 to 461 
468 to 475 
483 
433 
43 1 

507 to 526 
.... 477 


488 

500 

5°4 


75i 

754 

757 

760 

762 


In other parts of the treatise are discussed various special types of 
reinforced concrete construction and details of design, including: 


Arch design. 533 

Retaining wall design. 659 

Footings. 644 

Building construction. 607 

Chimney design. 630 

Analysis for circular beams and chimneys. 765 

Conduits. 679 

Tunnels. 689 

Dams. 674 

Reservoirs and tanks. 695 

Specifications for first-class or high carbon steel . 38 

Protection of metal from corrosion and fire. 327 

The notation adopted in the formulas is the Standard Notation as 
adopted by the Joint Committee...*. 529 


GENERAL PRINCIPLES OF REINFORCED BEAMS 

A concrete beam, when reinforced with iron or steel rods properly placed, 
develops a capacity for carrying loads several times greater than its carry¬ 
ing capacity when without reinforcement. It is evident that the location 
of the reinforcement in the beam must conform to the principles of mechanics 
so that the concrete shall be strengthened in its weakest part. Hence, since 
concrete is comparatively weak in its resistance to pull, reinforcing metal 


































REINFORCED CONCRETE DESIGN 


401 


should be placed where it will aid the concrete in carrying tension. In a 
beam or slab the metal should be as near to the surface on the tension side 
of the beam as is consistent with properly imbedding it and providing a 
sufficient thickness of concrete to protect it from rust and lire. 

Since concrete is a brittle material and steel a comparatively ductile one, 
it might be expected that the stretching of the tension surface of a beam 
would result in the formation of cracks on the under surface of the concrete, 
and that all the pull would be imposed upon the steel. Tests by Prof. 
Frederick E. Turneaure* and others have shown that cracks in the concrete 
are actually produced by the tension and that the tension load is thus trans¬ 
ferred to the metal. However, while these cracks reduce the strength of the 
concrete, they are so minute, being at first invisible to the naked eye, and 
so distributed over the section, that the reinforcing metal, as shown by 
tests, is protected by the concrete from corrosion even up to the point of the 
elastic limit of the steel.f 

Not only must the steel be correctly located, but it is essential to have the 
proper quantity of metal in the beam. It is obvious that if the cross-section 
of the metal is too large as compared with the area of the concrete in com- 

5 

pression, the beam, in case of failure, will give way by compression in the 
concrete, whereas, if the area of the metal is too small, weakness will show 
itself as soon as the metal has reached its yield point, which is usually not 
far from one-half the actual breaking strength of the steel. The area of the 
reinforcing metal in rectangular beams and slabs is apt to vary according 
to the conditions from about \% to i\% of the area of the cross-section of 
the reinforced beam above the steel. For example, a beam 10 inches wide 
and 11 inches deep with steel one inch above its bottom surface (100 square 
inches net area) requires, according to circumstances, from | square inch 
to 1^ square inches section of steel. In any given design this area of rein¬ 
forcement should be determined from the character of the member and the 
strength and elasticity of the concrete and the steel. More than 1% of 
steel is not usually economical in a rectangular beam unless the concrete is 
allowed to be stressed beyond the high pressure of 750 pounds per square inch. 

In designing a beam composed of concrete with steel imbedded in it, 
the bending moment produced by the superimposed load,—which is termed 
the live load,—plus the weight of the beam itself, the dead load, must be no 
greater than the moment of resistance of the beam ( i.e ., the moment of the 
internal resisting forces of the strength of the concrete and steel) divided by 
a proper factor of safety. 

♦Proceedings American Society for Testing Materials, 1904 

-j-See page 410. 


402 


A TREATISE ON CONCRETE 


That which differentiates the study of a reinforced concrete beam from 
that of a beam composed of a single homogeneous material is the determina¬ 
tion of the pull, which is borne by the steel alone, and of the compression, 
sustained entirely by the concrete. The problem is rendered the more com¬ 
plex because the strength and elasticity of concrete vary through a wide 
range according to the nature of its ingredients and their proportions. 
Current practice, borne out by experiments made at various American uni¬ 
versities, indicates that beams may be designed on the assumption that the 
concrete in the upper part of the beam resists all the compression and the 
steel in the bottom of the beam takes all of the pull. This is always on the 
safe side, since the concrete assists the steel in tension to a slight degree. 
The theories of the distribution of the stresses in reinforced concrete, which 
are based on the elasticity of the concrete and the steel, are sufficiently 
accurate for the practical purposes of design. Before giving formulas and 
tables to be used in the design of reinforced beams, the principles govern¬ 
ing the assumption of the distribution of stresses and the properties of the 
materials will be considered. 

A Plane Section Before and After Bending. While experiments at 
the Massachusetts Institute of Technology indicate that the law of plane 
sections before and after loading docs not apply exactly to reinforced 
concrete beams, nevertheless, it is sufficiency accurate for practical 
purposes to assume it correct, viz: that if a plane section is taken through 
a beam before loading, after loading, this section, even though inclined to 
its original position by the bending due to the load, remains a plane section. 
From this it follows, as in the common theory of beams, that the stretching 
or shortening per unit of length of any fiber which cuts the section consid¬ 
ered may be assumed as proportional to the distance of this fiber from the 
neutral axis of the section. 


MODULUS OF ELASTICITY OF STEEL 

The modulus of elasticity of steel varies from 28 000 000 pounds per 
square inch to 31 000 000 pounds per square inch; 30 000 000 is customarilv 
taken as an average value, and is the value adopted in this treatise. 

All Steel, irrespective of its Ultimate Strength, Elastic Limit or Chemi¬ 
cal Composition, has Substantially the Same Modulus of Elasticity. It 
follows therefore from the principles of elasticity that the stretch under a 
given pull is independent of the character of the steel. 


REINFORCED CONCRETE DESIGN 


403 


MODULUS OF ELASTICITY OF CONCRETE 

The modulus of elasticity is an important item in reinforced concrete 
design and is discussed at length in the pages which follow. For practical 
design it is recommended that the ratio of the modulus of elasticity of 
steel to that of concrete be taken at 15 , corresponding to a concrete modu¬ 
lus of 2 000 000. 



DEFORMATION PER UNIT OF LENGTH • 

Fig. 129. Stress Deformation Diagram, Limestone Concrete Cylinders of 
Medium Consistency and Extra Good Quality.* {See p. 404). 


Determination of Modulus of Elasticity. The modulus of elasticity, E, 
may be taken as the quotient of the stress per unit of area divided by the 
deformation (that is, the elongation or the shortening) in a unit length. In 

* Bulletin No. 344, U. S. Geological Survey, p. 33. 



















































404 


A TREATISE ON CONCRETE 


customary English units where the modulus is in pounds per square inch, 

stress per square inch 
deformation per linear inch 

It is determined in the laboratory by measuring the deformation for the 
loads successively applied and plotting them as shown in Fig. 129. The 
cuives in the diagram represent the deformations, at different stages of the 
loading,for atypical cylinder 8 inches in diameter by 16 inches high of extra 
strong 1:2:4 concrete, tested at the St. Louis Government Laboratory in 
1907. The set, which is the permanent deformation when the load is 
released, is not indicated in the diagram because the total deformation is 
that which must be used in reinforced concrete analysis. 

The form of the deformation curve is approximately a parabola,* but 
the tests at St. Louisf indicate that for first-class concrete the modulus is 
nearly constant for about one-third of the ultimate strength. The modulus 

at this point is —, or 3 200 000 pounds per square inch, in the four 
0.00025 

weeks old concrete tested. 

Results of Tests. Numerous tests have been made to determine the 
modulus of elasticity of concrete which indicate as large a range in results 
obtained by different experimenters, even with concrete of the same pro¬ 
portions of cement to aggregate, as from 1 500 000 to 5 000 000 per square 
inch. The reasons for this are not yet fully determined; it has been 
conclusively proved, however, that the age of concrete, its richness and 
its density have undoubtedly a large influence on this variation. 

The following table, compiled from various tests, may be of value as 
suggesting approximate values of the modulus for different proportions of 
concrete based upon the total deformation at one-third the crushing 
strength of cylinders at an age of thirty days. Two columns are given, one 
for ordinary wet concrete of medium quality,, and one for concrete very 
carefully made with a dense mixture of mushy consistency and kept wet 
during hardening. -The “ordinary” values are slightly below those which 
should be expected in practice on construction work. 

The modulus of elasticity of concrete probably bears a definite relation 

to its ultimate strength, but the factors which enter into this relation 

probably will never be determined exactly. Plotting the results of a large 

number of tests made at the Watertown Arsenal, at the Government Labora- 

% 

* See discussion by Prof. Talbot in University of Illinois Bulletin, No. io, Feb. i, 1907, p. zu 

■j" Bulletin No. 344, U. S. Geological Survey, pp. 36-53. 




REINFORCED CONCRETE DESIGN 


405 


tory at St. Louis, and at many of the colleges, indicates an approximate 
ratio of 1300 between the modulus of elasticity and the ultimate strength. 

Kimball’s Tests. The moduli at different loads from tests of Mr. George 
A. Kimball made at the Watertown Arsenal upon 12-inch cubes are given 


Moduli of Elasticity of Concrete of Different Proportions. Approximate 

Average Values. (See p. 404.) 



PROPORTIONS. 

ORDINARY WET CONCRETE. 

EXCEPTIONALLY STRONG 

CONCRETE. 

Crushing 
Strength 
at 30 days, 
lb.per sq.m. 

Modulus 

of 

Elasticity 
lb. per sq. in. 

Crushing 
Strength 
at 50 days, 
lb.per sq in. 

Modulus 

of 

Elasticity 
lb. per sq. in. 

Broken stone or 






gravel concrete 

I : : 3 

2300 

2 500 ooo 

2800 

3 600 OOO 


1:2:4 

1700 

2 ooo ooo 

2500 

3 200 OOO 


1 : 2} : 5 

1500 

1 800 ooo 

2200 

2 800 ooo 


1:3:6 

1300 

1 600 ooo 

1900 

2 500 ooo 


1:4:8 

900 

1 300 ooo 

1500 

2 ooo ooo 


1:2:5 

700 

900 ooo 

1000 

1 300 ooo 


Note —A modulus of z ooo ooo, corresponding to a ratio of 15, is recommended for general 
use. 


in table below. The moduli are computed with the set deducted from 
the deformation, so that the values are slightly higher than would be obtained 
from total deformation. 

Elastic Properties of Broken Stone Concrete 12-inch Cubes. 


Portland cement,* bank sand and broken conglomerate stone. 
By George A. Kimball at Watertown Arsenal. (See p. 405.) 


COMPOSITION 

Age 

MODULUS OF ELASTICITY BETWEEN LOADS 
PER SQUARE INCH OF 

Compressive 
strength 
per sq. in. 

lb. 

Cement 

Sand 

Broken 

Stone 

IOO 

and 

600 

lb. 

IOO 

and 

I ooo 

lb. 

1 ooo 
and 

2 OOO 

lb. 

I 

2 

4 

7 days 

2 593 ooo 

2 054 OOO 

1 351 ooo 

I 730 

I 

2 

4 

1 mo. 

2 662 ooo 

2 445 000 

I 462 ooo 

2 567 

I 

2 

4 

3 mos. 

3 671 ooo 

3 170 000 

2 I 58 OOO 

2 975 

I 

O 

4 

6 mos. 

3 646 ooo 

3 567 ooo 

2 582 OOO 

3 9 8 9 

I 

I 

3 

6 

7 days 

I 869 ooo 

I 530 ooo 


1 511 

I 

3 

6 

1 mo. 

2 438 OOO 

2 135 OOO 

I 219 ooo 

2 260 

I 

3 

6 

3 mos. 

2 976 OOO 

2 656 OOO 

I 805 ooo 

2 741 

I 

3 

6 

6 mos. 

3 60S ooo 

3 5°3 000 

1 868 ooo 

3068 

I 

I 

6 

12 

1 mo. 

I 376 ooo 



1 146 

I 

6 

12 

3 mos. 

I 642 ooo 

I 364 OOO 


'i 359 

I 

6 

12 

6 mos. 

I 820 ooo 

I 522 OOO 

0 


1 592 

-- N 









































406 


A TREATISE ON CONCRETE 


Various other tests of modulus of elasticity may be found in Tests of 
Metals, U. S. A., during the years 1898 to 1907. 

Tests of Mortar Prisms. Elastic properties of prisms of neat Portland 
cement and cement mortar, from tests made by Mr. Howard* at the 
Watertown Arsenal, are presented in the following table: 


Elastic Properties 0} Cement and, Mortar Prisms 6 by 6 by 18 inches . 
Watertown Arsenal. (See p. 406.) 


Brand 

of 

Cement 

COMPOSITION 

Age 

Days 

MODULUS OF ELASTICITY BETWEEN 
LOADS PER SQUARE INCH OF 

Permanent sets after 
loads per 
square inch of 

^ Compressive 

cr strength 

per square inch. 

Cement 

Sand 

IOO 

and 600 

lb. 

IOO 

and 1 000 

lb. 

I OOO 

and 2 000 

lb. 

600 

Inch 

1 000 

Inch 

2 OOO 

Inch 

Alpha 

Neat 

0 

7 

7 143 000 

5 OOO OOO 

8 333 000 

O. 

O. 

0. 

4 783 




7 

4 167 000 

3 600 000 

3 448 000 

0. 

O. 

.0002 

5 000 

Alpha 

1 

I 

J 5 

3 125 000 

2 812 OOO 

2 326 000 

-.0002 

-.0002 

.0007 

3 846 




36 

2 381 OOO 

2 500 OOO 

2 941 000 

0. 

.0002 

.0012 

4 763 




36 

2 632 OOO 

2 727 OOO 

3 030 000 

.0001 

.0002 

.0010 

4 948 

Alpha 

1 

2 

15 

1724 OOO 

i 47s 000 


.0005 

.OO23 


1 376 




36 

2273 OOO 

2 195 OOO 

1 538 000 

.0001 

.OO06 

.0040 

2 184 




33 

K> 

-<r 

00 

0 

0 

0 

2812 OOO 

2 325 000 

0. 

.0004 

.0020 

2 755 


Gaged length, io inches. 


Modulus of Elasticity in Beams vs. Columns. The modulus of elasticity 

in beams as determined by measurements and computations by Professor 
Talbot is approximately the same or possibly slightly lower than in col¬ 
umns. 

Effect of Consistency of Concrete upon the Modulus of Elasticity. An 

excess of water in the concrete not only decreases the strength (see page 
382), but also affects the deformation curve so as to show a more vari¬ 
able modulus near the beginning of the test. The moduli of concrete 
of different consistencies and at different ages are shown in the tables from 
tests of the authors on following page. 

Relation of Stress Deformation Curve to the Theory of Beams. The 
theory of beams is worked out under the assumption that a section plane 
before bending remains plane after bending so that the deformation or stretch 
at any point in the compressive portion of the beam is proportional to the 
distance of this point from the neutral axis. According to this assumption 
the distribution of stresses is also proportional to the distance from the 
neutral axis so long as the modulus of elasticity is constant. This distribu- 


* Tests of Metals, U. S. A., 1898. 





























REINFORCED CONCRETE DESIGN 


407 


tion may be then represented by a straight line as shown in Fig. 131, p. 417. 
When, however, the modulus of elasticity changes Hook’s law—that stress 
is proportional to deformation—is no longer applicable, since the intensity 
of stress is no longer proportional to the distance from the neutral axis but 
changes according to the relation of the moduli of elasticity at different load¬ 
ings, and the line representing the distribution becomes a curve.* 


Modulus of Elasticity of Concrete of Different Consistencies.'] Proportions by 

Volume 1, : 4 * 

By Taylor and Thompson. {See p. 406.) 


Approximate 
age in 
months. 

DRY. 

MEDIUM. 

VERY WET. 

Compressive strength* 
Pounds per sq. in. 

Modulus at $ ultimate 
strength. 

Pounds per sq* in • 9 

Compressive strength. 
Pounds per sq. in. 

Modulus at i ultimate 
strength. 

Pounds per sq* in' 

Compressive strength. 
Pounds per sq. in. 

Modulus at k ultimate 

strength 

Pounds per sq. in* 

1 

437 ° 

4 050 000 

33 6 ° 

4 500 OOO 

2110 

2 IOO OOO 

2 

543 ° 

4 050 000 

3940 

4 55 ° 000 

2770 

3 400 OOO 

6 

5 * 7 ° 

5 255 °°° 

5 I 7 0 

3 760 OOO 

335 ° 

2 880 OOO 

17 

55 i° 

3 Q 2 O OOO 

4720 

3 75° 000 

243° 

2 080 OOO 


Since the modulus is nearly constant within the working limits the authors 
have adopted the straight line theory of distribution of stress as simplest and 
most practical.! 

Formerly the parabolic distribution of pressure in concrete above the 
neutral axis was used in preference to the straight line theory because 
it corresponds somewhat more nearly to actual test. The two theories, 
however, require practically identical percentages of steel and the only 
difference is in the determination of the unit stress in the concrete. When 
using the parabola theory, about 15% lower compressive stress in the con¬ 
crete must be used than when figuring by the straight line theory to obtain 
similar results. For example, 650 pounds per square inch safe compres¬ 
sion by the straight line theory corresponds to about 565 pounds per square 
inch by the parabola theory. 


* A comprehensive analytical discussion of the effect of a varying modulus of elasticity upon the 
pressure in a beam under different loadings is presented by Prof. Talbot in Journal Western Society 
of Engineers, Aug. 1904. 

f “The Consistency of Concrete,” by Sanford E. Thompson, American Society for Testing 
Materials. Vol. VI, 1906* 

J It is also recommended by the Joint Committee, 1909. 





















408 


A TREATISE ON CONCRETE 


Value to Use for the Ratio of Elasticity in Compression. For beam 

and slab design and also for column design, tests indicate that a practical 
value of 15 for the ratio of the moduli of steel to concrete corresponding to a 
concrete modulus, E c = 2 000 000, best satisfies the conditions for ordinary 
1:2:4 concrete, and without serious error mav be used for all classes of 
concrete, and is therefore recommended for general use.* For calculations 
relative to deflections where the tensile strength of the concrete is taken into 
account, a ratio of elasticity of 8 to 12 may be used as giving re¬ 
sults corresponding more nearly to actual conditions. The value of 15 
has been adopted in the American, British, German and Austrian rules 
up to 1909. The French rules for 1907 authorize a range from 8 to 15, 
according to conditions. 

A lower modulus of elasticity for concrete (that is, a higher ratio) should 
be used in determining the location of the neutral axis in beam design than 
the values obtained at working loads in compression tests, to compensate 
for the neglect, in the ordinary formulas, of the effect of tension in the 
concrete. The use of a high ratio is generally on the safe side also, since it 
lowers’the apparent location of the neutral axis and increases the amount 
of steel required. These reasons explain the selection of a ratio of 15, 
which is a higher value than is obtained in compression tests. On the 
other hand, when the modulus is to be used to determine the deflection of 
a beam, a lower ratio (i. e., a higher modulus) should be used to make up 
for the omission of the tensile stress unless this is allowed for in the formulas. 

In column design, while the use of a low ratio is most conservative, a 
high ratio (i. e., a low modulus) corresponds more nearly to actual co. di- 
tions, because if there is a weak spot in the column or unusual loading, the 
steel will be brought into action to an amount indicated by the lower 
modulus. 

The ratio of modulus of elasticity within working limits in beams figured 
by the parabola and by the straight line methods is indicated by Prof. 
Talbot’s studies^ to be in the ratio of about 13 to 12. 

Modulus of Elasticity in Tension. But few tensile tests of concrete have 
been made, but these indicate{ that the elastic modulus in tension is 
probably the same as the modulus in compression. 

ELONGATION OR STRETCH IN CONCRETE 

According to tests of Professor Turneaure, already mentioned, reinforced 
concrete under a pull, as in the lower portion of a beam, will usually stretch 

* It is thus recommended by the Joint Committee, 1909. 

•(•University of Illinois, Bulletin No. 4, April 18, 1906. 

j Prof. W. Kendrick Hatt, Journal Association Engineering Societies, June 1904, p. 32. 


APPLIED LOAD IN POUNDS 


REINFORCED CONCRETE DESIGN 


409 



Fig. 130. Typical Deformation and Deflection Curves of a Reinforced Beam 

By Prof. A. N. Talbot. {See p. 410.) 





















































































































































































































4io 


A TREATISE ON CONCRETE 


o.oooi to 0.0002 of its length, that is, o.oi per cent to 0.02 per cent, before 
showing minute cracks or “water-marks.” Cracks become noticeable at 
a stretching varying in different specimens from 0.0003 to 0.0010 of their 
length. At this stretch, the steel imbedded in the concrete will have a stress 
of 9 000 to 30 000 pounds per square inch. Even then, however, the cracks 
are still so small and are so well distributed by steel properly placed that 
they are not apt to be noticed in a reinforced structure until the steel has 
nearly reached its elastic limit. 

The concrete in a reinforced beam stretches similarly to the concrete in 
a plain beam except that the plain concrete beam breaks when the limit of 
stretch is reached, while if reinforced, the pull is borne partly by the steel 
and partly by the concrete, and they both stretch together up to the point 
where cracks, so minute at first as to be almost invisible, occur in the con¬ 
crete. 

The action of the reinforced concrete is shown in the deflection curve in 
Fig. 130. The inclination of this curve changes at about the same load 
that is required to break a similar beam of plain concrete. 

The diagram shows a typical result of Prof. Talbot’s tests of the defor¬ 
mation of the concrete and the deformation of the steel, the deflection of 
the beam, and the various measured positions of the neutral axis during 
flexure. Among other conclusions, Prof. Talbot draws the following: 

1. The composite structure acts as a true combination of steel and con¬ 
crete in flexure during the first or preliminary stage, and this stage lasts 
until the steel is stressed to, say, 3 000 pounds per square inch, and the 

lower surface of the concrete is elongated about-of its length. 

10 000 

2. During the second or readjustment stage there is a marked change 
in distribution of stresses, the neutral axis rises, the concrete loses part of 
its tensional value, and tensile stresses formerly taken by the concrete are 
transferred to the steel. During this stage minute cracks probably exist, 
quite well distributed, and not easily detected. 

3. In the third or straight-line stage the neutral axis remains nearly 
stationary in position and the concrete gradually loses more of its tensional 
value. Visible cracks appear and gradually grow larger, though no change 
in the character of the load-deformation diagram results. It would seem 
probable that at these cracks the stress in the steel is more than is indicated 
by the average deformation for the full gage length. 

Professor Talbot states that at the load when the curve changes charac¬ 
ter,—which in the beam shown in the diagram is about 8 000 pounds total 
load,—there are probably invisible cracks in the lower portion of the beam. 
This change in direction of the curve, indicating a suddenly increased load 
upon the steel, is strong proof of the loss in tensional resistance of the con- 



REINFORCED CONCRETE DESIGN 


411 


Crete. Professor Turneaure, moreover, in his experiments, at loads some¬ 
what beyond the point of change in direction, actually discovered these 
minute cracks. He tested his beams upside down, that is, the load was 
applied upward, and the minute cracks or water-marks were shown by 
hair lines on the wet surface of the concrete. Professor Turneaure* says: 

It has been found that by testing the beams when somewhat moist, a 
crack is made visible when exceedingly small, it appearing first as a narrow, 
wet streak perhaps J inch wide and a little later as a dark hair-like crack. 
It was not necessary to search for the lines with a microscope as under these 
conditions they were readily found. 

That the wet streak, called a “watermark” hereafter, shows the presence 
of an actual crack was demonstrated last year by sawing out a strip of the 
concrete containing such a watermark; the strip fell apart at the water¬ 
mark. 

In the plain concrete no watermarks or cracks were observed before 
rupture. Comparing the observed and calculated elongations of the 
reinforced concrete with those for the plain concrete at rupture, it will be 
seen that the initial cracking in the former occurs at an elongation practi¬ 
cally the same as in the latter. 

The significance of these minute cracks is an open question. It has been 
supposed that concrete reinforced by steel will elongate about ten times 
as much before rupture as will plain concrete. These experiments show 
very clearly that rupture begins at about the same elongation in both cases. 
In the plain concrete total failure ensues at once; in the reinforced con¬ 
crete rupture occurs gradually, and many small cracks may develop so 
that the total elongation at final rupture will be greater than in the plain 
concrete. In other words, the steel develops the full extensibility of a 
non-homogeneous material that otherwise would have an extension cor¬ 
responding to the weakest section. 


These results are somewhat at variance with the conclusions reached by 
Mr. Consideref in France. He was not able to locate these fine cracks 
and therefore concluded that while the stretch of plain concrete was about 
0.0001 of its length or about 0.01%, in combination with steel it could 
actually attain a stretch twenty times this, or 0.2%. Because of this appar¬ 
ent action of the concrete, Mr. Considere in his formula for beams assumes 
the concrete to resist a certain amount of tension. 

The stretch, or deformation, in the concrete of a reinforced beam may be 
estimated approximately from the pull, or stress, upon the steel and the 
modulus of elasticity of the latter, since 


elastic deformation = 


stress 

modulus of elasticity 


* Proceedings American Society for Testing Materials, 1904. 
•j- Considered Reinforced Concrete, p. 35. 



412 


A TREATISE ON CONCRETE 


For example, if the steel is pulled to 16 ooo pounds per square inch, the 
stretch per unit of length (disregarding initial tension) is 

16 ooo 

- = 0.00053 

30 ooo ooo 

Knowing the stretch in the concrete (and therefore the stretch in the steel 
imbedded in it) the stress in the steel is readily computed from the same 
formula. 

Tensile Resistance in the Concrete. Professors Talbot and Turneaure 
both concluded from their tests in 1904 that the tensile strength of concrete 
may be disregarded in the consideration of the ultimate load carried by a 
beam. This has since been adopted as current practice in design and is 
in accordance with the recommendations of 1908 and 1909 in America and 
Europe. The tensile resistance of the concrete affects the deformation and 
deflection of the beam under the smaller loads, but if, as is customary, the 
working strength is taken as a definite fraction of the resistance at the elastic 
limit of the steel, the tensile resistance of the concrete need not be con¬ 
sidered in the design of reinforced beams. 

Prof. Turneaure says: 

The presence of the cracks of course seriously affects the tensile strength 
of the concrete, and, as they appear at an elongation corresponding to a 
stress in the steel of 5 ooo pounds per square inch or less, it would seem that 
no allowance should be made for the tensile resistance of the concrete. 
Furthermore, if such cracks are present the calculation of the tensile resist¬ 
ance of reinforced concrete by the method used by Considere leads to no 
useful result. In his tests Considere determines the stress in the steel from 
measurements of its elongation and then assumes the concrete to carry the 
remainder of the load. Assuming the value of E to be uninfluenced by the 
concrete, this would be correct so long as the stress in the steel and in the 
concrete is uniform between points of measurement. As stated by Considere 
himself, such results are only average values. But the concrete may be 
cracked entirely through and yet possess a very considerable average tensile 
strength over a length of several inches. Obviously in that case an average 
is of no value; the strength of the concrete is really zero. 

In practical design the most important question which arises is how far a 
concrete beam may be cracked without exposing the steel to corrosive 
influences. In this respect it seems to the writer that the minute cracks 
which appear in the early stages of the tests can have very little influence. 
However, the entire question of the effect of cracks and pores in the concrete 
on the corrosion of the steel needs careful investigation.* 


♦For later information on this point, see p. 328. 



REINFORCED CONCRETE DESIGN 


H 3 


QUALITY OF REINFORCING STEEL 

It is generally recognized in reinforced beam design that the yield point of the 
steel should be considered as the point of failure of this material. Tests 
show that when the metal reaches its yield point, the beam sags, and this 
deflection, due to the stretch of the steel and in some cases to the slipping 
of the steel because of its reduced cross-section, is likely to produce crush¬ 
ing in the concrete. 

The yield point of ordinary mild steel purchased in the open market, as 
determined by the drop of the beam in testing (the true elastic limit is several 
thousand pounds lower) cannot safely be fixed at a higher value than 30 cco 
pounds per square inch, although frequently, and in fact in the majority of 
cases, a value of at least 36 000 pounds, and in many cases 40 000 pounds 
will be found. 

High steel, that is, steel containing a high percentage of carbon, has a 
much higher yield point than mild steel. If of first-class quality,* a mini¬ 
mum yield point may be placed at 50 000 or 55 000 pounds per square inch 
and much of it will reach 60 000 pounds. The ultimate strength should 
be not less than 85 000 pounds per square inch. Thus, if it can be safely 
employed in reinforced concrete, it is adapted to carry much higher stress 
than mild steel, and, conversely, a smaller percentage of it is required for 
the same moment of resistance. Many engineers do not approve of the use 
of high steel because of its brittleness when of poor quality, and the danger 
of sudden accident, and because of the fact that it is prohibited in ordinary 
structural steel work. 

Brittleness in steel, however, is less dangerous in reinforced concrete 
than in many classes of structural steel work because the concrete protects 
it from shock, and also because smaller sections of steel are used in concrete 
beams than in steel beams, and the large and irregular shapes of the latter 
render them much more sensitive to irregular cooling during the process of 
their manufacture. 

Mild steel, that is, ordinary market steel, is manufactured and sold under 
such standard conditions that for unimportant structures it often may be 
used without other test than the bending test given on page 415. High 
steel, on the other hand, must be very thoroughly tested. When tested, 
however, as per our specifications, page 38, it is entirely safe and to be 
preferred to mild steel. The objection to it for reinforced concrete is 
based largely upon the use of a poor quality of material and the extra 
cost. Another objection which has been raised is that before the elastic 


* See Specifications for First-class Steel, p. 38. 


414 


A TREATISE ON CONCRETE 


limit is reached, the stretch in the high steel may produce excessive cracking 
in the concrete in the lower portion of the beam, and thus expose the 
steel to corrosion. The mere fact that cracks are visible does not prove 
that they are dangerous, because the steel is always designed to take the 
whole of the tension. Mr. Considered and Professors Talbot’s and 
Turneaure’s tests indicate that there is no dangerous cracking even with 
high steel until the yield point of the steel is reached. 

Tests made in Europe in 1907 (see p. 336) prove quite conclusively that 
the cement protects the steel from ordinary and even extraordinary corrosive 
action until the elastic limit of the steel is nearly reached. In cases where 
very minute cracking of the concrete may cause anxiety (even although not 
dangerous), the steel, whatever its quality, should not be stressed beyond 
the ordinary limits of, say, 16 000 pounds per square inch. 

A yield point in steel of 30 000 pounds per square inch corresponds to a 
stretch of 0.0010 of its length and a yield point of 50 000 to a stretch of 
0.00167. (See p. 411.) 

If steel could be made with a high modulus of elasticity it would be par¬ 
ticularly serviceable for reinforced concrete, because the higher the mod¬ 
ulus of elasticity of a material, the less is the deformation under any given 
loading. Unfortunately, however, all steel, whether high or low in carbon, 
has substantially the same modulus of elasticity (30000000 lb. persq. in.). 

It maybe stated, then, that high carbon steel, say, 0.56% to 0.60% carbon, 
of the quality used in the United States for making locomotive tires, is 
better than mild steel for reinforced concrete provided the steel is well 
melted and rolled, and is comparatively free from impurities, such as 
phosphorus. However, a high carbon steel, unless limited by chemical 
analysis, and made under careful inspection, is in danger of being more 
brittle than low carbon steel. Its use, therefore, should be limited strictly 
to work important enough to warrant the ordering of a special steel and the 
taking of sufficient trouble on the part of the purchaser to insure strict 
adherence to the specifications. Since manufacturers cannot always be 
depended upon to exactly follow specifications of this nature, it is necessary 
that an inspector be sent to the works either by the dealer or the purchaser. 

The specifications for first-class steel on page 38 are sufficiently explicit 
so that steel which comes up to them can be safely used and a working stress 
of 20 000 lb. per sq. in. will not be excessive. A steel which can be em¬ 
ployed with safety for all the locomotive and car wheels of the country certainly 
cannot be discarded as unsafe for concrete, provided similar precautions 
are taken in its purchase; on the other hand the extra cost may prohibit 
its use except under special conditions. 


REINFORCED CONCRETE DESIGN 


4i5 


Bending Test for Steel. The most important test in the specifications 
is the bending test and no steel which fails to pass this bending test 
should be used under any circumstances. The bending test is as follows: 
Test specimens for bending shall be bent cold to the following angles 
without fracture on the outside of the bent portion: 


Around twice their diameter. 
Specimens 1 inch thick, 8o°. 
Specimens f inch thick, 90°. 
Specimens ^ inch thick, no°. 


Around their own diameter. 
Specimens J inch thick, 130°. 
Specimens T 3 y inch thick, 140°. 
Specimens ^ inch thick, 180°. 


Steel with high elastic limit, whether due to high carbon or to manipula¬ 
tion in manufacture, should be purchased with these reservations even if 
the working stress is to be no higher than is used with mild steel, say, 16 000 
pounds per square inch, because it is liable to be brittle. In case a lot of 
steel has been delivered without previous test by the purchaser, one bar 
selected at random in every 100 should be subjected to this test and if it 
fails to pass, the portion from which it is taken should be rejected. 


THE STRAIGHT LINE THEORY 

For reasons discussed in the preceding paragraphs, the authors have 
selected the straight line theory of distribution of stress with the concrete 
taking no tension. 

This theory assumes the following hypothesis as a basis for practical 
design: 

(1) A plane section before bending remains plane after bending. 

(2) Tension is borne entirely by the steel. 

(3) Initial tension or compression is absent in the steel. 

(4) Adhesion of concrete to steel is perfect within working limits. 

(5) Modulus of elasticity of concrete within the usual limits of stress is 
a constant. 

Our reasons for selecting this theory may be briefly recapitulated as 
follows: 

(a) Beams designed by it and properly built will be unquestionably safe. 

(b) Fine cracks are formed in the tension portion of the beam at an 
early stage in the loading which actually destroy nearly all of the tensile 
resistance of the concrete. 

(c) The modulus of elasticity in many tests has been shown to be approxi¬ 
mately a constant within working loads. 


4i6 


A TREATISE ON CONCRETE 


(d) This theory is the simplest, and the most easily understood. 

(e) It has been adopted by the highest authorities in America and 
Europe. 

(f) The results from it may be readily compared with other theories. 

These assumptions lead to the formulas given in this chapter. 

During the period termed by Prof. Talbot the first stage (see p. 410) it is 

necessary in scientific computations involving the deflection of the beam 
to take the tension of the concrete into account by the methods given on 
page 760. 

LOCATION OF NEUTRAL AXIS 

The location of the neutral axis after the load has been transferred to the 
steel, is given in formula (6) on page 420 and numerical values for different 
moduli of elasticity and different percentages of steel on page 521. As is 
evident from the formula, it varies with the strength and elasticity of both 
the concrete and steel. Because of the peculiar action of the deformations, 
as illustrated in Fig. 130, page 409, the location of the neutral axis changes as 
the load is applied. The question is much simplified in practice by assum¬ 
ing a constant ratio of moduli of 15. 

An empirical formula suggested by Prof. Talbot for the location of the 
neutral axis under normal loading is given on page 479. 

Tests show that the neutral axis for small loadings is just below the center 
line of the beam. For greater loadings it moves gradually nearer to the 
compression side. As the first cracks develop, the change in position of the 
neutral axis is more sudden, and the distance of the neutral axis from 
the compression side soon reaches its minimum, which for usual percent¬ 
ages of steel is 3/10 to 4/10 of the depth from the top, after which the change 
for additional loading is inappreciable. At failure the change is sudden 
again. 


DESIGN OF A RECTANGULAR BEAM 

In a simple rectangular beam we may represent the stresses by the dia¬ 
gram shown in Fig. 131, page 417. At any vertical section through the 
beam the concrete in the upper portion resists the forces which tend to 
compress it, and the steel in the low r er part of the beam resists the forces 
which tend to stretch and break it in tension. The compressive resistance 
acts in one direction and the tensile resistance in another direction, as desig¬ 
nated by the large arrows in the diagram. The center of tension in the 
steel is at the center of the rod, or, if there is more then one tier of rods, 
through the center of gravity of the set of rods. The center of pressure of 


REINFORCED CONCRETE DESIGN 


4i7 


the concrete passes through the center of gravity of the triangle which repre¬ 
sents the compressive stresses. The reason for the assumption of the 
uniformly increasing pressure from the neutral axis to the outside fiber is 
discussed above. 



Fig. 13 i. Resisting Forces in a Reinforced Concrete Beam. 

(See p. 417 and 420.) 

On page 420 are given simple formulas to review a beam already 
designed and the various letters in Fig. 131 are there defined. 

A complete analysis of rectangular beams is presented in Appendix II, 
and the reader is referred to the discussion of the theory there given and the 
derivation of the formulas. (See p. 751.) 

The theory of beams requires that the total internal pressure be equal 
to the total tension or pull in the steel. The safe resisting moment of the 
beam, which of course must be equal to or greater than the bending moment, 
is the product of the moment arm (that is, the distance between centers of 
tension and compression) times either the total safe pressure or the total 
safe pull. In case the design is unbalanced so that the beam is stronger in 
compression than in pull, the strength of the beam is limited by the safe 
moment of resistance determined from the allowable tension or pull in the 
steel. If, on the other hand, the tensile resistance is greater than the com¬ 
pressive resistance, the concrete governs the strength of the beam. 

A beam, then, must have breadth and depth sufficient to prevent excessive 
compression in the concrete in the top of the beam and enough steel to 
take all the pull without exceeding the working stress of the steel. Rules 
for this are given in the simple formulas which follow. The steel must 
also have sufficient bond (see p. 456) arid in many cases inclined or 
vertical reinforcement is required as treated in connection with diagonal 
tension, pages 448 to 459. Continuous beams also require reinforcement 
over the supports, as described in pages 427 to 431. 

Having computed the maximum bending moment due to the loads (see 























418 


A TREATISE ON CONCRETE 


p. 439) the breadth of the beam, b, is assumed and the depth of the steel is 

found from the following formula: 

Let 

d = depth of beam from compressed surface to center of steel in 
inches. (See Fig. 131, p. 417) 

jd = moment arm or distance between centers of tension and com¬ 
pression. 

b = breadth of beam in inches. 

p = ratio of cross-section of steel to cross-section of beam above the center 
of gravity of the steel, 

A s = area of cross section of steel in square inches. 

M = moment of resistance or bending moment in general in inch-pounds. 

C = a constant for a given steel and a given concrete. 


‘- C <T 

(1) 

A„ = pbd 

(2) 


The constants C and p to be substituted in the above formulas may be 
taken from the table on page 519 corresponding to the allowable working 
stresses in steel and concrete and to the ratio of their moduli of elasticity. 

Selected working stresses for tension in steel, / 3 , and compression in 
concrete, f c , require a definite percentage of steel, and the percentage 
cannot be altered without changing the ratio of these working stresses.* 
Fora working compression in the concrete of 6504 pounds per square inch, 
a working pull in the steel of 16 ooof pounds per square inch, and a ratio 
of modulus of steel to concrete of 15!, for concrete having a compressive 
stress in cylinder form of 2 000 pounds per square inch at 28 days. 


I I 

M 

(3) 

it= 7o \f 

J 

A = .0077 

bd 

(4) 


Example 1: What depth of beam having a span of 18 feet and what area 
of steel are required, using above unit stresses, for a freely supported beam 
with a load of 600 pounds per running foot? 


* See page 752, formula (5). 

J Recommended by the Joint Committee, 1909 


t More exactly, 4=0.096 ^ — 





REINFORCED CONCRETE DESIGN 


419 


c , . -n , ,, . WP . 600 X l8 X l8 X 12 

Solution: Bending moment, M, for -g-is-^- =291600 


inch pounds, and using formula (3) 

, * /291600 . 

d== io\ 8 " = 19 inches 


8 


With 2 inches of concrete below the steel, the total depth of beam is thus 
21 inches. 

The area of steel from formula (4) is 

A= .0077 X 8 X 19 = 1.17 square inches, 

thus (from Table 1, page 507) requiring four f inch round bars, or their 
equivalent. 


Depths and Loads for Different Bending Moments. The depth maybe 
obtained in terms of the unit load, if desired, by substituting iorM in formula 
(1) its value in terms of the load and the span. This may be readily trans¬ 
posed also to give the load, w, which a given beam will carry. 

The following table is used for determining on the one hand the depths 
of a beam to be designed, and on the other hand the safe loads of a beam 
already designed, for uniformly distributed loads. In the formulas in the 
table: 

d = depth of beam from compressive surface to center of steel in inches. 
b = breadth of beam in inches. 

w = load in pounds per running foot of beam (including weight per linear 
foot of beam). 

I = span in feet. 

C = a constant from Table 10 on page 519. 


Formulas for Depth and Loading of Rectangular Beams for Different Bending 

Moments. {See p. 519 for values of C.) 


DEPTH, d, AND 
LOAD PER 
FOOT, W. 


d 


w 


ivl 2 

I 2 

O 

wl 2 

8 

wP 

4 

wl 2 

2 







\l. 2 W 

ri I 1 -*™ 

Cl l 3W 

Cl i 6w 

Cl V b 

CL \ b 

CL \ b 

b 

d-b 

d-b 

d 2 b 

d 2 b 

d 2 b 

CH 2 

1.2 C 2 1 2 

i.S&P 

3 C 2 1 2 

6 C 2 P 


Formulas to Review a Beam already Designed. To review a beam 
already designed, the following formulas may be used, the derivation of 
which is given in Appendix II, page 751. 































420 


A TREATISE ON CONCRETE 


f c — unit compressive stress in concrete per square inch. 
f s = unit tensile stress in steel per square inch. 
d = depth of beam from compressive surface to center of steel in inches. 
j = ratio of distance between the centers of compression and tension to 
depth of beam. 

jd = d ^ i — -j = distance between the centers of compression and tension. 


b = breadth of beam in inches. 

A s = area of cross-section of steel in square inches. 

p — ratio of cross-section of steel to cross-section of beam above center of 
gravity of steel. 

k — ratio of depth of neutral axis to depth of beam d. 

M =•- bending moment in inch-pounds. 
n = ratio of elasticity of steel to concrete. 


Then 


P bd 
M 


(5) 

(7) 


k = V 2 pn ( pn ) 2 — pn (6) 


2 M 
* c = btpjk 



The values of j and k are dependent upon the percentage of steel and th e 
ratio of moduli of elasticity of steel -and concrete and may be taken from 
table, pages 520 and 521. 

For a beam with about 0.8 per cent of horizontal steel (in which case, the 
tension in steel f s is about 16 000 pounds per square inch and the compres¬ 
sion in concrete f c about 650 pounds per square inch) the distance between 
the centers of compression and tension jd, is about J J and the above formulas 
may be expressed with scarcely appreciable error as 



M 

o. 87 A s d 


(7a) 


6 M 

= ~bj 


(8a) 


Neither the allowable tension in steel nor the allowable compression 
in concrete should be exceeded. Tables for determining the dimensions 
aid loading of rectangular beams are given on pages 509 to 511, and the 
methods of practical computation and details of design are illustrated in 
Example 6, page 469. T-beams are treated on page 423. 

The selection of bending moments to use in design of continuous beams 
is treated on p. 439. 






A TREATISE ON CONCRETE 


421 


DESIGN OF SLABS 

A slab, as far as the computation is concerned, is a rectangular beam and 
the depth and percentage of steel are therefore obtained by the formulas 
just given. 

Since the bending moment is figured for a width of slab equal to one foot, 
b in formulas (1) and (2) becomes 12 inches and the formulas change 
(using notation on page 418) to 

d = 0.29C VM (9) 

A s = 12 pd (10) 

For stress recommended by the Joint Committee, 1909 

f c — 650 pounds per square inch, f 8 = 16 000 pounds per square inch 
and n — 15, substituting corresponding value for C from 
Table 10, page 519, the above formulas become 

d = 0.028 1 /M (11) 

A 8 = 0.092 d (12) 

The use of these formulas is illustrated in Example 6, page 469. 

Slabs which are continuous over the supports, such as those in a floor or 
in a buttressed retaining wall, must be designed with provision for the nega¬ 
tive moment at the supports. For uniformly loaded spans continuous over 
2 or more intermediate supports, a moment M = yV w/ 2 may be used 
both in the centers of the spans and also at the supports, while for end 
spans a moment M = to wl 2 is necessary. 

In practice to provide for the moments over the supports some designers 
bend up all the bars near the J point, but a better way, in order to be sure 
that no point in tension is unprovided with steel, is to bend up one-half, 
two-thirds or three-quarters of the bars and run them over the supports 
allowing the remainder to continue at the bottom of the slab. To provide 
the rest of the steel at the support, the bars in the adjoining span can be 
carried back over the support. Where the bars are so long as to extend 
over several spans, they can be arranged to break joints at different places, 
and so keep as much steel over top of supports as at center of span. 

The bend in the bars should be near the £ points in the span, and usually 
at an angle of about 30 degrees with the horizontal. Too sharp an angle 
may tend to crack the slab, while, on the other hand, they must be brought 
to the top of the slab far enough from the support to properly provide for 
the negative moment. 


422 


A TREATISE ON CONCRETE 


Tables for determining the dimensions and loading of slabs can be found 
on pages 512 to 515 and the methods of practical computation and details 
of design are illustrated in Example 6, page 469. 

Cross Reinforcement of Slabs. Cross reinforcement, that is, bars at right 
angles to the principal bearing rods, is customarily used to prevent 
shrinkage and temperature cracks, and to give added strength. Although 
this reinforcement is not absolutely essential, it stiffens the construction 
floor and often renders expansion joints unnecessary. 

The amount of steel to use for this usually is selected somewhat arbitrarily, 
a cross-sectional area of bars equivalent to0.2 percent to 0.4 percent (p = 
0.002 to 0.004) of the cross-section of the floors being the most usual 
practice. 

The top of the slab over a girder or beam which is parallel to the 
principal reinforcement bars should be reinforced transversely not only for 
stiffening the T-beam (see p. 443) but also to provide for the negative bend¬ 
ing moment produced with the bending of the slab next to the beam or girder. 
This reinforcement is also necessary even when the beam is simply a small 
stiffener. 

Computing Ratio of Steel. The ratio of steel in a slab is most readily 
found by dividing the cross section of one bar by the area between two bars, 
this area being the spacing of the bars times the depth of steel below top of 
slab. For example, a slab with steel 4 inches below the top and £ inch 


= 0.0082, or 0.82 


round bars spaced 6 inches apart has a ratio, p = ~ 
per cent steel. 2 4 

Square and Oblong Slabs. Flat plate design by the elastic theory is 
treated on page 483. A rule for ordinary cases is to require that when the 
length of the slab exceeds 1^ times its width, the entire load should be 
carried by transverse reinforcement. For slabs more nearly square the 
following table represents the proportion of steel which should be run 
across the slab. These values, while not exact, are on the safe side. 


Steel in Oblong Slabs 


Ratio of length to breadth of slab. 


Ratio of steel across the slab in terms of the 
total steel. 


I 

I . I 
I . 2 
i-3 
1.4 


o. co 

o-59 
o. 67 

o-75 

0.80 








REINFORCED CONCRETE DESIGN 


423 


Thus if a slab is square, the reinforcement may be placed half in one 

72 

direction and half in the other. If the bending moment is , the rein- 

12 

w 

forcement in each direction must satisfy —. The total amount of rein- 

24 

forcement thus determined may be reduced 25 per cent by gradually in¬ 
creasing the rod spacing from the one-third point to the edge of the slab. 


DESIGN OF T-BEAM 


The quantity of concrete in a beam may be reduced when it is built 
at the same time as the slab so that there is no joint between them, by 
considering it to be a T-section, that is, computing a portion of the slab 
as acting with the upper part of the beam in compression. In Appen- 




• Fig. 132. Section of T-beam. (Seep. 423.) 


dix II, pages 754 to 756 inclusive, we present analyses of the two cases 
which may occur, depending upon the location of the neutral axis: Case I, 
neutral axis below the slab or flange; Case II, neutral axis at the under¬ 
side of the flange; or within the flange. These analyses are not required 
for design and therefore only the working formulas are here reproduced. 

The theory of the design is similar to the theory of a rectangular beam, 
namely, that the total compression in the concrete in the upper part of the 
beam is equal to the total tension or pull in the steel at the bottom of the 
beam. 

In the design of a T-beam, the thickness of the flange is fixed by the thick¬ 
ness of slab required to support its load, and the width of flange to use is 
selected in accordance with rules given below. The values to be deter¬ 
mined by computation are then the depth of the beam, the width of stem 
or web, and the amount of reinforcement. 































424 


A TREATISE ON CONCRETE 


The width of the slab, b, to use for the flange of the T-beam in compres¬ 
sion is selected somewhat arbitrarily. In no case of course can it be taken 
greater than the distance between beams. The Joint Committee has rec- 
commended a width not exceeding one-fourth the span length of the beam 
and also has limited the width to use on either side of the web to four times 
the thickness of the slab. It is probably safe to use a somewhat greater 
ratio of width to thickness than this in many cases. 

Cross-section of Web as Determined by the Shear. The width of the 
web of a T-beam is governed by the layout of the tension rods (see p. 459) 
and by a study of the shearing stresses (see p. 446). 

The total vertical unit shear in a beam effectively reinforced with bent 
bars or stirrups, or both, is limited by the Joint Committee to 120 pounds per 
square inch for ordinary concrete having a compressive strength (in cylin¬ 
ders) of 2000 pounds per square inch at 28 days. This is conservative but 
was selected to prevent the opening of diagonal cracks. 

To determine, then, the area of reinforced web required for shear involv¬ 
ing diagonal tension, let 

b' = breadth of the stem. 
t 

d — = moment arm, the depth from center of slab to steel, the 

2 

thickness of slab being /. 

V = total vertical shear. 

then from formula (30) for determining the horizontal unit shear 

v ( (13) 

\ 2 / 120 

That is, the area of web at any point in the beam (considering this up to 
the middle of the slab) must not be less than the total shear divided by the 
maximum allowable unit shear for the beam with its reinforcement. 

The design is illustrated in Example 6, page 470. 

Minimum Depth of T-Beam. The minimum depth is the depth at which 
concrete and steel are stressed simultaneously to their working limits. It 
is governed by the compression in the flange which must not exceed the 
working compressive strength of the concrete. Greater depth than the 
minimum is generally used for economical reasons. 

The minimum allowable depth may be found from the folding diagram, 
page 525. If preferred, the rectangular beam formula (1), page 418, may 
be used where the depth of the beam is not greater than four times the 
thickness of slab, using in this formula the breadth of the flange, b, for 


REINFORCED CONCRETE DESIGN 


425 


the breadth of the beam. For ratios of depth of T-beams to thickness of 
slab larger than four the rectangular beam formula gives unsafe results and 
the formulas given in Appendix II, page 755, must be used. 

The methods are illustrated in Example 6, page 470. 

Economical Depth for a T-Beam. Usually a greater depth than the 
minimum is desirable for economy, because deepening the beam reduces the 
area of steel proportionally. Professors Turneaure and Maurer* analyze 
the depth for maximum economy and suggest from this the most economical 
values. 

Using the notation 

d = depth of T-beam from compressed surface to center of steel in inches. 
t = thickness of flange in inches. 
b' = breadth of the stem in inches. 

M = bending moment in inch pounds. 

f 8 = allowable unit tension in steel in pounds per square inch. 
r = ratio of unit cost of steel in place to unit cost of concrete in place 
(using same units for steel and concrete). 



From this formula the most suitable depth may be selected after two or 
three trial computations for different widths of stem. The ratio of costs, r, 
ranges between 38 and 75. For cost of concretef in place 20 cents per 
cubic foot, and cost of steel in place 3 cents per pound, the ratio of costs equals 
75, while for concrete at 40 cents per cubic foot and cost of steel 3 cents 
this value will be reduced to 38. In calculations where no unit costs are 
given, a value of 60 may be selected for r. 

The depth of the T-beam should not be made too great in proportion to 
the breadth of stem. Many designers make the ratio of the depth of a 
T-beam to its width of web between 2 and 3. For very deep and large 
beams a ratio of 4 may be accepted, while, on the other hand, if head room is 
limited, the depth of the beam may be fixed and the width of stem be deter¬ 
mined by area required for shear, so that ratio, — may be even less than 2. 

b 

Another plan sometimes followed in studying designs is to make the depth 


* Turneaure and Maurer’s “Principles of Reinforced Construction/' Second Edition, p. 238. 

•j- The cost of concrete need not include form construction since a variation in depth affects this 
but slightly. 




426 


A TREATISE ON CONCRETE 


of T-beam an arbitrary ratio to its span. Comparison of a number of 
representative designs shows an average ratio of span to depth of beam as 
about io to 12, which suggests the approximate rule to make the depth in 
inches equal to the span in feet. 

Sectional Area of Steel in a T-Beam. The area of cross-section of steel 
in tension may be obtained very closely by the following formula : 

Let 

A s = cross-section of steel in square inches. 

M = bending moment in inch-pounds. 

fa = allowable unit tension in steel in pounds per square inch. 
d = depth of T-beam in inches. 
t = thickness of flange in inches. 

then 


This formula assumes that the center of compression of beam is at the 
center of the slab. This gives slightly high results for a T-beam with very 
t nn flange in proportion to the dimensions of the web, and too low results 
or a shallow T-beam with thick flange; ordinarily the error is so slight as 
to e inappreciable but if d is less than 3 t use formula (4), page 418, taking b 
as breadth of beam. Formulas for more exact computations or for review¬ 
ing T-beams are given in Appendix II, page 749, and quoted below* It is 
recommended that an inexperienced designer check his results obtained by 
approximate formulas by the more exact ones. 

From the diagram, page 525, the area of steel maybe obtained directly 
and comparisons made between different designs. 


Details of Design. The design of a T-beam must also be studied for 
s ear reinforcement (see p. 448), bond of steel to concrete (see p. 4 c6), and 

especially for the design at the support, which must be adapted to the nega¬ 
tive bending moment (see p. 428). 

The example on page 470 illustrates the use of the formulas and the princi¬ 
ples of design. The selection of bending moments is treated on page 439. 


* Let kd - depth of neutral axis; „ = ratio of elasticity; 
fibre compression in concrete. Then, 


b = breadth of flange; f c = outside 


2 tid An + b t~ 

2 ti As + 2 bt* 


3 kd — 2 t t 
2 kd — t 3 


: jd = d - z; f s = 


M . M kd 

A s jd y fc ~ bt (kd - ftjjd’ 


z 






REINFORCED CONCRETE DESIGN 


427 


BEAMS WITH STEEL IN TOP AND BOTTOM 

Although concrete is always cheaper than steel to use for compression, it 
is frequently desirable to place steel in the compression as well as in the 
tension side of the beam. In a continuous beam, for example, the steel is 
carried horizontally into the support and may be figured with the concrete 
to assist it in taking the compression provided its length is sufficient to 
provide bond. 

Analysis of the design with steel located to take compression and tension, 
with no tension considered in the concrete, is presented in Appendix II, 
P a ge 757 * For convenience, the diagram, Fig. 133, is here reproduced, 
and the working formulas are given. 




Fig. 133. Resisting Forces with Steel in Top and Bottom of Beam. 

p, 427 and p. 757.) 


C See 


Let 

b = breadth of beam in inches. 

d — depth of beam from compressed surface to center of steel in 
inches. 

a — ratio of depth of compressive steel to depth of beam. 

p = ratio of cross-section of steel in tension to cross-section of beam bd 
above this steel. 

p' = ratio of cross-section of steel in compression to cross-section of beam 
above the steel in tension. 

f c = unit compressive stress in outside fiber of concrete in lb. per sq. in. 

f 8 ■■= unit tensile stress, or pull, in steel in lb. per sq. in. 

f s ' = unit compressive stress in steel in lb. per sq. in. 

M = moment of resistance or bending moment in general in in. lb. 

C c , C s , Cg = constants from Table 8, pages 516, 517. 


The location of the neutral axis varies greatly with the location and the 
area of the steel, so that an approximate formula cannot easily be made. 






























428 


A TREATISE ON CONCRETE 


The allowable stresses must not be exceeded either in the concrete or the 
steel. The bending moment, therefore, must not exceed the moment of 
resistance of the concrete and the steel and the beam must satisfy the equa¬ 
tions (see p. 757 for derivation): 


M = f c bd 2 C c 

(17) or 

f.~ 

M 

bFc c 

(18) 

M = f,b<P C, 

(19) or 


M 

bd 2 C 

(20) 


These formulas may be solved readily by introducing values of C c or C 8 
from the table on page 516. The constants are dependent upon the values 
of p, p', a and n and therefore vary with the reinforcement of the beam. 

The working strength of the steel in compression cannot be reached with¬ 
out exceeding the compressive strength of the concrete in which it is im¬ 
bedded, but, if its value is desired, it may be determined from the formula 
(39), page 759, which, with the substitution of C/ for the square brackets, 
becomes 


M 

= bd 2 a. 


(21) 


The value of C/ is obtained directly from the table on page 516. The use 
of the formulas is illustrated in Example 6, page 470. 


DESIGN OF A CONTINUOUS BEAM AT THE SUPPORTS 

The formulas and table just given for a beam with steel in top and bottom 
are of the greatest value in designing the ends of a continuous beam. 

A number of concrete buildings have been built in the past with beams 
having insufficient steel through the top of the supports to take the pull and 
insufficient concrete at the bottom of the ends of the beam to take the compres¬ 
sion, and when these have been loaded as designed, cracks, and in many cases 
serious ones, have occurred at the supports. Just as much care, therefore, 
is necessary in designing the end of a reinforced beam as the middle. 

The tendency to overstress the supports is due to the T-beam design. 
In the middle of the T-beam the slab takes the compression, but at the 
support, the compression being in the bottom of the beam because of the 
negative bending moment, there is only the web of the beam to resist it. 

In designing, a slightly higher compression may be allowed in the con- 




REINFORCED CONCRETE DESIGN 


429 


crete at the end than at the middle of the beam, using 750 pounds per 
square inch for 2 000 pounds concrete instead of 650, (see page 528) 
because the negative moment decreases so rapidly that only a short section 
is under maximum stress. Besides this, the steel in the lower part of the 
beam (if sufficiently bonded to the concrete) may be reckoned in compres¬ 
sion by the formulas just given. If this is not sufficient to fulfill the require¬ 
ments, the lower surface of the beam near the support may be dropped so 
as to form a flat haunch. 

By bending up half of the horizontal steel in the beams on each side of 
the support, and carrying it across over the support, lapping far enough to 
attain its full strength in bond, the tension in the top of the support will be 
provided for, since this gives the same tension steel as in the center of the 
beam. If desired, the stress, f 8 , in the steel may be figured from formula 
(20) above. 

Although bond tests with hooked bars (p. 467) indicate that a right angle 
5 diameters in length or a semi-circular bend of similar length, properly 
imbedded, will develop the elastic limit of the steel before giving way, it 
is the safest plan in ordinary construction to rely upon a straight lap of the 
required length (see p. 464). However, where this is impossible, as at the 
wall line in a building, or in a retaining wall, the effectiveness of the hook 
permits thorough bonding of the members together. 

Since the bending moment is a maximum at or near the center of the 
support, the moment at the edge of the support is slightly less and it is, 
therefore, frequently worth while to recompute it or estimate it by .curves 
on page 436. 

If compression in concrete at the bottom of the member as obtained by 
formula (18), p. 428, exceeds the working strength, the steel in the 
bottom of the beam or else the concrete or both must be increased in 
area. The simplest plan in most cases is to make the beam deeper next 
to the support by forming a flat haunch. When this is not permissible, 
extra horizontal steel may be inserted instead. While the forms for this 
haunch are somewhat troublesome to construct, their cost for beams and 
girders of usual size should not exceed 25c. to 50c. each. 

The amount of increased depth required may be obtained by trial from 
formula (18) above, assuming a new depth, and then with the aid of the table 
on page 516, determining whether the conditions are as specified. This is 

illustrated in the example on page 472. 

Under ordinary conditions the computation need be made only at one 
point, that is, next to the support, since the point to end the slope can be 
readily figured from the following formula: 


43 ° 


A TREATISE ON CONCRETE 


For a uniformly loaded beam, let 

M b = negative bending moment next to the support. 

M r = moment of resistance of the inverted T-beam without the haunch, 
governed by the concrete. 
x = length of haunch. 

/ = span of beam. 

Then 


l M b - M r 

5 >4 


(approximately) * 



An illustration of the use of this formula is given in Example 6, page 472. 


EFFECT OF VARYING MOMENT OF INERTIA UPON THE 

BENDING MOMENT 

However the bending moment may be computed, if the beam is built 
continuously with the next bay, pull or tension is bound to occur over the 
support with compression at the bottom of the beam. The assumption is 
sometimes made that if the middle of the beam is designed as freely sup- 

ported, that is, on a basis of —, the supports will be relieved and a read- 

justment will take place. This is only partially true, and usually should 
not be* counted upon in design. 

The assumption of reduced bending moment at the support, is based on 
the smaller moment of inertia at the support, but a thorough study by the 
authors of different conditions shows that a very large difference in the 
moment of inertia, as great a difference as it is possible to have in any ordi¬ 
nary floor design, causes a reduction in bending moment of less than 10% 
and under most conditions the reduction is even much less than this. Con¬ 
sequently a beam at the support should be designed, as suggested in the 
preceding paragraph, for the full negative bending moment as required by 

. , . wl 2 

the formula -- 

12 


* This formula is based upon the fact that the point of zero moment is at approximately A of the 
span, and from the curves of bending moment on p.436, it is evident that the variation in the 
moment between the support and the 4 point is very nearly a straight line. Hence the difference 
between the bending moment and the moment of resistance is in approximately the same ratio to 
the bending moment as is the ratio of the distance from the point where the haunch is needed to 
the point of zero bending moment. When the point of zero moment is not approximately at -j span 
the fraction may be altered accordingly. 





REINFORCED CONCRETE DESIGN 


43 i 


SPAN OF A CONTINUOUS BEAM OR SLAB 

It is customary to consider the span of a continuous beam or slab as the 
distance between the centers of its supports. In general this is the simplest 
plan to follow and one which is always on the side of safety. If the support 
is exceptionally wide, as when a slab runs into a wide beam, or a beam or 
girder into a large column,* an arbitrary length of span may be taken, if 
desired, as the net span between supports plus the total depth of the member 
which is being designed. The maximum negative bending moment may 
be considered then either at the center of the support or, if the width of the 
support is greater than the depth of the member, at a point within the sup¬ 
port equal to half the depth of the member. 

DISTRIBUTION OF SLAB LOAD TO THE SUPPORTING BEAMS 

If slabs are reinforced in both directions, the loads carried to the beams 
supporting them will not be uniformly distributed over the length of the 
beam, but may be assumed to vary in accordance with the ordinates of a 
triangle. 

Assuming that the slab transmits a load to its nearer support, we have 
the following formulas for determining the moment to use in computing 
the long and the short supporting beams. 

Let 

l t = the longer span of a rectangular slab in feet. 

/ = the shorter span of the slab in feet. 

w = load per linear foot of beam if the slab is considered as supported 
by longer beams only. 

M t = bending moment in foot pounds of longer beam. 

M 8 = bending moment in foot pounds of shorter beam. 

Then the moments of the two beams, assuming them as freely supported, 
are found by the application of simple mechanics, to be 

Mi = \ wl i[ i - ^ ]j) < - 23 - ) andM, = wlf^ - ( 2 4) 

For continuous or fixed beams the fraction J may be changed to its proper 
ratio. 

Formula (24) does not apply to girders supporting one or more beams. 
This case is treated under the heading which follows. 


* The deflection and the bending moment of a member are changed as soon as it enters the sup¬ 
port because of the change in the moment of inertia. 


43 2 


A TREATISE ON CONCRETE 


Example 2: What will be the bending moments in the two continuous 
beams supporting an oblong panel the whole length of which is twice the 
breadth and which is reinforced so as to transmit its load both ways? 

Solution: Using j 1 ^ wl 2 for the continuous beams instead of £ wl 2 and 

substituting: 


x 

Moment in longer beam, Ml = — wl 2 


1 II ? 

3 h 2 ) ~ 144 w 1 


in terms of the longer span, and 


122 12 

Moment in shorter beam, Ms — u>L ~ — “ wl. 

’ 12 * 3 


18 


DISTRIBUTION OF BEAM AND SLAB LOADS TO GIRDERS 

When one or more beams run into a girder, the load upon the girder con¬ 
sists of the concentrated live and dead loads from the beams acting at their 
points of intersection with the girder, the uniformly distributed weight of 
the girder itself, and the unsymmetrically distributed weight of a small por¬ 
tion of the floor slab, with its live load, which bears directly upon the girder. 



Fig. 134. Distribution of Beam and Slab Loads to Girder. {See p. 432.) 

To avoid the computation of several moments, a series of studies have 
been made by the authors for different conditions, and it has been found 
that the maximum bending moment of a girder may be obtained without 
appreciable error by considering, as a uniformly distributed load, the weight 
of the girder plus the weight of slab and its live load, for an area whose 
length is the length of the girder and whose width is the average length of 
the beams running from each side into the girder. The sum of these loads 
divided by the length of the girder gives a uniformly distributed load for 
which the ordinary formula may be used. 

Thus in Fig. 134, instead of computing the moment on the girder as the 
















REINFORCED CONCRETE DESIGN 


433 


sum of the moments produced by loads of the triangles, a b c, plus the con¬ 
centrated loads from the beams at c, the entire load d d d d may be 
considered as uniformly distributed over the girder in the length a a. 

With only one condition is there an appreciable variation from the exact 
maximum moment, and this is a case where two beams run into a girder at 
the one-third points. Here the maximum moment obtained by the uniformly 
distributed method gives slightly too conservative results, and may be 
reduced by 10%. 

Moments in a girder other than the maximum must be. computed for 
individual conditions. 


BENDING MOMENTS AND SHEARS 

Bending moments and shearing forces have to be computed so frequently 
in reinforced concrete design that the more common rules and formulas 
are given here, and besides this elemental matter diagrams are presented 
for estimating the moments and shears in various kinds of loading, and 
recommendations are made for the computation of bending moments in 
design. Shear and diagonal tension in beams are taken up at length. 

Rule to Find Reactions at Supports. The reaction at a support must be 
found in order to determine the bending moment. The sum of the upward 
forces, which in ordinary beams are the reactions at the supports, is equal 
to the sum of all the downward vertical forces or loads. In a simple beam 
supported or fixed at the two ends, the reaction at either end is found by 
taking moments of all forces about the other support and solving for the 
reaction desired. 

Expressed as a formula, if 

R = desired reaction. 

P — any vertical load. 

I = span. 

x = distance of load from the support at which the reaction is desired. 

I = sum, using — for downward and + for upward forces, then 


R = 


IP (l — x) 

~T 



Example y In Fig. 135, where there is a uniform load over the entire span 
and also concentrated loads Pi = 200 and P 2 = 350 at the £ points, what 
is the left reaction? 


(200 X 8) + (350 X 4) + (1 00 X 12)6 


= 850 pounds, 


Solution : R = 


12 






434 


A TREATISE ON CONCRETE 


The determination of reactions and moments of continuous beams is 
referred to on page 439. 


Pj= 20 

O LB R,= 35 

0 LB. 

^ 4 FT. > 

4 FT. 

IOO LB. PER FT. 

UNIFORM 

LOAD 

r 12 FT y 



Rj=850 LB, R 2 ” 900 LB. 

Fig. 135. Beam Loaded with Distributed and Concentrated Loads 

1 (See pp. 438 and 439.) 

Rule to Find Bending Moment at Any Point in a Beam. Consider either 
side of the vertical section passing through the point and disregard the other 
side. Multiply each load and reaction by its average distance from the 
section and add the products, taking loads acting downward as negative 
and those acting upward as positive. 

This sum is the bending moment at the section. 

Moments in English measure are usually taken in inch-pounds. Hence, 
the distance must be in inches and the weights in pounds. 

Example 4: In Fig. 135, what is the bending moment in inch-pounds at the 
middle of the span? 

Solution: M — R x (6 X 12)—Pi (2 X 12) —(100 X 6) X 3 X 12 = 34 800inch 
pounds. 

Rule to Find Shear at any Point in Beam. Consider either side of the 
section passing through the point and disregard the other side. Add the 
loads and reactions, taking the loads acting downward as negative and 
those acting upward, such as a reaction, as positive. The sum is the shear 
at the section. 

Example 5. In Fig. 135 what is the shear at the left support and at the 
center ? 

Solution: R x =850 pounds at left support and at the center the shear is 
R k — P —(100 X 6) =50 pounds. 

Table of Common Bending Moments and Shearing Forces. The fol¬ 
lowing table for convenient reference gives values of the shearing forces and 
bending moments for common cases. The values for external forces are 
independent of the structure of the beam. 














REINFORCED CONCRETE DESIGN 
Bending Moments and Shearing Forces * 


435 




Section 

Considered. 

Shearing Force. 

Bending Moment. 

Description. 

Loading. 

At distance 

X 

from support. 

Greatest. 

At distance 

X 

from support. 

Greatest. 

Beam fixed' 
at one end, 
unsupport¬ 
ed at other.. 

At end 

► 

Uniform. 


w 

w / \ 

tO-*) 

w 

w 

W (1 - x) 

?(-*)■ 

Wl 

Wl 

2 


► 

At 

middle. 1 

’ Between 
support 
and 
middle. 

w 

2 

w 

2 

w 

- X 

2 

Wl 

4 

Beam sup¬ 
ported at • 
both ends. 

Uniform. 

Beyond 

middle. 

w 
~~ 2 

W / I \ 

1 U ~ x / 

w 

2 

x X 

1 1 

—- X 

£ 1 " £1*3 

Wl 

8 



’ Between 
support 
and load. 

W (1 - a) 

1 

W (1 - a) 

W (1 - a) 



At dis¬ 
tance a 
from 
support. 

1 

1 x 

Wa(l — a) 

4 

Beyond 

load. 

Wa 

1 

Wa 

1 

Tf-*) 

1 


* W = total load; 1 = span; x =• distance of section considered from support. If moment is in 
inch pounds, 1 and x must be in inches and W in pounds. If load is distributed so as to be 
in terms of weight per unit length, substitute wl for W in the formulas. 


Table of Moments of Inertia. The table on page 438 gives the moment 
of inertia for beams of a few sections which might be used in concrete con¬ 
struction. The reinforcement, if any, maybe considered as replaced by an 
area of concrete which is the area of the steel times the ratio of elasticity, 
n, and is located at the same distance from the neutral axis. 

SHEAR AND BENDING MOMENT DIAGRAMS 

The diagrams in Figs. 136 and 137, pages 436 and 437, give bending 
moments and shears for beams continuous over four spans. In diagram 
136, various distributions of uniform loading are given; in the first place, at 
the top of the page, with all the spans loaded and ends fixed; next, all spans 
loaded and the ends supported; and below these curves, different spans 
loaded in such a way as to produce maximum and minimum bending 






































SUPPORTED SUPPORTED SUPPORTED SUPPORTED SUPPORTED FIXED 


436 


A TREATISE ON CONCRETE 



Fig. i 36.—Bending Moments and Shears for Continuous Beams, Distributed Loads. 

(See p. 435.) 


SUPPORTED SUPPORTED SUPPORTED SUPPORTED SUPPORTED 























































































































































































































































































































































































































































































































FIXED FIXED FIXED 


REINFORCED CONCRETE DESIGN 


437 


moments and shears. The cases chosen are sufficiently representative to 
be used without appreciable error as maximum and minimum values for 
beams of any number of spans and any distribution of uniform loading. 

As stated with the diagrams, the curves are all drawn to scale on cross- 
section ruling so that proportionate values may be read. The loads are 
given in terms of w, the load per unit of length. The horizontal scale has 
twelve divisions per span, so that the moments and shears can be readily 



Fig. 137. —Bending Moments and Shears for Continuous Beams, Concentrated Loads 

(See p . 437.) 

estimated at J, J, and \ points. The values which are printed for the bend¬ 
ing moments are in common fractions for convenience of comparison, 
although in order to scale them they must be changed from the common 
fraction to a decimal. Each vertical division for the bending moment 
scale represents 0.01 and for the shear scale represents 0.1. Bearing this in 
mind, the bending moment -and shear can be scaled at any part of the 
span. 

Concentrated loads are treated in Fig. 137, the loads being located at the 


SUPPORTED SUPPORTED^SUPPORTED 

































































































































































































































































438 


A TREATISE ON CONCRETE 




Moments of Inertia 

{See p. 435.) 



Area 

A 

Moment of Inertia. 

I 

Distance of Neutral Axis 
from most Strained Fiber * 
Y 

T 

1 

A 

1 

fjr 

bh 

bh 3 

h 

1 -1 

1 

12 

2 

1 

L 





RECTANGLE 

— b -H 



SQUARE 

K— -B--A 



b» 


b» 


±1 

12 


12 


BH —bh Jj(BH 3 - bh 3 ) 


b 

2 


\ b \f~2 


2 


RECTANGULAR CELL 


h—6i- -*i 

m 


I 

c* 

f* 


i_ Lm 



<M 


J. 


62^ 

T SECTION 


Area of flange 
+ area of web 

= Ai + A2 


Aiht 2 4- Aoli-j 2 


12 


Xi=- 


. AiA 2 (hi + I12) 2 
4(Ai + A2) 


Aih 2 —A 2 I 11 
2(Ai + A 2 ) 

A1I12—A2hi 

2(Ai+ A 2 ) 



CIRCLE 



HOLLOW CIRCLE 


ir r 2 


7 r(r 2 — ri 2 ) 


7 r r 4 

4 


7r(r 4 — ri 4 ) 
4 



HOLLOW ELLIPSE 


7r(ab — aibi) 


7ra 8 b 7rai 3 bt 
4 4 


* Applicable only to homogeneous (not 1o reinforced! beams. 


































REINFORCED CONCRETE DESIGN 


439 


quarter points, middle points, and third points respectively. This diagram 
is of special use in studying girders supporting cross beams. The stresses 
are computed for a beam of four spans and as the curves are symmetrical 
at each end, the diagram is broken in two, one-half being shown with fixed 
end and the other half with end supported. The results with a larger num¬ 
ber of spans will not be appreciably different. 

The vertical scale for concentrated loading is 0.05 per division for bend¬ 
ing moments and 0.2 per division for shears. 

The concentrated loads are given in terms of W, the load which is con¬ 
centrated at each point. 

The continuous beam is statically indeterminate, so that the moments 
and reactions have to be found by the theory of flexure, using the form¬ 
ula of three moments first evolved by Clayperon.* 

In applying this to the various cases, the assumption is made that the 
moment of inertia of the beam is constant throughout its length. While 
this is not strictly true, extensive studies of various cases in reinforced con¬ 
crete show that a large change in the moment of inertia makes a very small 
change in the bending moment, so that the relations are substantially 
correct until a member enters a much larger member. 

BENDING MOMENTS TO USE IN DESIGN OF REINFORCED BEAMS 

An examination of the curves in the diagram of bending moments for 
different loads, Fig. 136, page 436, indicates that in concrete beams built 
continuously it is safe to use for the positive bending moment in the center 
of the beam, except for the end spans, and also for the negative bending 
moment at the ends of the beams, 

wP 

M = 

12 

and for end spans, for the center and also for the adjoining support 

wP 

M = — 

10 

the customary American and English units being adopted, viz: 

M = bending moment in inch pounds. 

w = load uniformly distributed in pounds per inch of length 
l — length of beam in inches. 


* See Lanza’s “Applied Mechanics.” 



440 


A TREATISE ON CONCRETE 


In case the load is in pounds per foot of length and l is in feet, the moment 
in inch pounds to satisfy the former equation is simply the product of the 
load per foot times the square of the length in feet. 

The value of — for the bending moment has been widely adopted in 
12 

Continental Europe, is being used in general practice in Germany, and is 
recommended in the 1909 recommendations of the American Joint Com¬ 
mittee and in the 1907 French rules. However, it is absolutely neces¬ 
sary, when designing by this formula, that the beam be really con¬ 
tinuous both in design and construction; that the stresses due to negative 
bending moment at the support be provided for; that the steel be accurately 
located; and that, to obtain the best workmanship, the concrete be laid by a 
responsible builder and superintended by a man experienced in concrete 
construction. 

An examination of the diagrams referred to will show that under these 
conditions the value is conservative, since a uniformly distributed load, 

il'E 

except in the end spans, does not exceed — and the worst panel loading 

24 


shown for the middle of a span gives --. 

I 2 - 5 

Many of the building laws in the United btates, to provide for the possi¬ 
bility of poor construction or unforeseen conditions, give the more conserva¬ 
tive figure, 


wP 

M = 

10 


(26) 


and for this reason and also because other assumptions may be made by 
multiplying by a decimal, this value is used in many of the tables in this 
book, and in fact it is advised for constructors who are not thoroughly 
familiar with reinforced concrete. 

The same diagram, Fig. 136, shows that the negative bending moments are 
usually greater than the moments at the middle of spans. However, partial 
floor loading greatly reduces the negative moment, and as a live load is 
scarcely ever uniform over two full panels, it is considered safe to use the 
same value for negative moment as is used for the positive moment in the 
center of the beam, that is 

wl 2 

M = — (27) 

12 

At the end support, the beam, if it runs into a column or heavy wall girder, 



REINFORCED CONCRETE DESIGN 


441 


may be practically “fixed” and thus require top reinforcement for the 
• wl 2 

negative moment, — —, and the rods running into the support must be 

bent or otherwise anchored. Sometimes, if the slab has cross reinforcement 
running into the wall girder, it may be assumed to assist in connecting the 
beam and girder. 

Some designers, in making more exact computations, separate the dead 
and live load, considering the dead load extended over all panels and find¬ 
ing the most unfavorable position for the live load. Unless the live load is 
a very exact quantity this is needless refinement. 

Bending Moments for Independent Concentrated Loads. If the princi¬ 
pal live loads on a beam are concentrated, as they often are upon a girder 
bridge, the moments and shears at all points must be specially computed. 
For occasional concentrated loads in connection with uniform live and dead 
loads, and for loads produced by beams running into girders, it is suggested 
that the maximum moment under the load be computed as if the beam or 
girder was supported, and this be reduced by the same ratio used in the 
distributed loading. Thus, since the maximum moment for a concentrated 
load at the middle of a supported beam is \ Wl , if T l oWp is used in distributed 
loading instead of the \wP required forasupported beam, x 8 2of \Wl,or\Wl, 
may be used for concentrated center loads. The negative bending moment 
with concentrated loading usually may be taken the same as the maximum 
positive moment due to concentrated loading, reduced as indicated, except 
that with loads at J or \ points, this gives for the support next to the end a 
negative moment which is slightly low (see diagram, Fig. 136, page 436), 
and in some cases it should be separately figured or else estimated from 
this diagram. 


SHEARING FORCES IN A BEAM OR SLAB 

The bending of a beam produces a tendency of the particles to slide upon 
each other or shear. It is therefore necessary to study 

(1) Vertical shear. 

(2) Horizontal shear. 

(3) Diagonal tension. 

Most important of all is the resultant of the shearing forces with the tension 
which produces the pull in a diagonal direction termed diagonal tension. 

Vertical Shear in a Beam. Concrete is strong in direct shear (see p. 382) 
and capable of standing a working shearing stress of at least 200 pounds 
per square inch, so that a concrete girder or beam or slab, unless perhaps 



442 


A TREATISE ON CONCRETE 


of hollow or tapered construction, always has sufficient area of section to 
withstand this direct shear. However, since the direct shear is a measure 
of the diagonal tension (see p. 446), which is excessive when the direct shear 
is comparatively low, it must always be computed in a beam or girder for 
use in the computation of diagonal stresses, as described on page 447. 

The vertical shear is a maximum at the support, where it is equal to the 
reaction. Maximum shears for various loads are given in the diagram (Fig. 
136, page 436), in terms of the loads. While with uniform or symmetrical 
loading the reaction, and therefore the maximum vertical shear, is one-half 
the total load upon the beam, it will be noticed from the diagram that where 
the end beams in a series of continuous beams are supported, which is very 
nearly the case when a beam runs into a light wall girder, the shear at the 
first support away from the end may be 25 per cent greater than normal, 
and should be specially provided for in cases like a warehouse where the 
full live load is liable to be constantly maintained. A further study of the 
two diagrams (Figs. 136 and 137, pp. 436 and 437) will illustrate the cases 
where allowances should be made. 


K - b -*- 

C B B c 

^ ' 

4 



A 

< > 

A 



Fig. 138.—Section of a T-Beam. {See p. 442.) 

In case the concrete in a beam or slab has cracked vertically next to the 
support because of accident or poor design, the bearing value of the hori¬ 
zontal rods may have to be estimated. 

Longitudinal Vertical Shear in Flange of T-Beam. Vertical shear in 
a longitudinal direction is present in the wings of a T-beam due to the 
load upon a beam being maximum next to theflange, as shown bv lines BA 
in Fig. 138. 

The area of concrete in a solid horizontal floor slab is generally sufficient 
to take care of this shear, but the following method may be used for comput¬ 
ing it if desired: 

Let 1 

v h = unit horizontal shear at A A. 

v v = unit vertical shear at BA 

b' — breadth of stem. 

b = breadth of flange. 

t = thickness of flange. 













REINFORCED CONCRETE DESIGN 


443 


The shear along the two planes BA may be considered as caused by the ( 
external forces acting not on the whole breadth, but only on the projecting 
flanges of the T-beam BC. 

Then it is readily shown* that 


v 


V 


v A V (P ~ V) 

2 tb 


(28) 


Although this vertical shear through the flanges is readily borne by the 
concrete, it is advisable, as stated on page 422, to place horizontal rods across 
the top of the beam, even if the bearing rods in the slab run parallel to the 
beam, in order to resist unequal bending moment which is liable to occur 
and to assure T-beam action. 

Fillets at the angles between the flange and the beam, that is, between the 
slab and the beam, are not theoretically necessary, but they may be used 
for appearance sake and as an additional security in a deep beam with 
relatively shallow flanges or slabs. Small fillets are also advisable to aid in 
the removal of forms. 

Horizontal Shear. The concrete in a solid rectangular beam or in a 
T-beam is nearly always sufficient to sustain the direct horizontal shear 
which at any part is equal to the direct vertical shear. In a skeleton beam 
the horizontal shear may be excessive, but the reinforcement for diagonal 
tension will also take care of this, so that the direct horizontal shear as such 
need never be considered. Formerly, before tests of direct shear proved the 
high strength of concrete in shear, horizontal shearing stress was determined 
when designing a beam and the vertical stirrups or bent-up rods were spaced 
to act in shear, using a value of 10 000 pounds per square inch in the steel 
to resist it. More recent tests have proved the stirrups and bent up rods 
to be in tension instead of shear. 

Diagonal Tension. Not only does the high strength of concrete in direct 
shear indicate that cracks which form in the web of a beam are not caused 
by this, but tests of beams themselves show that such cracks are diagonal 
and in the direction which would be expected from the theory of diagonal 
tension. A typical crack due to diagonal tension is shown in Fig. 139, page 
444. 

Such cracks as these can be due only to a combination of the shearing 
stress with the horizontal tensile stress, whose resultant forms diagonal 


* The above principle may be expressed by the equation vv zt — 
will give formula (28). 



b-V 
b ’ 


which solved for 



444 


A TREATISE ON CONCRETE 


tension. It is this diagonal tension which must be sustained in a reinforced 
concrete beam by the area of concrete or by bent up rods and stirrups, as 
indicated in paragraphs which follow. 

Tests by Prof. Talbot* and Prof. Witheyf indicate that for i 12:4 
concrete the first diagonal crack in a beam without stirrups or inclined rein¬ 
forcement is apt to occur when the maximum shear is from 100 to 200 
pounds per square inch. Since failure by diagonal tension is sudden, it is 
advisable to provide a high factor of safety. In a beam with diagonal 



Fig. 139.—Beam under Load at University of Illinois Cracked by 

Diagonal Tension. (See p. 443.) 

tension reinforcement, the first diagonal crack occurs at a period but slightly 
later than in a beam with horizontal rods alone, but in this case it is very 
small and not dangerous if the steel is designed to take the stress. However, 
it is desirable that there should be always a sufficient area of concrete, even 
when reinforced, to prevent the diagonal tension from exceeding the crack¬ 
ing point in the concrete. 

♦Bulletin No. 12, University of Illinois, 1907. 
t Bulletin of University of Wisconsin, Vol. 4, No. 2, 1907. 








REINFORCED CONCRETE DESIGN 


445 


REINFORCEMENT TO PREVENT DIAGONAL CRACKS IN BEAMS 


The failure of a beam from diagonal tension is more sudden than from 
ordinary tension or compression, and therefore must be guarded against 
even more carefully. Formerly when beams were designed with full rect- 



Fig. 140. —Beam with Break in Center illustrating no Shear. (See p. 446.) 



Fig. 141.—Beam with Break near End, illustrating Action of Vertical Stirrup. 

(See p. 446.) 



Fig. 142. —Beam with Break near End, illustrating Action of Inclined Rod, 

(See p. 446.) 


angular section the concrete often had sufficient area to resist the diagonal 
tension without assistance from the reinforcement. With the advent of 
the T-section and the consequent reduction in the width of the stem, it 
nearly always becomes necessary to introduce stirrups or inclined rods to 
take the diagonal tension. 









































































































446 


A TREATISE ON CONCRETE 


An elementary illustration of the action of the stirrups or inclined rods 
is shown in Figs. 140 to 142, page 445. In Fig. 140 the uniformly loaded beam 
is cut through in the middle, leaving simply a compression block at the top 
and tension rod at the bottom. There is pull in the rod at the bottom but 
no shear or tendency for one side of the section to slide upon the other. In 
Figs. 141 and 142, on the other hand, where a section of concrete A BCD is 
cut out nearer the end of the beam (this being cut in a diagonal direction to 
illustrate better the effect of diagonal tension) leaving a compression block 
AB at the top and a rod CD at the bottom, the load to the left of the break 
being heavier will tend to drop, and this downward force or shear, combined 
with the pull, may be resisted either by the vertical rod BC, Fig. 141, or in 
Fig. 142 by the inclined rod EF. 

Computation of Shear and Diagonal Tension. Beams may be designed 

safe against diagonal tension failure by application of the formula for shear 
given below, because the shear may be taken as a measure of the diagonal 
tension.* A working stress for shear is therefore selected based, not upon 
tests of direct shear, but upon tests where the failure was by diagonal tension. 

Prof. Talbot in the analysis of shearing stressesf in a reinforced concrete 
beam has presented a formula for the unit shear at any point in a beam 
which is a very close approximation. 

Let 

V = total shear. 
v = unit shear. 
b = breadth of beam. 
b' = breadth of web of T-beam. 

jd — depth between center of compression and center of tension (approxi¬ 
mately, in a T-beam, distance between center of slab and steel). 


* The relation between the shear, as determined by the above formula, and the diagonal 
tension varies with the horizontal forces. From Merriman’s “Mechanics of Materials,” p. 265, 
1905 edition, 

If 

/ = diagonal tensile unit stress. 

0 

f' — horizontal tensile unit stress in concrete. 

v = horizontal or vertical shearing unit stress. 

Then 

^ ~ 2 K + \ 4 f'c 2 4- v 2 

The direction of this maximum diagonal tension, as Prof. Talbot points out, makes an angle with 

the horizontal equal to one-half the angle whose co-tangent is 1 . If there is no tension in the 

2 o 

concrete the last formula reduces to j — v. The maximum diagonal tension makes an angle of 

d • 

45 degrees with the horizontal and is equal in intensity to the vertical shearing stress, 
f Bulletin No. 14, University of Illinois, 1906, p. 20. 



REINFORCED CONCRETE DESIGN 


447 


Then 


V 

bjd 


( 2 9 ) 


or for a T-beam, v = 


V 

Vjd 


(30) 


That is, at any section of a beam, the unit shear, either vertical or horizontal, 
is the total shear at the section produced by the loads divided by the product 
of the breadth times the moment arm. 

The Joint Committee recommends that beams be reinforced against 
diagonal tension when the shear exceeds a limit of 2 per cent of the com¬ 
pressive strength at 28 days or 40 pounds for 2000 pounds concrete. The 
laws governing the internal stresses in a beam with a reinforced web are 
not yet clearly defined, but it is established that a comparatively small 
amount of reinforcement by bent-up bars appreciably increases the strength 
of the beam and, therefore, w r here a part of the horizontal reinforcement is 
bent up in a scientific manner and arranged with due respect to the shear¬ 
ing stresses, a value of 3 per cent of the strength at 28 days, or, for 2 000 
pounds concrete, 60 pounds per square inch may be allowed.* 

Since tests, however, show that web reinforcement can be introduced to 
increase shearing resistance to a value at least three times as great as when 
the bars are all horizontal, for beams thoroughly reinforced for shear a 
limiting value based on the section of the beam of 6 per cent of the strength 
at 28 days, or 120 pounds for 2 000 pounds concrete, may be used. 

In calculating web reinforcement, when the total shear is limited as above, 
the concrete may be counted upon as carrying | of the shearf that is, for 
concrete having a crushing strength of 2 000 pounds at 28 days, 40 pounds 
per square inch may be allowed on the concrete and the balance of the 
shear taken by the reinforcement. 

Following these recommendations of the Joint Committee and assuming 
that the distance between centers of compression and tension, jd, is approxi¬ 
mately %d: 


a. 


Stirrups are required with horizontal bars only when 


V 

bd 


is greater 


than i (40) =35. 


h. Stirrups are required in rectangular beams where a part of the hori¬ 
zontal reinforcement is bent up and arranged with due respect to the shear- 

V 

ing stresses (but not computed as taking diagonal tension) when — is 


greater than 52. 


* This is an arbitrary assumption based on observations of experiments by members of the Joint 
Committee. 

•j- Although it might be expected that the concrete, since it is assumed to have no tensile value, 
should not be assumed to assist in carrying diagonal tension, tests by Prof. Withey at the University 
of Wisconsin (Bulletin, Vol. 4, No. 2) indicate that the rule given is amply safe. 



448 


A TREATISE ON CONCRETE 


c. Since total shear should not exceed 120 pounds per square inch, bd 

V 

should not be less than —-. 

105 

For T-beams the same rules apply except that only the web of the beam 
is effective; hence, b' must be substituted for b. 

Vertical and Inclined Reinforcement. When the allowable working 
strength of the concrete in shear, as indicated in the preceding paragraphs, 
is exceeded, web reinforcement must be introduced. This may consist of 
the bent-up portion of the horizontal bars or of inclined or vertical members 
attached to or looped about the main reinforcement. Where inclined mem¬ 
bers are used, their connection with the horizontal reinforcement must be 
such as to insure against slipping. 

Let 

A s = cross sectional area of bars of a vertical stirrup. 

V, Vi, V2 = total vertical shear at different sections. 
v' = allowable unit shearing stress (or diagonal tension) in concrete 
alone. 

5 = distance between any two stirrups. 
d = depth from top of beam to center of steel. 

jd = distance from center of compression to center of tension in the 
beam (approximately id). 

b = breadth of beam. (In a T-beam, breadth of web or stem). 
f s = unit tensile stress in steel. 
a = angle of inclination with the horizontal. 


Since the shear at any place in the beam is used as a measure of the 
diagonal tension (see p. 446), the determination of the shear will indicate 
the diagonal tension or pull to be resisted by the stirrups and inclined 
bars.* 


Now the vertical shearing unit stress, v, at any section, is of course 
the total vertical shear produced by the loads divided by the area of the 
vertical section. Thus, at section A, Fig. 143, the vertical shearing 
unit stress (and also the horizontal shearing unit stress, since the two 


are equal) is and the shear in the full breadth, A A, of the beam for 


Vi V 

a unit of length is -—while similarly, at section B, it is—The total 

Jd jd 

shear, therefore, on the horizontal plane A1B1 between the two vertical 
sections B and A, which are a distance, s, apart, is \ ^ 1 ~^~ ^ s,or,when 


V 


jd 


Tat C is the average shear, is — X s. Since, as has been stated, the 

Jd 


* For more complete discussion of the relation of stirrup stress to shear, see page 764 . 







REINFORCED CONCRETE DESIGN 


449 


shear is used as a measure of the diagonal tension, the allowable working 
strength in tension of the concrete and the steel to resist this diagonal 
tension must equal this stnar stress. 

If the unit shear on a section does not exceed 120 pounds per square 
inch (for concrete testing 2000 pounds per square inch at 28 days), tests 
indicate (see p. 447) that the concrete may be assumed to take one-third 
of this, i.e., 40 pounds per square inch, while steel must be provided to 
take the balance. In this case if a stirrup is placed at C and the distance 
between stirrups is s, the area of cross section of the steel in the vertical 
stirrup, A s , must be sufficient to resist two-thirds of the diagonal tension 

5 V 

over the plane ^ 4 . 4 1B1 B, or, A s f s = § — . 

J d 


“7 

CENTER OF CO 

: 1 

MPRESSION 

r b 1 

• 

\> 4 

■> h 
' AN 

• 

c \b 

. 


l- r 

ELEVATION 

A: Ci Bi 


J 

. 

1 - 

-1 

\ 

► 

' 

r-*- 

1 

! 

1 

T 

1 

! 


A C B 

PLAN 


Fig. 143. —Illustration of Shearing Stresses. 
.(See p. 448.) 


As a more general case, the shear 
(involving diagonal tension) to be 
taken by the concrete, v'bjd, may 
be deducted from the total shear, 
using (V —v'bjd) instead of V. 
Formulas are presented for both 
cases, those at the left to be used 
only when the concrete is assumed 
to takeone-thirdof shear involving 
diagonal tension, and the steel two- 
thirds; those at the right when 
shear exceeds three times allow¬ 
able strength of concrete. 




(V -v'bjd) s 

7 Jd 


(3i«) 


The spacing of the stirrups is treated under a separate heading which 
follows. 

For bars inclined at 45 degrees, it may be assumed that the stress in 

A f 

any single reinforcing member is and the required area of bar, 

(assuming the steel in formula (32) to take two-thirds of the shear, 
and in formula (32 a) to take all in excess of that assumed for the con¬ 
crete) is 



0.7 sV 

fsjd 




0.7 (V — v' bjd) s 


(3 2 <*) 


For other angles of inclination, it may be assumed as approximately 
correct for the present to use the formula 


A 


s 


s’nasF 

fsjd 




sina (V — v'bjd) s 

fsjd 


( 33 fl ) 

































45° 


A TREATISE ON CONCRETE 


The use of these formulas is illustrated in the example 6, page 473. 
Formerly, as already stated, stirrups were figured to take direct shear 
across the rod, but this has been proved by tests to be incorrect. 

Stirrups in a Continuous Beam. In a continuous beam in the part 
near the support subjected to negative bending moment, the diagonal 
tension acts in the opposite direction to that in the part subjected to 
positive bending moment. The maximum stress then is in the upper 
end of the stirrups, so that they should be inverted near the supports. 
In any case the stirrups should be anchored in the tensile portion of the 
beam with their free ends (straight or preferably hooked) extending into 
the compressive part of the beam. 

Spacing of Stirrups. The spacing of stirrups must be less than the 
effective depth of the beam, and a practical limit for spacing is suggested as 
three-fourths the depth of the beam. Closer spacing than this, however, 
may be required in order to make the rods small enough to have sufficient 
bond, as given in the following paragraphs. 

Let 

x = distance in feet from left support to point at which required spacing 
is desired. 

Xi = distance in feet from left support to point beyond which stirrups are 
unnecessary. 

/ = span of beam in feet. 

w = uniform load in pounds per foot. 

V = total vertical shear at section x feet from left support in pounds. 
v = total unit shear at section in pounds per square inch. 
v' = allowable unit shear (or diagonal tension) on concrete alone. 

A 8 = cross-sectional area of vertical stirrup in square inches. (In a U- 
stirrup this is the sum of the area of the two legs). 
f a = allowable unit stress in stirrups in pounds per square inch. 
jd = depth of beam in inches from center of compression to center of 
horizontal reinforcement. (In a T-beam this may be taken as 
distance between center of slab and steel; in a rectangular beam as 
0.87 of the total depth to steel.) 
b = breadth of beam in inches. 

j = spacing of stirrups in inches at point x feet from left support. 

The required spacing of stirrups of given size in any part of the beam 
from formulas (31) and (31a), is 


S^sfsjd 

2 V 



A s fs j d 
V — v bjd 



Use left equation only when the concrete is assumed to take one-third 
of the shear involving diagonal tension (see page 449). 




REINFORCED CONCRETE DESIGN 


45 1 


These equations become for a uniformly loaded beam* 
3 A s f s jd . 2 AJJd 


s = 


( 35 ) 


5 = 


( 35 fl ) 


w{l- 2x) w ” w{l —2 x) -2 v' bjd 

For/y = 16000 lb. per sq. in., formulas (34) and (34 a) become 


24000 A Jd v 

* = - y - ( 36 ) 


and formulas (35) and (35a) change to 


48000 A J d . v. 

■5 = -rr-=4 ( 37 ) 


5 = 


16000 AJd 
~V-v' bjd 


32000 A s jd 


( 3 6<z ) 


w {l — 2 x) ' Jl w (l — 2 x) — 2 v' bj d 

See also page 452 and table on page 518£. 


( 37 ®) 


The above formulas, while applying strictly to supported beams, may be 
used for continuous beams with safety. 

Stirrups should thus be spaced by equation (34) or (35) up to a section 
where the unit shear equals the working shearing strength of concrete, bear¬ 
ing in mind, however, that the maximum spacing should not exceed three- 
fourths the depth of the beam. The distance from the support to the point 
where no stirrups are required, for uniform loading isf 

1 v'bjd 

x, — - — 

2 w 


(38) 


From formulas (34) and (36) it is evident that the necessary spacing of 
stirrups is inversely proportional to the total shear V at any point and there¬ 
fore is the smallest at the end of the beam and increases toward its middle. 

Many constructors advise the insertion of occasional stirrups throughout 
the entire length of the beam even if they are not theoretically necessary. 

For a small beam where the stirrups are spaced uniformly, for convenience, 
only the minimum value of 5 needs to be figured by substituting for V in 
equation (34) and (36) the total shear at an arbitrary distance \ d from 
the support, or in equation (35) and (37) substituting h d for x. 


wl 

* By substituting in equation (34), V— — — wx as the total shear at any point in a uniformly 

2 

loaded beam. 

V 

•j- The unit shear v = ^ y Stirrups are unnecessary at section where v — v' or less, or 
V' 

v > = • For the case of uniform load V — — wx Y Substituting this for V' and solving 

bjd 2 

i v' bjd 

for x lf we have xi = ~ — ^ 










452 


A TREATISE ON CONCRETE 


Graphical Method for Spacing Stirrups.* In a large and important beam, 
the spacing should vary with the shear. The following graphical method 
will be of use in such cases: 

Lay out half of the span — to an) convenient scale as shown in Fig. 144. 

2 

Compute the values of 5 at three or four points (point 1, 2 and 3 in the 
figure) and lay them out on the perpendiculars erected at the respective 
points to the same scale as the span. Draw a smooth curve located by the 
points on the perpendiculars. From point a on the perpendicular at the 



point where the first stirrup will be placed, draw a line at 45 degrees to 
intersect with the line representing the span and erect at the point of inter¬ 
section, B, a perpendicular to cut the curve in point b. A line drawn from 
b at 45 degrees will intersect the span in point C, where the above process 
is repeated. The points, A , B, C, D , E, thus obtained are the points in 
which stirrups are required. 

For uniformly loaded beams it is only necessary to compute the minimum 
spacing of stirrups, that is, at the support. The spacing at two other 

l 

points may be obtained from the fact that the spacing for a: = — is 

8 

l 

four-thirds the minimum and for ^ = — is twice the minimum. For 

4 

x = - the spacing is infinity. 

2 

Types of Shear Reinforcement. Fig. 145 illustrates different types of 
diagonal tension reinforcement, showing beams reinforced with stirrups 
alone, with bent bars, and with a combination of bent bars and stirrups. 
The method of providing for the negative bending moment over the 
support is also indicated. 


* For spacing with uniform loading, see page 5186. 


















REINFORCED CONCRETE DESIGN 


453 


Fig. 146, page 455 shows different types of stirrups. 

Diameter of Stirrups. The diameter to select for stirrups is governed 
by the limiting spacing of the stirrups as given in the preceding paragraphs, 
by the bond of the stirrup prongs, and by convenience in selecting and 
placing the reinforcement. The effective length of the stirrup should be 
taken less than the total length because of the slight change in the inten¬ 
sity of shear below the neutral axis and because also a lower bond 
strength may be expected there. 

Tests by Prof. Talbot indicate that it is safe to use up to at least A of 
the total length of the stirrup in figuring the bond. 



Fig. 145. Reinforcement of 'a Continuous Beam. (See p. 452.) 

The maximum diameter of stirrups which can be used by these assump¬ 
tions without danger of slipping is determined by the bond and can be 
figured by the formulas given below. 

Let 

i = diameter of stirrup bar. 

A = area of stirrup bar. 

0 — circumference of stirrup bar. 

































































































































































454 


A TREATISE ON CONCRETE 


0 


d = depth from surface of beam to center of tension steel. 
it — allowable bond stress per unit of surface of bar. 

C 8 and C b = constants to use in formulas (39) to (42). 

Then for vertical stirrup with straight upper end.* 

A _ u A _ 

— < o. 6 - d or — < J C 8 d 

S 

A 

For round or square stirrups — = \ 


Hence 

i < C 8 d 

For rods inclined at 45 0 the above formulas change tof 

i < C b d for round or square sections 
A _ 

and — < \ C b d for other shapes. 


( 39 ) 


(40) 

(41) 

(42) 


The table below gives the values of C 8 and C b for different values of 
tension and bond when units are inches and pounds. 


Values of Constants to Use in Formulas ( 39 ) to ( 42 .) ( See p. 454 .) 


C s 


C& 


a 00 

3 <D 
u 
(L) 

*-=< CO 

IJ 


VERTICAL BARS 

Allowable unit tension in stirrups in 
lb. per sq. in. 


BARS INCLINED 45° 

Allowable unit tension in bars in 
lb. per sq. in. 


Lb. 

per 

sq. 

in. 

12 000 

14 000 

16 000 

18 000 

20 OOO 

12 OOO 

14 OOO 

16 OOO 

18 OOO 

20 OOO 

80 

0.016 

0.014 

0.012 

0 . 011 

0.010 

0.022 

0.019 

0.017 

0.015 

O.OI4 

100 

0.020 

0.017 

0.015 

0.013 

0.012 

0.028 

0.024 

0.021 

0.019 

O.OI7 

120 

0.024 

0.020 

0.018 

0.016 

O.OI4 

0-033 

0.028 

O.O25 

0.022 

0.020 

150 

0.030 

0.026 

0.023 

0 

0 

cO 

O 

O.OlS 

O.O42 

0.036 

O.O3I 

O . 028 

O.O25 


_ A _ h u A 

* f s A < 0.6 dou, hence < 0.6 r~ d Callo.6y — \ C$ and obtain — 

0 Js I s 0 

j-For rods inclined at 41;° substitute for d in the above equation \/ 2 d. 


= ic.d 


Hence ^ Cb 


_ « A — , n , 
./2 7 and — ^ t Cbd 

V J8 0 





























REINFORCED CONCRETE DESIGN 


455 


The above formulas and table apply directly only to straight rods. 

The bond stress between concrete and plain reinforcing bars may be 
assumed at of the compressive strength at 28 days, or 80 pounds for 
2 000 pound concrete (see p. 528), which for the allowable tension in steel, 
f s = 16 000 pounds per square inch gives a diameter of i = 0.012 d. For 
deformed 'bars the bond may be increased to 100 or 150 pounds per 
square inch, varying with the character of the bar. Using the highest 
figure and 16 000 pounds per square inch as the allowable tension in steel, 
a beam 20 inches deep to center of steel, making no allowance for the value 
of a bent end, would require stirrups not to exceed 0.5 inch or ^-inch diame¬ 
ter if deformed bars are used, or |-inch diameter plain stirrups. De¬ 
formed bars are therefore useful for stirrups to permit larger diameters, 
although the total quantity of stirrup steel required with a given allowable 
tensile stress is not changed. 






r=ij 


% 

• •• 

■==! 

9 


• • • 


• 

© 

? 


•—© 


y 


A BCD 

Fig. 146. Types of Stirrups. {Seep. 453 -) 







. Recent tests (p. 467) show that a right-angle bend of 5 diameters or a 
semi-circular bend of similar length is sufficient to stress the steel to its 
elastic limit provided the hook is well imbedded in the concrete so that it 
cannot kick out. With an imbedment in concrete in all directions equal 
to 8 diameters of the bar, a hook of 5 diameters may be assumed to 
develop the elastic limit of the steel and larger stirrups can be used than 
the table indicates. 

Ratio of Span to Depth in Rectangular Beam which Renders Stirrups 
Unnecessary. In a T-beam stirrups are almost always needed and every 
case must be computed by rules already given. For a beam which is rect¬ 
angular throughout its length stirrups are unnecessary if at the section of 
maximum shear the intensity of diagonal tension does not exceed the allow¬ 
able stress in the concrete. For a rectangular beam uniformly loaded 
we may deduce the following expression for the ratio of span to depth which 
will render stirrups unnecessary. 


n ( oT 

































45 6 


A TREATISE ON CONCRETE 


Let 

l = span of beam in inches. 

d = depth from surface of beam to steel in inches. 
v = maximum unit shear at end of beam in lb. per sq. in. 
C = a constant from Table io on page 519. 

wl 2 

a = denominator in formula M = — 

a wl 2 

Then it may be shown* that, when M = — 

l _ a 

d ^ 1.74 C 2 v 


( 43 ) 


Adopting values of working compression in concrete of 650 pounds per 
square inch, working unit shear of 40 pounds per square inch, working 
tension in steel of 16,000 pounds per square inch, and a ratio of elasticity 

l 

of 15; for a — 12 , ~= 15.6. 


If the ratio of span to depth (both in same units) is therefore equal to or 

a 


less than the value of 
needed. 


0.77 


as 


given by this formula, no stirrups are 


BOND OF STEEL TO CONCRETE IN A BEAM 

The bonding of the steel to the concrete is discussed on page 461, the 
values being based on the resistance to withdrawal of a steel rod imbedded 
in concrete. In a reinforced concrete beam the bond of the tension steel 
per unit of length must not exceed its safe working value. The concrete 
surrounding the steel acts as a web between its tensile and compressive parts, 


* In addition to above notation let, w = load per linear inch of span, b — breadth of beam 
in inches, M = bending moment. 

wl 

With uniform load the shear is a maximum at the support and is equal to ~. Taking 0.S7 d as 

the approximate depth from the center of compression to the center of tension, the maximum 
intensity of shear (and consequently of diagonal tension) in the concrete is therefore (See formula 

. wl wl 2 

(29) p. 447) v = 2 — x 0 87 bd ' From page 754, formula (11), it is evident that for M = 


wl = 


a bd 2 


a 


1 


£ 2 1 Substituting this value of wl in the above expression for v and solving for bearing 

l _ a 

in mind that the maximum unit shear must not be exceeded, we obtain — >-— * 

d 1.74 C 2 v 

wl 2 l — 6.8 u)/ 2 / 1 . ic 

Similarly when M = > • For a cantilever where M = - , — = -- 

12 d C 2 v 2 d C 2 v 


For a cantilever where M 





REINFORCED CONCRETE DESIGN 


457 


and the pull in the rods as it becomes less and less, because of the reducing 
bending moment, passes into the beam, thus producing a bond stress between 
the steel and the concrete. If the bond is insufficient the rod will slip. 

Care must be taken, therefore, to see that the size of horizontal bars in a 
beam is not too large to give sufficient bond surface between the steel and the 
concrete. Using the formula suggested by Prof. Talbot.* 

Let 

V = total shear. 

v = unit shear in pounds per square inch. 
u = unit bond in pounds per square inch of surface area. 
o = perimeter of bar in inches. 
lo = sum of perimeters of all bars. 
m — number of bars in tension. 

jd = distance between centers of tension and compression. 
d = depth from surface to center of tension steel. 

Then 


u 


V 

jd lo 


( 44 ) 


The unit bond stress recommended by the Joint Committee for concrete 
whose strength is 2 000 pounds at 28 days is 80 pounds per square inch, and 
assuming also as a close approximation that jd — J d, the total perimeter 
of bars which are required at any point of a beam is 


V 

70 d 


(45) 


In a continuous beam this formula applies to the steel which is in tension 
whether it is located in the top or the bottom of the beam. Since the nega¬ 
tive bending moment decreases quite rapidly, the bond stress at the support 
of a continuous beam is more apt to exceed the safe working limit than in 
the middle of the beam, thus requiring more attention and frequently 
limiting the diapieter of the bars. 

The above formula does not apply to the compression steel and therefore 
has no relation to the steel in the bottom of a continuous beam at the support. 


* Bulletin No. 4, University of Illinois, 1906, p. 19. 

The formula may be derived from the relation of the bond to the shear. 

The tendency to slip, or the bond stress, is equal to the shear because the measure of both of 
them is the increment of the moment. Hence uSo = vb, from which, since 





45 8 


A TREATISE ON CONCRETE 


Tests by Prof. M. 0 . Withey* indicate that the bond of tension bars in 
a beam is much less than shown by tests in which bars are pulled out from 
blocks of concrete, probably because of the compression on the head of the 
block in the latter case. For 1:2:4 concrete, the ultimate bond strength 
at the age of 60 days averaged 276 pounds per square inch. 


POINTS TO BEND HORIZONTAL REINFORCEMENT 


The bending moment in a reinforced concrete beam decreases toward 
the ends, reducing in the same ratio the pull in the tension bars. Since 
these must be designed to take the maximum moment at the center of the 
beam, the steel at the ends, when the bars are carried horizontally through 
the whole length of the beam, is stressed away below its working strength. 
By bending up a part of the bars not required for tension, the inclined por¬ 
tion assists in providing for the diagonal tension, and by carrying the ends 
horizontally over the top of the supports the tension due to negative bending 
moment may be resisted there. 

If part of the rods are bent up at a certain point, those remaining must 
have sufficient sectional area to carry the' tension beyond this point, and 
must also have sufficient length imbedded to prevent slipping. The limit¬ 
ing locations for bending the rods may therefore be found as follows: 

Let 

m = number of bars at the center. 
ni x = number of bars to be bent. 

M = maximum moment — in which 

a 

a — denominator in the expression for bending moment. 
x x — distance from support to point where m x bars may be bent up leaving 
sufficient steel to carry the pull. 

Then it may be proved that the distance in feet from support to point 
where m x bars may be bent up and still leave sufficient steel to take the pullisf 


^Proceedings American Society for Testing Materials, 1909. 

f The ratio of pull at the middle to that at the point under consideration equals the ratio of 
moments in these points. Thus if the steel is stressed equally at both points, 


Substituting 


t 2 7Z 

M Xl : M = (m — mi) • 

4 


m f-iz 

4 


M = 


wl 2 wl 2 

and M x , = 
a ’ a 



2 


< ~ 

1 2 



and solving for x 2 


— xv 


2 







REINFORCED CONCRETE DESIGN 


459 


*1 < 



( 47 ) 


The last equation 

tv/t 

moment M = —.. 

a 


may be used for beams designed for any bending 
For a — 8, the formula changes to 



(48) 


Having thus determined see that the remaining horizontal bars are 
secure against slipping by the use of formula (44), page 457. 

The use of the formulas are illustrated in the Example 6, page 472. 


SPACING OF TENSION BARS IN A BEAM 

The tension bars in a beam must be a sufficient distance apart to properly 
transmit the pull to the concrete in the beam and prevent cleaving the con¬ 
crete between them.* At most points in a beam, with bars of ordinary size, 
the bond stress as determined from formula (44) page 457, is low, and there * 
is therefore but little tendency to slip and the bars may be placed as close 
together as proper placing of the concrete between them will permit. At 
points where a part of the rods are bent up, and especially in the top of the 
beam over the supports, the bond stress may be high, and it is advisable to 
make a rule that the rods shall not be spaced nearer together in the clear 
than 1J times their diameter. To permit the concrete to be readily placed 
between them and to give sufficient concrete on the sides of the beam for 
fire protection, it is advisable further to make the minimum spacing between 
the rods 1 inch and the minimum distance of the rods from the sides of the 
beam 1^ inches in the clear. 

There is less danger of vertical splitting, and where two layers of rods 
are used the rods in a vertical plane may be placed directly over each other, 
and with sufficient space simply to permit the mortar to run between them. 
The Joint Committee specifies a limiting clear space of ^ inch. 

Prof. McKibben has suggested a mathematical demonstration for deter¬ 
mining the width of concrete required between the rods in order to make the 
resistance in shear equivalent to the adhesion of the concrete to the steel. 

*The relation of bond to shear is discussed on the following page. 


I 


460 


A TREATISE ON CONCRETE 


Let 

l = length of rod considered in inches. 

s b = distance in the clear between two rods in inches. 

i — diameter of rod in inches. 

u = adhesion or bond between concrete and steel per square inch of 
surface of steel. 

v = direct shearing strength of concrete in pounds per square inch. 

If the beam splits at the rods, it is apt to shear through the concrete 
between the rods, and break the adhesion between the upper half of the rod 
and the concrete. When such splitting occurs the shearing strength of the 
concrete between the rods, on a plane with their centers, is equal to or less 
than the adhesion of the concrete to the half circumference of one of the 
rods and the minimum spacing is then* 

s b — 1 - 57 ' (49) 

If, for example, the working bond stress, u, is assumed as 80 pounds per 
square inch and the working strength of the concrete in direct shear is 
taken at 120 pounds per square inch, the formula becomes 

s b = i.osD (50) 

that is, the minimum net distance in the clear between the rods is approxi¬ 
mately equal to the diameter of the rod. Since the concrete is not easily 
placed between the rods it may have a lower strength there and hence a 
clear spacing of diameters (with a minimum of one inch), as suggested 
above is advisable unless it is determined by computation that the bond 
stress is much lower than is assumed here. Deformed bars, if stressed to 
their full bond value should be spaced farther apart than plain bar. 

In the middle of a beam the bond stress is low, so that the formulas 
are most useful in considering the rods in the top of the beam over the 
support. 


DEPTH OF CONCRETE BELOW RODS 

The selection of the thickness of the concrete below the rods is governed 
more by the proper fire and rust protection of the metal than by the stresses 
in the beam. 


* For a short length of rod /, equate the strength in shear of the concrete between the rods 
the adhesion between the concrete and the upper half circumference of the rod. 

Hence 


*b lv 


ft i l u 


3 b = J -57 



to 


2 


REINFORCED CONCRETE DESIGN 


461 


Prof. Charles L. Norton, who has made a careful study of the subject, 
considers a thickness of 2 inches essential for efficient fire protection. (See 
p. 333.) Since an excessive thickness adds to the danger of cracking, 
because the tension in the concrete increases with the depth below the steel, 
with but slight corresponding gain in strength to the beam, this thickness, 
measured from the lower surface of the steel, and not from its center of 
gravity, may be taken as a maximum. Thus, in important members which 
are liable to severe fire, 2 inches may be considered the standard require¬ 
ment, while for secondary members and floor slabs, a less thickness, rang¬ 
ing from ^ inch to 2 inches, is probably warranted. 

The following thicknesses of concrete below the steel may be employed 
under ordinary conditions: 

Thickness of Concrete below Steel. 

Depth of slab or beam, Thickness below lower surface of 

inches rods,* inches 

d to 2 i 

2^ to 4 | 

4! to 84 1 

9 to 12 

13 to 18 

19 to 2 0 

Greater than 20 

♦Values up to depth of 20 inches are from tables of Mr. Edwin Thacher, except that his 
depths are taken below center of gravity of steel. 


4 
1 1 
2 


The Joint Committee, 1909, recommends slightly greater thickness than 
given in the above table, and its recommendations should be followed 
wherever the conditions are especially hazardous. The Committee suggests 
that “the metal in girders and columns be protected by a minimum of 2 
inches of concrete; that the metal in beams be protected by a minimum of 
ii inches of concrete, and that the metal in floor slabs be protected by a 
minimum of 1 inch of concreted’ 


BOND OF CONCRETE TO STEEL TO RESIST DIRECT PULL 

Tests by different experimenters show that with similar materials the 
bond is proportional to the area of the surface in contact, and varies with 
the character of the surface and the nature of the concrete or mortar. 

Feretf found that the bond of concrete to iron is nearly proportional to 
the percentage of cement in a unit volume of concrete, and that theie is an 

•j- Thonindustrie-Zeitung 25 (153)2, 213-2, 215, translated in Cement, July 1902, p. 213. 


462 


A TREATISE ON CONCRETE 


increase of strength of about 50% in concrete two years old over that three 
months old. The best consistency for concrete he considers to be so plastic 
as to be almost sloppy. He found that the bond of a very dry concrete was 
only about one-fourth that of an almost sloppy concrete which gave the 
maximum density. The bond increased rapidly as the proportion of water 
increased until the concrete reached its maximum density, when for larger 
proportions of water there was a slow decrease in bond strength, very wet 
concrete showing a bond about three-fourths that of the slightly dryer 
concrete having maximum density. 

In tests made by Prof. M. O. Withey at the University of Wisconsin* in 
1906, the results of which are contained in the following table, the bond 
developed by different specimens averaged about 0.3 of the compressive 
strength and increased nearly proportionally with it. 


Variation of Bond with the Compressive Strength* 
1:2:4 Concrete—Age 28 days. (See p. 462.) 
By Prof. Morton O. Withey. 


Size 

of 

rod. 

In. 

Area of 
Rod. 

Sq. in. 

Depth 

im¬ 

bedded. 

In. 

Maximum 

load. 

Lb. 

Unit stress in 
rod. 

Lb. per sq. in. 

Elastic limit 
of steel. 

Lb. per sq. in. 

Bond 

Lb. per sq. in. 

Compressive 
strength of 
concrete. 

Lb. per sq. in. 

Is 

0.248 

6* 

7200 

29 000 

36 400 

627 

2155 

Is 

0.248 

H 

55 °° 

22 200 

36 400 

509 

2000 

Is 

0.248 

6i 

6700 

27 000 

36 400 

607 

1850 

Is 

0.248 

6i 

4625 

18 600 

36 400 

418 

1485 

Is 

0.248 

6* 

4250 

17 100 

36 400 

3 8 4 

1435 

Is 

0.248 

6 

4100 

16 500 

36 400 

3 8 7 

1150 

* 

0.196 

6 

3600 

18 400 

38 600 

382 

1150 

! 

0.196 

5l 

1500 

7 600 

38 600 

i66f 

79 51 

* 

0. 196 

6± 

1840 

9 400 

38 600 

187! 

5 8 4 t 


As shown in the table, which gives in a condensed form the results of 
tests made by Prof. Talbot at the University of Illinois^ in 1905, a 1 : 2 : 4 
concrete realized a bond resistance averaging about 13 per cent, higher 
than a 1 : 3 : 5^ concrete. The effect of the surface of the bar upon bond 
resistance is also indicated. Plain round mild steel bars developed a bond 
resistance ranging from 355 to 465 pounds per square inch of contact sur- 

* Bulletin, University of Wisconsin, Vol. 4, No. 2, Nov. 1907. 

t Made upon concrete in which sand and limestone screenings containing 40% of dirt were 
used as aggregate. 

X Bulletin No. 8, University of Illinois, Sept. 1906. 















REINFORCED CONCRETE DESIGN 


463 


face, a bond about 2.7 times that of cold rolled shafting and tool steel and 
also much greater than that of flat mild steel bars. Deformed bars give a 
much higher bond resistance. In cases* where the embedment was not so 
great as to stress the bars beyond their elastic limit, the results indicate a 


Tests of Bond of Union Between Concrete and Steel. 
Age of Concrete , 60 days. (See p. 462.) 

By Prof. Arthur N. Talbot. 


Type of rod. 

Size. 

Inches. 

Proportions. 

S ’ 1 Encased length. 

tn 

Surface in contact. 

M • 

3 

f-t 

cr Maximum load. 

"3 

3 

O 

tt 

Lb. per 
sq. in. 

FRICTI 

RESIST 

a 

3 

- § 

O J* 

H £ • 

Lb. 

ONAL 

\NCE. 

_C 

cr 

u 

u 

« CU 

■3 

J=> 

Ratio of Frictional Re¬ 

sistance to bond. 

Plain Round 

h 

1 :2.4 

6 

9.4 

3 S 93 

412 

2135 

227 

55-2 

Plain Round 

5 

8 

1 '.2 :4 

6 

11 . 8 

5376 

465 

34 S 5 

297 

64.0 

Plain Round 

X 

0 

1 '.2 14 

12 

18.8 

7605 

404 

4982 

266 

65 • 5 

Plain Round 

1 

1 '.2 :4 

12 

2 3 • 5 

97 3 6 

414 

5284 

223 

54-0 


Average 

1 ’.2 '.4 



6652 

424 

397 1 

253 

59 • 7 

Plain Round 

* 

1: 3 ' 5 ? 

6 

9.4 

349 s 

372 

i 9 8 .3 

2 10 

57 *° 

Plain Round 

t 

i: 3 : 5 i 

6 

11 . 8 

417° 

355 

2700 

227 

64.0 

Plain Round 

i 

1: 3 : 5 i 

12 

18.8 

7°35 

373 

5°66 

268 

72.0 

Plain Round 

A 

8 

1 : 3 : 5 t 

12 

23-5 

945 8 

402 

53 66 

228 

56.8 


Average 

1 : 3 : 5 ^ 



6040 

375 

3779 

233 

62.4 

Cold Rolled 

1 

1: 3 : 5 i 

6 

18.8 

2570 

136 

1256 

67 

49.2 

Shafting 










Cold Rolled 

h 

i: 3 : 

6 

9.4 

1476 

i 57 

466 

5 ° 

3 1 • 8 

Shafting 










Mild Steel 

-h~ l \ 

1 : 3 : 5 i 

6 

20.2 

2 53 6 

125 

1713 

84 

67 . 1 

Round Tool 










Steel 

i 

1:3:6 

6 

14 . 1 

2077 

147 





bond strength for deformed bars in ordinary 1:2:4 concrete of from, say, 
400 to 700 pounds per square inch of contact surface.f 

Tests by Mr. Frank A. BoneJ indicate that the bond of bars in 


* Bulletin No. 1, University of Illinois, Sept. 1904, Table 7; Proceedings American Society for 
Testing Materials, Vol. VII, 1907, p. 467; Engineering Record, Dec. 22, 1906, p. 694. 
fBulletin, University of Wisconsin, Vol. 4, No. 2, Nov. 1907. 

^Engineering News, May 21, 1908, p. 571. 































464 


A TREATISE ON CONCRETE 


concrete which is being stressed to a high compression is much greater 
than in unstressed concrete. 

The results of many bond tests are without value because the yield point 
of the steel was exceeded. 

The bond stress of the tension bars in a beam is determined by methods 
discussed on page 457. 


LENGTH OF BAR TO PREVENT SLIPPING 


In a reinforced concrete member it is necessary not only to have at a 
given section the required amount of steel to take the pull or the compression 
but it is also essential for each bar to have sufficient length of imbedment 
in the concrete so that the bond (that is, the resistance to slipping) of the 
bar in the concrete is great enough to develop the necessary direct pull or 
compression in the body of the bar. Unless a bar is bent up or anchored 
by some mechanical means (see p. 466) its resistance to slipping is deter¬ 
mined by the length of imbedment and the value of the unit bond between 
the concrete and the steel. 

The length of imbedment necessary to develop a required holding power 
through mere bond between the concrete and steel maybe determined thus: 

Let 

f a = wmrking tensile or compressive stress per square inch in the body 
of the bar. 

i — diameter of bar in inches. 

u = bond in pounds per square inch of surface. 

l x = necessary length of imbedment of bar in inches. 

Then* 



(46) 


This formula holds for square as well as for round Lars. Using the limit¬ 
ing bond stress suggested by the Joint Committee for round bars of mild 
steel, 80 pounds per square inch, the length of imbedment when the steel 
is stressed 10 16 000 pound per square inch is fifty diameters. Deformed 


* If the bar is round the total force to be developed in the body of the bar is 

holding power of the bar, or its resistance to slipping is n i u l. 

Equating these and solving for /, we obtain 

Ns 


7Z r 

- i a while the 

4 Ja 



REINFORCED CONCRETE DESIGN 


465 


bars may be given a greater bond stress, while, as indicated in the preceding 
paragraphs, a smooth steel of the nature of tool steel must be given less. 
It has been suggested that the bond of deformed bars be taken the same as 
the bond of plain bars except using for their diameter the diameter of a 
cylinder based on the longest projections, that is, of a cylinder which would 
be sheared out by the deformed bar. Ordinarily then, as indicated on page 
528, a bond stress for deformed bars varying with the character of the bar 
from 100 to [50 pounds per square inch may be used, corresponding to an 
imbedment of 40 to 27 diameters. For smooth metal of the nature of tool 
steel not over 30 or 40 pounds per square inch, that is 133 to 100 diameters 
should be permitted. Flat steel or structural steel with flat surfaces should 
be given a similarly low value per square inch. 

The bond in all cases is based on the surface area of the imbedded bar. 
Later tests by Prof. Withey, which show much lower bond strength when 
the concrete in the specimens is not affected by the compression, are referred 
to on page 458. These indicate that a strength in bond for 1:2:4 con¬ 
crete cannot be assumed greater than 273 pounds per square inch of surface 
of round bars, so that the value of 80 pounds per square inch suggested 
above, is a fair working unit bond stress. 

All of these bond values are based on a concrete whose strength at the 
age of thirty days; when tested in cylinders, is 2000 pounds per square 
inch. The length of imbedment also varies with the working stress in the 
steel in tension or compression. In compression, steel is not apt to be 
stressed over 8 000 to 10 000 pounds per square inch, so that a shorter 
length of imbedment is required. Furthermore, the concrete in com¬ 
pression provides a greater grip. 

The following table gives the length of imbedment of round or square 
bars for different unit stresses in the steel: 


Length of Imbedment Required for Round and Square Bars. 


TENSION IN 
STEEL fS' 

LENGTH OF BARS TO IMBED IN TERMS OF THE DIAMETER. 



Allowable 

bond stress, 

pounds per square inch. 


Lb. per sq. in. 

40 

60 

80 

100 

120 

1 50 

8 000 

5 ° 

33 

25 

20 

l 7 

13 

12 000 

75 

50 

37 

30 

25 

20 

16 000 

100 

67 

5o 

40 

33 

27 

20 000 

125 

83 

62 

5 ° 

41 

33 


Note: The length of imbedment may be obtained by multiplying the value 
selected from this table by the diameter of the bar. 






















466 


A TREATISE ON CONCRETE 


VALUE OF HOOKED BARS IN BOND 

The results of a valuable series of tests on hooked bars, made for the 
Eastern Concrete Construction Company at the Massachusetts Institute 
of Technology under the direction of Prof. H. W. Hayward are presented 
in a table which follows. 

In all the tests f-inch round bars were imbedded in blocks 12 inches 
square and 15 inches long, to a depth of 12 inches with an additional bend 
of different lengths. In one case the straight portion of the bar was greased. 
Right-angle bends and semi-circular bends on a 3-inch diameter were 
tested. Seven specimens of each type were tested, the individual results 
being extremely uniform except in type 1, where the straight bar test gave 
the usual variations expected in ordinary bond tests. 


Tests of Hooked Bars in Bond, Massachusetts Institute of Technology, 1909, for 

Eastern Concrete Construction Company 

Proportions of concrete 1:2:4. Age 28 days. Crushing strength con¬ 
crete 1130 lb. per sq. in. at 34 days. Round bars f-inch diameter. 

Yield point of steel 35 900 lb. per sq. in. or 15 870 lb. for f-inch bar. 
Elastic limit of steel 29 000 lb. per sq. in. or 12 820 lb. for f-inch bar. 


<0 

o, 

>> 

H 


Length of 
straight 
bar 


Length and Kind 
of hook 


First slip* 
lb. 


Maximum 

load 

lb. 


c 

CO 

(h 

a 


- o 
"O . 
G C 
O 
« 


Condition at maximum load 


in. 
x 2 
12 

(greased) 
12 


12 

12 

12 

12 
12 


4" square bend 


U U 


r 


2 

6 " 


(no backing of 
concrete) 

3" return bend 

3" “ “ 

(with 3" extra length 


lb. 

7 770 
16 000 
18 700 

J not 

f recorded 
17 000 dr 

9 600 


17 100 
17 300 


lb. 

16 000 
21 450 

17 770 
19 530 
1 5 590 


22 660 

23 630 


275 


Bars pulled out 
Concrete crushed at bend 
finally split block. 
Concrete crushed; bars 
partly straightened. 

Bars straightened out; 
Block not split. 

Bars pulled out, or split 
concrete by kicking back 
End of bars raised up and 
crushed concrete; bars 
pulled through 
Concrete split 


* As shown by drop of beam except in type (6), where the bent ends begin to straighten, the 
drop of the beam coming either at the same period or at about I ooo lb. later. 
















REINFORCED CONCRETE DESIGN 


467 


In all the tests except those with straight bars (type 1) and those where 
there w r as no concrete back of the bend, the elastic limit of the steel was 
passed before the bars began to pull out as indicated by the drop of the beam. 

1 he crushing strength and also the bond strength of the concrete was 
low because the specimens were stored at a low temperature, but this does 
not affect appreciably the value of the results. 

The following conclusions may be drawn from these tests: 

(1) A 4-inch right-angle bend in a f-inch round bar (5 diameters) is 
sufficient to stress the steel to its elastic limit. A longer bend than this 
is not necessary. 

(2) A semi-circular bend on a diameter 4 times the diameter of the bar 
appears to be even more effective than the square bend. 

(3) No crushing of the concrete occurs until the elastic limit of the steel 
is passed. 

(4) A backing of concrete whose thickness is 4 times the diameter of 
the bar appears to be effective to prevent kicking back before the elastic 
limit of the steel is reached, provided the area of section is large enough 
to prevent cracking on a plane with the bend. 

Tests at the Case School of Applied Science indicate that a section of 
concrete six inches square is not enough to prevent a f-inch bar from 
cracking the concrete before the steel reaches its elastic limit. 

The most important conclusion from the Institute experiments is that 
a bend 5 diameters in length in a J-inch rod and probably,—from compari¬ 
son of the results from the 2-inch hooks with the others,—that even a bend 
of 2\ diameters is sufficient, when the hooks are properly imbedded in 
concrete, to permit the steel to reach its elastic limit before starting to pull 
out. In a number of the tests the deformations were measured and show 
no initial slip previous to the periods given in the table. The result agrees 
with tests also made at the Institute upon hooks not imbedded in concrete 
where the elastic limit of the steel was reached before the hooks lost their 


g n P* 


468 


A TREATISE ON CONCRETE 


EXAMPLE OF BEAM AND SLAB DESIGN 

The use of the formulas given in the preceding pages can be best illustrated 
by the design of a floor bay consisting of slabs, beams and girders. The 
design of reinforced concrete structures permits of so many variations by locat¬ 
ing steel in different ways that more than one type of design for the same 
member is almost always possible. The dimensions and reinforcement shown 
illustrate common methods, and the ariangement of details in the different 
members is also given as typical. The principles of design follow the recom¬ 
mendations of the Joint Committee on Concrete and Reinforced Concrete, 
1909. 




FLAN 

Fig. 147.— Design of Floor System. (See page 469.) 

















































































REINFORCED CONCRETE DESIGN 469 

The computations are given with but few comments, but references are 
entered to the pages upon which each part of the calculation is based. 

Example 6 ; Design a typical slab, beam and girder for a reinforced floor 
to support a live load of 250 pounds per square foot with columns spaced 
18 by 19 feet on centers. 

Solution : The girder will be made 18 feet long and the distance between 
centers of beams 6 feet. The beams are 19 feet long on centers. 


Refer to page 


Take allowable fiber stress in concrete, 650 lb. per sq. in. 528 

Take allowable tension in steel, 16 000 lb. per sq. in. 529 

Take ratio of elasticity of steel to concrete, 15 529 

Take direct shear in concrete, 120 lb. per sq. in. 528 

Take shear in concrete involving diagonal tension, 40 lb. per sq. in. 528 

Take bond between concrete and plain bars, 80 lb. per sq. in. 528 

Notation used in Example is Joint Committee standard 529 


Slab. Span of slab is 6 ft. 

-“ Live load. 250 lb. per sq. ft. 

Assumed dead load, 50 lb. per sq. ft. 

Total loading, 300 lb. per sq. ft. 

wl 2 300 X 6 2 X 12 . 

Use for moment, M = —■, then M* = I2 = 10 800 m. lb. 440 


Same value may be found directly from curves 524 

Since f c = 650, / s — 16 000 and n = 15, then 

C = 0.096 and p = 0.0077, from table 10 519 

Hence, depth to steel is, d = 0.29 X 0.096 \/ 10800 = 2.9 in. 421 

Taking f in. concrete below steel, thickness of slab is 3! in. 461 

Area steel, As, = 2.9 X 12 X 0.0077 = 0.268 sq. in. _ 421 

Round rods | inch in diameter spaced 5 inches on centers will give 
required area. Table 1. 5°7 

The same results may be obtained by using the slab table 5: 513 


Since this table is based on M = — and we use here M = the total unit 

lO A ~ 

weight of 300 pounds per square foot may be reduced £ or to 
250 pounds and this value treated in the table, which gives a 3! inch 
slab. 

Rods must be bent up to give same steel at top of slab over supports. 

Beams. Span 19 feet. 

Distance between beams, 6 feet. 

Dead and live loads of the slab per foot of length of beam, 

6 X 300 = 1800 pounds. 

Assumed dead load of stem of the beam, 200 pounds per foot 
of length. 

Total unit loading, 2000 pounds. 

wl 2 ,, 2000 X i9 2 X 12 . , 

Use for moment M = — , then M = -—-= 722 000 inch-pounds, 

Reaction at support, which is the maximum shear, is 

2000 x 19 . 

V = -- = 19 000 pounds. 


* Only one 12 is inserted in the numerator to change the 6 ft. to inches because the 300 is pounds 
per foot. 






A TREATISE ON CONCRETE 


470 

PAGE 

Breadth of Flange. Taking 8 times the thickness of slab plus the breadth 
of stem of beam (assumed as 10 inches) b = (8 X 3 f) + 10 = 40 inches. 

Minimum Depth. Referring to Table on page 525, since the area of 
flange times the working strength of concrete, fc b t, is 97 500 lb. and the 

assumed ratio of depth of beam to thickness of flange is 3.5 (fi- e -* t = ^ ) 

the minimum distance from center of slab to steel in beam, jd, for a 
moment of 722 000 is 12 in., or adding \t, the depth d is 14 in. 426 

A larger value of d however will be used for economical reasons as given 
below, since it reduces both the stress in concrete and the amount of 
steel. The decrease of depth of beam on the other hand would increase 
the stresses in concrete above the permissible working strength. 425 


Cross-section of Web as Determined by the Shear. 

V = 19 000 pounds (see above) hence 


424 


b' 




_19 000 

> 120 


or 158 


t 


Economical Depth. From formula (14), d —— = 
unit cost of steel to cost of concrete, r = 70 


formula (13), 424 



the ratio of 


425 


for b' = 8, d — — = 19.85 inches or d — 21.7 inch. 

b' = 9, d — = 18.7 “ or d — 20.6 

t 

b ' — 10, d — — = 17.8 “ or d = 19.7 “ 

For convenience in placing steel take 

b’ — 10 inches, d = 2inches, h = 22^ inches 459 

Sectional Area of Steel. From formula (15) 426 


722 000 

A s = o — a. - =2.4 square inches 

18.625 x 16000 ^ n 

4 round bars | inches diameter will be sufficient. Two of these may be 
bent up and lap over the top of the support 429 

Steel at Top and Bottom. Negative bending moment at support equals 
positive M at middle or — M = 722 000 inch pounds. 440 

At support the flange of T-beam being in tension is negligible and since 
four |-in. round bars are in tensile and two in compressive part of 
beam, the T-beam changes into a rectangular beam with steel in top 
and bottom. 

The ratios of steel in tension and compression are respectively 

2.4 p 

p = - w -- = 0.0117 and p' — — = 0.0058 

r 10 X 20.5 ' r 2 0 

With these values of p and p' and for n = 15, and a — 0.1 we obtain 
from table (p. 516) C c = 0.227 an< ^ O s = 0.0103. Maximum pressure 
in concrete is 

722 000 

fc = io~>f 20.5 2 X 0.227 = 760 lb - per sq ‘ in -’ formula ( l8 ) 428 

722 000 

U= io~X 2o.5 a X 0.0103 = 16 700 lb - persq - inch,formula (ig) 428 






REINFORCED CONCRETE DESIGN 


47 i 


PAGE 


Allowable compression in concrete at the support may be 15% larger 
than that at middle, hence, no haunch necessary. 429 

Girder. Span 18 feet, breadth to use for T-beam, 44 in. (assuming 

breadth of stem as 14 in.) 424 

Concentrated loads at ^ points. 

Assumed dead load of the stem of the girder, 360 pounds per linear foot. 
Load transmitted by the beams is considered as concentrated. 441 

Reaction of concentrated loads, V = 38 000 pounds. 434 

Maximum moment of concentrated loads with ends of beam simply 
supported would be, M = 38 000 X 6 X 12 = 2 740 000 inch pounds. 439 

wP wP . 

This corresponds to formula M = g~; to correspond to M = --- it may be 

reduced by the ratio T 8 a or 44 1 

M = 2 740 000 X jj — 1 82 7 000 inch pounds. 

Moment of dead load, M = 116 600 inch pounds. 44° 

Total moment, M = 1 943 600 inch pounds.* 

Minimum Depth. From Diagram 4, p. 525, since the area of flange times 
the working strength of concrete, f c bt = 107 250 pounds and the 
assumed ratio of the depth of beam to the thickness of flange 
equals 6. the minimum depth, d = 24 inches. 525 

A somewhat greater depth is economical as shown below. 425 

Cross-section Determined by Shear. V =38 000 + 3600 = 41 600 pounds 424 
Using a limit of 120 pounds for total shear 

/ t \ 41 600 

b' d - - 


120 


347 square inches 


424 


Select by judgment 

b' = 14 inches, d = 26.5 inches, h = 29 in. (to allow for 2 layers of 
steel). 

Steel Area. For M=i 956 000 from Diagram 4, p. 525, A s = 4-9° square 
inches, 8 round bars % inch diameter will satisfy the moment. 

Check of Results by Exact Formulas (14) to (17) t 755 

(This check is unnecessary in practice for an experienced designer.) 
b' = 14 inches, b = 30 + 14 = 44 inches, t = 3! inches. 

A s —• 4.90 square inches. 

4-90 X 2 X 15 X 26.5 + 44 X 3 - 75 2 = 390 ° + 62 0 = 45^0 = [nches 

kd 2 X 4 - 9 ° X 15 + 44 X 3.75 X 2 147 + 330 477 ’ 9 5 

3 X 9.5 - 7.5 3-75 • , 

z = --- =1.72 inches. 

2 x 9. 5- 3-75 3 

jd = 26.5 — 1.72 = 24.78 inches. 

The value for jd would be a bit lower, when the compression in the stem 
is also considered. It is evident that the approximate value used 

in previous figuring, d — ~ = 24.63 inches, is practically identical with 

the more exact moment arm. 

Girder at Support. —M = 1 943 600 inch . pounds. 440 

Reinforcement at supports consists of % inch round bars. 

Eight bars are in tensile and four in compressive part of beam, hence 

4.9° 


ratio tension steel, p = 


ratio compression steel, p' = 


14 X 26.5 
0.0132 
2 


= 0.0132 


= 0.0066 


* By method suggested on page 433 the result would be 2 159000 less 10 per cent or 1 943000 
pounds, a result almost identical with the more exact one. 










47 2 


A TREATISE ON CONCRETE 


PAGE 


From Table 8 (p. 516), C c = 0.241 and from formula (18) 
maximum compression in concrete, 


428 


f = 1 943 600 

' c ~ 14 X 26.52 X 0.241 

which is excessive. 


820 pounds per sq. in. 


429 


Depth and Length of a Haunch. For depth try a = 0.1, d = 28 inches 429 
For this depth of beam the ratios of steel in tension and compression change 
26.5 0.0125 

to p = 0.0132 x •—= 0.0125, p’ — —-- = 0.0063 the corresponding 

2 o 2 

values C c = 0.236 and C s = 0.0109 

Maximum compression in concrete, 428 


fc = 


1 943 600 


14 X 28 2 X 0.236 
and maximum tension in steel 
1 943 600 


= 750 pounds per sq. inch 


428 


fs = 


14 x 28 2 X 0.0109 


= 16 250 pounds per sq. inch; formulas (18) and (19) 


This stress is allowable and the depth of haunch from top of beam of 28 
inches will be accepted. 

Length of haunch may be approximated. Moment of resistance of beam 
without haunch, allowing 15% excess compression or 750 lb. persq. in., 428 
MR — 750 X 14 X 26.5 2 X .241 = 1 780 000 inch pounds. Formula (17) 

Mb = 1 943 600 inch pounds. 428 

Hence from formula (22) length of haunch 430 


x — 


176 000 
1 943 600 


18 

5 


X 12 = 3.9 inches 


Since maximum negative moment occurs in middle of column and neces¬ 
sary length of haunch is only 3.9 inches, no haunch will be introduced 
outside of the column. 

Diagonal Tension Reinforcement of Beam. Vertical stirrups. 

Take into consideration the beam designed on page 469 for which 
V = 19 000 pounds w = 2000 pounds. 
b' =10 inches jd = 18.625 inches and the unit shear 


v = 


19 000 


102 pounds per sq. in. (formula 30), 


447 


10 X 18.625 

The allowable unit shear in concrete equals 40 pounds, hence stirrups 
are necessary. 447 

Diameter of Stirrups. From formula (40) and Table on page 454 for a 
bond stress of 80 pounds diameter of a straight-pronged stirrup should 
not exceed i = 0.012 X 20.5 inches. However, since in the present 
case the upper ends of stirrups are to be bent, § inch round bars may be 
considered as secure against slipping. 467 

Location of Stirrups. Stirrups are unnecessary with the unit load w = 
2000 pounds, at a distance from support 

18 40 x 10 x 18.625 

2 2000 


= 5.3 feet (formula 38) 


Xi = 


2000 


45i 








REINFORCED CONCRETE DESIGN 


473 


Spacing of the f-inch stirrups, the area of both prongs being A 8 =0.22 
square inches, is obtained by plotting in Fig. 148 values of s from 

24 000 X 18.6 X 0.22 


PAGE 


formula (36). At support, s 1 = 


19 000 


= 5.2 inches. 451 


For x = 2 feet, s x = 6.5 inches; for x 2 = 4 feet, s 2 = 8.9 inches. A 
smooth curve drawn through the points determines the spacing at 
any part of the beam. The first stirrup is placed half of the mini¬ 
mum spacing from the edge of the support and the last stirrup must 
not be farther distant from the limiting point, where stirrups are un¬ 
necessary, than half of the distance between the last two stirrups. 
The graphical determination of points for the stirrups is shown in 
Fig. 148. 


45 2 




Fig. 148. Spacing of Vertical Stirrups (See p. 452). 


Bent-up Bars as Diagonal Tension Reinforcement for Girder. In the 

girder designed on page 471 four of the eight bars are intended to be 
bent. If properly placed the bars may be used for taking the diagonal 
tension. The maximum total shear, V = 41 600. Since the load is 
concentrated at points at which the beam runs into the girder the 
shear at the left of that point will be (See Fig. 149, p. 474). 

V =41 600 — (6 X 360) = 39 44c pounds and the unit shear, v =116 
pounds; at right of the point, V will be 41 600 — 6 X 360 — 38 000 = 
1440 pounds and v 2 = 4 pounds. Theoretically, shear reinforcement 
is needed to the point only where the beam intersects the girder. 

The diagonal tension equivalent to the horizontal shear at the support is 


^ 1 _ j^oo pounds per one inch of length of beam, at point A is 

^ NT = I< "’°° P oun( ^ s P er one i nc h °f length of beam. The total 

diagonal tension is represented by a trapezoid, the parallel sides of 
which are 1700 and 1600 and the length 6 feet. Hence total diagonal 


tension = I ^°° I ^°° x 6 X 12 = 118 800 pounds. One-third of 

2 

the shear, or 39600 pounds, is assumed to be taken by the concrete, 
hence the tension to be taken by the shear reinforcements is 79 200 
pounds. Since six £-inch round rods are to be bent, their area is 3.60 

. As X 16 000 

square inches and their tensile value from page 449 is - — -- 


=■= 82 000 pounds. Now comparing the above values it is seen that 



































































474 


A TREATISE ON CONCRETE 


tensile value of bars is in excess of stress to be provided for. . It is also 
necessary that the bent bars be properly distributed and since shear 
is nearly uniform between the supports and the intersection of the 
beam, the inclined bars should be spaced at points a, b, c. _ 

These points were found by dividing the distance on the center line A B 
into equal parts. They should be laid off on the neutral axis, but 
since the neutral axis changes for the positive and negative moment, 
the center line, as lying between the two neutral axes, was selected. 




PLAN OF BARS WHICH ARE NOT BELT 


Fig. 149. —Reinforcement for Girder (See p. 474) 


A study must be made to see whether the tensile stresses in the bottom 
of the beam will permit this. In this case the girder is loaded by con¬ 
centrated loads and the moment at the point where the beam inter¬ 
sects the girder is nearly the maximum. Approximate figuring of 
tensile stresses shows that the first two bars may be bent about 15 
inches from the center of the intersection of the beam, while to resist 
diagonal tension the bar to intersect the center line at a should be bent 
ate as shown by the dotted line. To provide for the diagonal tension, 
between point a and the beam stirrups will be introduced. Using 
Uinch rods for stirrups, the tensile value of which is 2 X -196 X 16 000 


6270 

= 6 270 pounds, it is necessary to space them "65 


5.85 inches apart, 


as shown in Fig. 149, the shear to be provided for in one inch of length 
of beam being 1 065 pounds. 


EXAMPLE OF BENT BARS AS REINFORCEMENT FOR DIAGONAL- 

TENSION 

As indicated in the design for the girder in the example just given it is 
possible to provide for the diagonal tension by bent bars without stirrups. 
When the loading is uniformly distributed instead of concentrated, the 
location of the bends in the different bars as well as the size of the bars to 
































































REINFORCED CONCRETE DESIGN 


475 

use should be governed by the distribution of the shear. This is illustrated 
in the example which follows. 



Fig. 150.—Spacing of Bent Bars. (See p. 475.) 


Example 7—Suppose the 18-foot girder in previous example is loaded uni¬ 
formly with 4 600 pounds per foot of length, find the locations of the points to 
bend up the bars to resist diagonal tension. 

Solution —The load selected will require a beam of same section and ten¬ 
sion reinforcement as the girder in previous example, where breadth of stem, 
b' = 14, depth to steel, d = 26.5, and depth from center of compression to 
tension, jd = 24.6. Then V = 41 400 pounds and from page 447, the unit 
V 41 400 

shear vb' = jd = ~ 6 ~ = 1 P oun ds per inch of length of beam. Two- 

thirds of this amount or 1 120 pounds per one inch of(jengthYof beam 
has to be provided for by diagonal tension reinforcement. The 
distance from the support of the limiting point where shear can be taken 

by concrete itself is =9 4° X 14 X 24,6 _ ^ f ee t ( formula (38), page 451. 

4 600 

From this point to the right the shear increases from zero to its maximum 
value of 1 120 pounds at the support, and maybe represented by the triangle 
ABC, Fig. 150. This triangle may be drawn in the following manner: From 
point A at the neutral axis draw a line A B at 45 degrees, and from point D 
a perpendicular to line A B through point of intersection B. Lay out the max¬ 
imum shear B C. Now, suppose we intend to bend four bars, all of the same 
diameter, to take the diagonal tension, then each of them will take an equal 
part. Divide the area of the triangle into three equal parts, find centers 
of gravity of each part, and from these centers of gravity draw lines to rep¬ 
resent the location of points to bend up the bars in the girder. The method 
of division of the triangle into an equal number of parts is clearly shown in 
the drawing where the line A B is divided into equal parts and dotted arcs 
of cricles are drawn with centers at A. 






























476 


A TREATISE ON CONCRETE 


MISCELLANEOUS EXAMPLES OF BEAM AND SLAB DESIGN. 

Example 8: What is the value of C and the ratio of steel if pressure in 
concrete is limited to 400 pounds per square inch and pull in steel to 
12 000 pounds per square inch, the ratio of moduli of elasticity being 15 ? 

Solution: Approximate values, which are sufficiently exact, may be ob¬ 
tained from the Table 11, page 519, by exterpolation above item (1), from 
which C equals 0.123, an d ratio of steel, p = .0053. 

Example g. What is the value of C for a beam in which the pressure in 
the concrete is 650 pounds per square inch, the pull in the steel 16 000 
pounds, and the area of steel 1.2%, the ratio of moduli of elasticity being 15 ? 

Solution: The requirements in the example are impossible. With the 
pressure in the concrete limited to 650 pounds per square inch, the pull in 
the steel, if 1.2% is used, cannot be as high as 16 000 pounds. From Table 
11, page 520, when p = 0.012 and fc — 650, C — 0.090 and the pull in the 
steel is 12 100 pounds. Furthermore, comparing this item with the line for 
0.008 steel in the same table, it is evident that an increase of 50% in the area 
of the steel, i.e ., from ratio 0.008 to ratio 0.012, decreases the value C, and 
therefore the depth of beam, scarcely 7%. 

Example 10: What safe load per square foot can be supported by a slab 
5 inches thick and io-foot span reinforced with £-inch round bars placed 
8 inches apart? 

Solution. From slab table, page 514, since the given reinforcement from 
page 507 is equivalent to 0.196 X i£ = 0.294 square inches for one foot of 
width, we find by inspection that for a 5-inch slab the nearest area of steel 
in column (18) is 0.288. Hence, the total safe load for a 10-foot span is 
slightly more than 136 pounds, say, 140 pounds per square foot; and deduct¬ 
ing the weight per square foot of the slab, column (15), gives 140 — 64 = 76 
pounds per square foot safe live load. If slab is square, continuous and 
reinforced in two directions, the safe load of 140 pounds may be multiplied 
by 2. Deducting the dead load of 64 pounds, the live load will be 280 - 64 
= 216 pounds per square foot. 

Example 11: What safe load per square foot can be placed upon an 8- 
inch slab, 16 foot span, having steel reinforcement of 0.007? 

Solution: Since by Rule 3, on page 513, total loads are inversely propor¬ 
tional to the squares of the span, the load for a 16-foot slab is \ the load 
for an 8-foot slab. For the total safe load of an 8-foot slab, we must inter¬ 
polate between steel ratios of 0.006 and 0.008, thus obtaining 

649 + 831 
2 

= 740 pounds per square foot. For the 16-foot slab the total safe load 


is therefore 


740 

4 


185 pounds, and deducting the weight of the slab from 


column (15) gives a net live load of 185 — 103 =82 pounds per square foot. 

Example 12: Using Table 4 of rectangular beams, page 510, what 
should be the dimensions and reinforcements for a beam 12 feet span, con¬ 
tinuous.and loaded uniformly with 1000 pounds per foot of length? 

Solution: The assumed stresses are the same as those adopted in the 
Beam Table. Assuming a width of beam 12 inches, a total load per inch of 


1000 

width of —■ - - = 84 pounds per running foot. Referring directly to the 


Beam Table, we find that the total depth corresponding to a 12-foot beam 
with this load is about 12 inches. The reinforcement from column (25) is 
0.083 X 12 = 1.00 square inch. 




REINFORCED CONCRETE DESIGN 


477 

Example 13: What total load per foot of length can be carried by a 12- 
foot simply supported beam 12 inches wide and 25 inches deep? 

Solution: There is no value in the Table 4, page 511, for a beam whose 
total depth is 25 inches, but since, from rule 4, loads are proportional to the 
square of the depth of the steel, we may calculate the load in this case from 
the load for a 26-inch beam 12 inches wide. Assuming in both cases 
that the depth to steel, d, is 2 inches less than the total depth, we have 
2 3 2 

364 X — X 12 = 4 000 pounds per running foot of beam. Since the table is 

wl 2 

based on M = -—for simply supported beams, deduct 20% from the above 
amount. Hence the safe load is 4000 — 800 = 3200 pounds. 


EXPERIMENTS UPON REINFORCED BEAMS 

Tests upon reinforced concrete beams have been conducted at various 
universities in the United States, and by leading scientists in Europe. 
Valuable data with reference to the location of the neutral axis, the defor¬ 
mation and the ultimate loads with various percentages and classes of steel 
have been recorded* in the United States by Professors Hatt, Howe, Lanza, 
Marburg, Talbot, and Turneaure, and in Europe by Messrs. Considere, 
von Emperger, Feret, Rabut, Ramisch, Ribera and Sanders. An extensive 
series of tests has been carried on at the United States Government Struct¬ 
ural Materials Testing Laboratories at St. Louis, using different materials, 
different methods of manufacture, and different types of reinforcement. 

Special results of many of these tests have been mentioned in the preced¬ 
ing pages. 

Tests of Prof. Arthur N. Talbot. At the University of Illinois, Prof. 
Talbot has made several valuable series of tests to investigate the laws of 
reinforced concrete, which cover an exceedingly wide range of percentages 
of steel and types of reinforcement. These are described in detail in 
various bulletins of the University.f 

The fundamental principles of rectangular beams are illustrated in some 
of the earlier experiments which are summarized in the following table. 
Although a leaner mixture of concrete was used in these than in his later 
tests which, therefore, correspond more nearly to practical construction, the 
principles are not affected. The proportions in these beams were 1:3:6 
based on loose measure of cement, or about 1 : 3^ : 7 based on a unit of 
100 pounds cement per cubic foot. The beams were 15 feet 4 inches long, 
12 inches wide, 13J inches deep, with the reinforcement 12 inches below 

* See also References, Chapter XXXI. 

■j- Bulletin No. 1, Sept. 1, 1904; Bulletin No. 4, April 15, 1906; Bulletin No. 12, Feb. 1, 1907; 
Bulletin No. 29, Jan. 4, 1909. 



47 8 


A TREATISE ON CONCRETE 


the upper surface. These were tested on a span of 14 feet by two loads 
which divided the span into three equal parts. The exact proportions of 
the concrete were 96 pounds Portland cement to 3I cubic feet sand to 6f 
cubic feet broken stone. The sand was well graded in size of grains and 
weighed 115 pounds per cubic foot loose and dry. The stone was Illinois 
limestone, with particles smaller than \ inch and coarser than i 4 inches 
screened out. The consistency was such that the water flushed to the 
surface under light ramming. The crushing strength of 6-inch cubes at 
the age of 60 days averaged 2030 pounds per square inch. 

Typical deformation and deflection curves are given in Fig. 130, page4Sq. 

Prof. Talbot gives the following description of the manner of failure of 
each beam except those numbered 27, 22, and 28, which crushed at the 
top at maximum load: 

Tests of Reinforced Concrete Beams. 


By Arthur N. Talbot. ( See p. 479.) 


Beam No. 

Kind 

of 

Steel. 

No. of Rods. 

5 ' Size of Rods. 

X 

CD 

■*-» 

U1 

U-t 

O 

ai 

O 

sq. 

in. 

Ratio of area of steel to 
beam above steel. 

cr Maximum Load. 

c? Load Considered 

te Total Elongation of 
• Steel. 

Ratio of depth of 
steel to depth of 
neutral axis 

k 

p' Estimated Total* 

T Bending Moment. 

g- Moment of Resistance 
calculated from 
“ formula 

(7) or (8), p. 420. 

Remarks. 

As Measured. 

Calculated by 
formula. (^.420) 

Talbot’s 

formula. (£479) 

(1) 

(2) 

( 3 ) 

( 4 ) 

( 5 ) 

(6) 

(7) 

(S) 

( 9 ) 

(10) 

(0) 

(12) 

(13) 

(14) 


21 

Round 

3 

X 

2 

o -59 

0.0041 

9 000 

8 000 

0.0665 

0.34 

0.33 

0.33 

261 000 

226 b'Qob 

2 bars turned up 

W 

U 

3 

JL 

2 

0-59 

0.0041 

9 200 

9 200 

0.0755 

0.36 

0.33 

0.33 

294 600 

226 S90 b 

2 bars turned up 

l6 

Square 

3 

X 

0-75 

0.00 52 

9 900 

9 900 

0.065 

0.37 

0.36 

0.35 

313 200 

284 7006 

2 bars turned up 

17 


3 

i 

0-75 

0.0052 

TO OOO 

9 500 

0.0 5Q 

0.37 

0.36 

0.35 

302 000 

284 700 b 

2 bars turned up 

27 

it 

4 

A 

4 

2.25 

0.0156 

26 900 

25 000 

0.066 

0.53 

0-54 

0.54 

725 500 

774 000a 

2 bars turned up 

9 

Ransome 

3 

JL 

2 

o -75 

0.0052 

22 800 

18 000 

0.142 

o -34 

0.36 

0.35 

540 000 

474 500c 

8 stirrups 

15 

Thacher 

3 

3 

4 

1.20 

0.0083 

18 400 

15 500 

0.0715 

O.4I 

0.43 

0.41 

466 000 

443 3006 

2 bars turned up 

10 


3 

3 

4 

1.20 

0.0083 

16 600 

14 500 

0.065 

o -43 

0.43 

O.4I 

438 000 

443 300 b 

2 bars turned up 

22 

Kahnf 

3 

3 

4 

2.40 

0.0167 

24 400 

22 OOO 

0.064 

0-57 

0.55 

0.56 

641 000 

786 200 a 

Bars sheared up 

4 


5 

X 

2.00 

0.0139 

23 000 

21 OOO 

0.069 

0-47 

0.52 

0.51 

615 000 

714 800 b 

Bars sheared up 

14 


4 

1 

1.60 

O.OIII 

17 200 

17 000 

0.062 

0.46 

0.48 

0.46 

505 500 

580 4006 

Bars sheared up 

5 


3 

1 

2 

1.20 

0.0083 

15 000 

13 OOO 

0.0625 

0.42 

0.43 

O.4I 

396 000 

443 20©6 

Bars sheared up 

28 

Johnson 

6 

3 

4 

2 .IQ 

0.0152 

34 300 

31 OOO 

O.IOI 

0-53 

o -53 

0.53 

893 500 

768 700 a 

4 bars turned up 

13 


7 

X 

2 

I.40 

O.OOQ7 

2 Q OOO 

27 500 

O.III 

0-45 

0.46 

o -43 

800 500 

681 400a 

4 bars turned up 

20 


5 

A 

I.OO 

0.0069 

20 900 

1 20 OOO 

0.132 

0 44 

0.41 

0-39 

593 500 

615 600 a 

3 bars turned up 

2 


5 

I 

I .OO 

0.0069 

20 600 

19 OOO 

0.119 

0-39 

0.41 

0.39 

565 500 

615 600a 

Horizontal bars 

7 


3 


0.60 

0.0042 

14 OOO 

13 OOO 

0.1175 

o -33 

0-33 

0-33 

401 OOO 

384 400c 

Horizontal bars 

3 


3 

1 

2 

0.60 

0.0042 

14 OOO 

! 12 OOO 

c 1065 

0.31 

0-33 

0-33 

373 000 

{384 400c 

2 bars turned up 








/ 

Average 

0.4 18 

O 422 

0.411 

506 906 

I507 388 



Note: — Columns (6) (n) (12) and (14) have been added by the authors. 

*As calculated by Prof. Talbot. Based on “Load Considered” column (8). 

a. Based on crushing strength of concrete of 2 030 lb. per square inch because the moment thus obtained 
is lower than the moment based on yield point of steel. 

b. Based on yield point of steel as 36 000 lb. per square inch. 

c. Based on yield point of steel as 60,000 lb. per square inch. 

fNet areas of steel in Kahn bars at load points are lower than gross areas given, so that 
moments of beams, 4, 14, and 5, by corrected computation are much higher than shown in col. 13. 













































REINFORCED CONCRETE DESIGN 


479 


A portion of the data resulting from the experiments is tabulated above. 
Column (io) is taken from a separate table of Prof. Talbot’s,* * * § and 
columns (n), (12) and (14) are added by the authors to compare the 
actual tests and the theory adopted in this treatise. 

Prof. Talbot suggests an empirical straight line formulaf for the location 
of the neutral axis with different percentages of steel, which avoids the more 
intricate calculations necessary with the usual theoretical formulas involv¬ 
ing the modulus of elasticity. Adopting the same notation employed through¬ 
out this treatise (see p. 420), let 

k = ratio of depth of neutral axis to depth of center of gravity of steel. 
p — ratio of area of section of steel to area of section of beam above center 
of gravity of steel. 

Then with a slight change to conform to the use of a ratio of 15 J 

k = 0.24 +18 p (58) 

Column (12) gives values of k calculated from this formula, using 0.26 
for this concrete instead of 0.24 The formula is adapted to concrete 
beams with percentages of steel ranging from 0.006 to 0.012. 

One of the most important conclusions in the authors’ opinion, which, 
may be drawn from Prof. Talbot’s tests, is the fact that computations made 
by the ordinary theory adopted in this treatise produce values for the 
neutral axis, and also for the ultimate moment of resistance, which are 
so near to the experimental results that these theoretical formulas (see 
p. 420) may be employed with confidence. 

Calculating the location of the neutral axis by formula (6), page 420, and 
employing a ratio of the moduli of elasticity of steel to concrete of 20,— 
which Prof. Talbot’s tests § of elasticity show to be an average value between 
loads of 1 000 and 1 700 pounds per square inch (stresses which correspond 
to the compression in the beam when the neutral axis is as given), the 
theoretical distances given in column (11) agree almost exactly with the 
actual measurements in column (10). The moments of resistance calculated 
in column (14) also agree closely with the total bending moments in column 

( : 3 )- 

T-Beam Tests by Prof. Frank P. McKibben. The T-beams tested 
at the Massachusetts Institute of Technology were made of concrete 


* University of Illinois, Bulletin No. i, September, 1904. 

-j- Prof. Taibot gives the derivation of this formula and a theoretical discussion of his tests in 
Journal Western Society of Engineers, August, 1904 

X The constant in Prof. Talbot’s original formula was 0.26. 

§ Journal Western Society of Engineers, August, 1904. 


480 


A TREATISE ON CONCRETE 


mixed in proportion 1 : 2 : 4 by volume based on a unit of 100 pounds 
cement per cubic foot. The stone used was crushed conglomerate well 
graded, the range of sizes of particles being from 1^ to T \ inch, while the 
sand was a mixture of coarse and fine sands in equal parts. The steel 
reinforcement consisted of plain round bars ranging in size from jf to 1 
inch in diameter. The age of beams when tested was about 30 days. 
Their dimensions were as follows: span 12 feet, total depth 11 inches, depth 
to steel 9.5 inches, thickness of flange 3 inches, breadth of stem 8 inches, 
breadth of flange 2 feet. The percentage of reinforcement varied from 2.22 
to 3.12 per cent based on the width of the stem, or from 0.74 to 0.104 
per cent based on the width of the flange, using in both cases the depth 
to steel in computing the area of conciete. The following table gives the 
results of the tests. 


Tests of Reinforced Concrete T-Beams 
• By Frank P. McKibben. (See p. 479.) 
Massachusetts Institute of Technology 


E 

a 

v 


o 

£ 


(0 

1 


o 

Pi 

~a 

a 

3 

O 


o 


(*) 

f 2 

1 

2 

1 

2 

\T 

/* 


g 

1—i 


-O 

O 

Pi 


o 

N 

C/5 


(3 

i 

if 

7 

t 

if 

f 

«/ 
if 
1 l 
if/ 


cr 
c n 


<D 

<U 


CO 


aj 

<L> 

Cl 

< 


(4) 

I.69 

I.71 

I .90 
2.07 
2-37 


32 

v 


<U 

4 J 


CO 


<u 

tuO 

3 

C j o 
u 

^ > 

<v 

Ph 


32 

k -3 


T 3 

O 

1-1 

E 

3 

E 

‘m 

nj 


(5) 


2.22 


2 . 2 ' 


5264 


2.50 

2.73 

3.12 


( 6 ) 

24240 


r 5 

2 43 6 5 

27215 

30940 


32 

J 


3 

v 


V 

G 

3 


W 

J 


"O 

o 

1-1 


(7) 

22000 

22000 

22000 

24OOO 

28000 


STRESS IN STEEL 


>M 

<u 

a- 

-Q 

h -3 


0 

ctJ 

Ih 

U 


4 -> 

< 


( 8 ) 

3 uo 

8230 

6440 

5400 

2040 


AT LAST 
MEASURE¬ 
MENT. 


CO 

g 

o 

* 4 —> 

C 3 

S 

C. 

o 

o 

E 

o 


<u 

CL 

32 

L-l 


HD 

IU 


3 <D 
cl, a 

§3 

U t-1 


(10) 

37460 

36900 


(9) 

345°° 

33300 

38100 33400 
21600 33500 
29600 34400 


3 

H 

h 

w 

Q 

o 


< 

u 

H 

O 

w 

£ 

U-> 

o 


~0 

aj 


<u 


00 

o-37 

0.44 

°-37 

°-43 

0.47 


s 

H 

CL 

W 

Q 

O 

H 


T 3 

<U 


3 

CL 


O 

U 


03 

O 


j£ "O 

1-1 3 

~ 2 

CL 

I 

B cj 

E ►-< 

o 


3 

W) W 

.5 E 
72 S 
S 3 

PQ 


00 

<U 


00 

g 

P 

O 

Oh 

Js 

u 

g 


<u 


P 

Oh 


o 

U 


<u 

Kh 

u 

G 

O 

u 


<0 • 

oj G 

4 —» . 

CO CT 1 
00 

"2 fc 

3 ^ 
CL • 
C 33 

3 1-3 

o M 

u 


00 (13) 

0.38 528000 

0.38 528000 

0.39 528000 
0.41 576000 
0.44 672000 


04) 

5i5000a 

503000a 

636000a 
6710006 
671000& 


(15) 

1510 

1495 

1410 

1570 

1780 


a Based on stress in steel obtained from last measurement. 
b Based on crushing strength of concrete, since beam failed by compression. 
Note: In figuring the moment of resistance the computed depth of neutral axis for n 
Percentage of steel in terms of width of flange is § of the values in col. (5). 


CO 

E 

CO 

Ph 

M-l 

o 

t-G • 
4 -> rt 

tUD -G 

c . 

O XT 
£ co 

C /3 u 

<u £ 

4-3 Cm 
r 3 

.§ -2 

4-3 hH 

C 


(16 

2220 

1740 

1700 

1680 

1610 


= 15 was used. 


The tests compare well with the results obtained from the formulas given 
on page 420. The stresses in steel, determined by measurements of stretch, 
do not vary appreciably from those obtained from the formulas. Beams 













































REINFORCED CONCRETE DESIGN 


481 


No. 4 and 5 failed by compression in the concrete, and the compressive 
stress in beam near to failure agrees quite closely with the strength of the 
prisms made of the same mix of concrete. A difference in deflection of the 
stem and the flange was detected by the tests, which indicates that the com¬ 
pressive stresses are not uniform throughout the whole width of the flange. 
This, however, in practice is undoubtedly more than balanced by assuming 
a width of flange smaller than the width of slab that actually assists-in taking 
the compression. First cracks occur, as evident, at very low stresses, but 
they are very minute and almost invisible and their presence is not dan¬ 
gerous. 

Tests of Repetitive Loading of Reinforced Concrete Beams by Prof. 
H. C. Berry. Fatigue tests of reinforced concrete beams made by Prof. 

Fatigue Tests of Reinforced Concrete Beams. Size of Beams: 8" X 11". 

Span: 13 ft. Age: 6 Weeks 

By H. C. Berry 


XJniversity of Pennsylvania. (See p. 481 ) 



NTTMRF.R 

WORKING STRESS 







BREAKING 

MAXIMUM 


REPETITIONS 

in Steel 

in Concrete 

LOAD 

DEFLECTION 



lb. per sq. in. 

lb. per sq. in. 

lb. 

in. 

4, round rods . . 

1 



I 2 OOO 

0.56 

4, round rods. . 

297 000 

18 300 

7 8 5 

I 2 3OO 

O . 48 

2, §" square bars. . 

395 000 

15 200 

628 

IO 500 

O . 46 

2, diamond bars 

2 



1 3 OOO 

0.62 



0 

0 

0 

00 

M 

V_ 

14 300 

7 8 5 



2.1" diamond bars 


then 







422 000 

17 IOO 

940 

13 600 

O.78 

3. §" corr. bars. . . . 

0 



20 OOO 

0.66 

3,|" corr. bars . . . 

295 000 

10 800 

940 

w 

^4 

^4 

O 

O 

0 • 55 


H. C. Berry* at the University of Pennsylvania in 1908 indicate that as 
many as one million repetitions of high working stresses do not materially affect 
the ultimate strength of a reinforced concrete beam, its maximum deflection, 
or the position of its neutral axis. Duplicate beams were made of concrete 
mixed in the proportions of 1 part cement, 1 \ parts bar sand and 4^ parts 
-4— inch crushed granite and were reinforced with plain and deformed bars. 
These beams were tested when 6 weeks old, one being subjected to a repe¬ 
titive loading sufficient to cause higher stresses than ordinarily allowed in 

* Engineering Record, July 25, 1908, p. 90. 



















482 


A TREATISE ON CONCRETE 


good practice, and I hen tested to failure, while the other was broken in the 
ordinary manner. 

It was evident that the greater part of the set in the deformation in the 
plane of the steel occurred in the first few thousand applications of the load 
and that the set in the deformation on the compressive side of the beam 
was also relatively large for the first few thousand repetitions and increased 
with the stress applied and the number of repetitions. 

The stresses realized and the deflections resulting from the repetitive 
loadings are shown in the accompanying table on page 481. The breaking 
strength of the beams sustaining the repetitive loading is substantially the 
same in every case as the corresponding beam with no appreciable repeti¬ 
tions. 


n 

< 

o 

-i 

z 

o 

p 

(- 

UJ 

a 

u 

CL 

u. 

o 

UJ 

a 

< 

t- 

z 

UJ 

o 

CL 

UJ 

a 


% 100% 

x 9°% 

H 

O 

Z 

U 0/ 

“ 80% 

CO 

2 

1 

< 

2 

£ 60% 

2 

X 

UJ 









- 















































































































































































































































































































































































































































1 























O INDICATES ONE MONTH COMP’N TESTS 

X, “ “ “ YEAR 

® “ “ “ MONTH BEAM 

§>. YEAR “ 













































l 














































































' 





































































I 
































































§)' 





• 






























< 









c. 

; 







































2 50% 









— 
























— 





































































































































































































L 







































0 4000 8000 12000 16000 20000 24000 28000 32C00 


NUMBER OF REPETITIONS NECESSARY TO PRODUCE FAILURE 

Fig. i 5 j. Fatigue of Reinforced Concrete Beams. (See p. 482.) 

By Prof. T. L. Van Ornum. 


Compression tests by Prof. J. L. Van Ornum* at Washington University 
made in 1907 agree with the above tests for repetitive loadings under 50 per 
cent of the maximum strength of the concrete, but for repeated loads greater 
than this he found that beams will be subject to failure. He concluded 
that the number of repetitions required to cause this failure depended 
essentially upon the ratio of the test load to the ultimate strength of the 
concrete. In these tests, as will be seen from the curve in Fig. 151, which 
summarizes graphically the results of these experiments, the influence of 


* Transactions American Society Civil Engineers, 1907, LVIII, p. 294. 

























































































































































































































REINFORCED CONCRETE DESIGN 4S3 

the fatigue of concrete is limited to an intensity of about 50 per cent of the 
ordinary ultimate strength of the concrete. 

Tests at Illinois University, at St. Louis,* and elsewhere confirm the 
principle illustrated and show that there is a fatigue limit to concrete corre¬ 
sponding in a general way to the elastic limit of metals. This varies with 
the character of the concrete from ^ to f the ultimate strength. Prof. Talbot 
finds in columns the deformation to be a measure of this fatigue limit, the 
latter usually occurring at about \ the ultimate deformation. 

This fatigue limit of concrete, while it does not influence the practice of 
conservative design, is a warning against the use of too high working stresses. 

FLAT SLABS 

Besides the usual systems for floors, using a combination of slabs, beams 
and girders, a floor system of a type of an entirely different design is some¬ 
times employed, which consists of a flat unribbed slab continuous over the 
whole floor and supported by columns only. The type originally introduced 
by Mr. C. A. P. Turner of Minneapolis is sometimes termed the Mushroom 
System. 

The reinforcement of the slab consists of bars running in four directions 
radially from the column, and the head of the column is usually enlarged 
in order to diminish the bending moment and increase the shearing resist¬ 
ance. The vertical steel in the column reinforcement or a portion of it 
may be bent and carried into the slab to add to the rigidity of the connection. 

The moments and stresses in this system are statically indeterminate, but 
in order to make an application of the theory of flexure possible, the whole 
floor is considered as a seiies of flat circular slabs concentric with the 
columns and firmly clamped to them, supporting the rest of the floor. Thus 
the analysis of the whole floor is reduced to that of circular plates clamped 
to the columns, and flat slabs supported on all edges by these circular plates. 

Let Fig. 152 represent a floor of this system, and consider the strip ab as 
separated from the rest of the floor. This strip when loaded will act as a 
fixed beam. The points of inflexion will be distant approximately one-fifth 
of the span from the circular lines of assumed support, which are the 
lines of maximum bending movement. The points of inflexion of the 
floor will thus be located on the dotted curve shown on the drawing. 
Instead of this curve we may assume the points to be on a circle, repre¬ 
sented on the drawing by dash lines, and consider the area within this 
circle as a round plate, loaded with a uniform load over its area and in 
addition loaded around its circumference with a load which, per unit of 


*See Bulletin 344 , U. S. Geological Survey. 


484 


A TREATISE ON CONCRETE 


length, is equal to the remaining load of the panel divided by the circum¬ 
ference of the circle. 

The part of the slab between the column and the points of inflexion will 
deflect downwards, while the rest of the slab will deflect as an ordinary 
supported beam. 

The authors have adopted Prof. Eddy’s analysis of stresses* in a homo¬ 
geneous circular plate, and, from his general formulas, deduced formulas 
applying to circular slabs free on their outer edge and clamped round the 
column. In this analysis the effect of lateral stresses has been taken into 
account, this being expressed by Poisson’s ratio, which is the ratio of the 
lateral deformation to that in the direction of stress. Very few tests have 
been made to determine the value of Poisson’s ratio, and the results ob¬ 
tained vary considerably. 
Many of the earlier tests give 
as high as 0.2, but, since 
some of the best experiments 
in our American colleges in¬ 
dicate a value ranging, with 
concrete of different propor¬ 
tions and strength, from 0.05 
to 0.15, the ratio of 0.10 is 
recommended for use with 
concrete where the correct 
value is unknown, as being 
undoubtedly safe for con¬ 
crete of 1:2:4 proportions. 
It must be noted that the in¬ 
crease of Poisson’s ratio tends 
to diminish the deflection and 
thus decrease the stress. A 
high Poisson’s ratio therefore 
means a thinner slab and 
less steel. 

The meaning of Poisson’s ratio as applied to a loaded column is the 
lateral deformation per unit of width divided by the longitudinal deforma¬ 
tion per unit of length. For example, if a certain load causes a 10-inch 
column to expand laterally 0.0003 inches, while at the same time it shortens 
0.03 inches in a gaged length of 100 inches, Poisson’s ratio for that load- 

. 0.0003 X100 T , 1 , , . 

mg is - - =0.1. In a slab supported on columns there is a 

0.03 X 10 

similar condition of deformations caused by horizontal stresses at right 
angles to each other which are taken into account in the mathematical 
work involved in the derivation of the formulas. 

The general formulas derived from the Eddy theory are complicated 
even after introducing a number of constants, but, disregarding the 
circumferential moments, which at the support are a minimum and 



/ 


V / 

/ / 

/ / 

/ / 

/ / 

_«/V'v . 

' f \\ Assumed line of / 

- l T 0 y | < / nla'ximum bending i 
l \ / 1 ( moment \ 

V— 'y '/ v 

f' -e .Theoretical line \ 

Column head Af of inflection \ 

y I ^Assumed line \ 
T - '— ^ of inflection x — 

Fig. 152. Plan of Flat Slab. ( See p. 483.) 




*Engineers‘ Society, University of Michigan, 1899 . 
























REINFORCED CONCRETE DESIGN 


485 


negligible, it is possible to reduce the working formula for the moment 
at any circle whose radius is r to the following simple form.* 

Let 


q uniformly distributed load around the outer edge of the plate in 
pounds per foot .of length. 

w — uniformly distributed load on surface of plate in pounds per sq. ft. 

7 0 — radius in feet to line of maximum bending moment (which is within 
the column head). 

r \ ~ outer radius of assumed plate in feet. 

r ~ an y radius in feet where moment is to be computed, for critical 
section, r is radius of column head. 

Qi C e = constants given in Table 9, p. 518. 

M r = total radial bending moment to be used ordinarily. 

h = distance in feet between lines of inflection. 


Then total radial moment at any point of plate is M r = wr] C 5 + qr 0 C e 



Fig. 152a. Section of Flat Slab. 


The values of C 5 and C e , as determined from r, i\, and r 0 , are ob¬ 
tained from Table 9 , p. 518. If q is in pounds per foot of length, w in 

* The more complete formulas which may be used with the aid of table on page 518 a if outside of 
the limits of the values on page 518 are as follows. 

In addition to above notation, let 

Ci, C 2, C3, Ci, Ca, Cb, Cc, Cd, = constants given in Table 9 , p. 518 a. 
g = Poisson’s ratio. 

Mi — moment causing circumferential fiber stiess \ ^ , ,. ,, 

M 2 = moment causing radial fiber stress j °r loading uniformly distributed over plate. 

M„ — moment causing circumferential fiber stress 1 ^ , , , , 

Mfj = moment causing radial fiber stress / or oa( b n § distninited along edge of plate. 

Then 


Mi 


’ { °' 1 (v) ,_ c ' (t)'~ c, '° s (v) + c ‘) 

(i) +c 
8 (v) +c *j 


M2 = wr 0 2 | 0.2 2 + Cl 

M a = qr Q | - C a (-E 


' o 
r 


— Cz ’og 


M b = 


' o 
r 


C c loo 


2 -C c log (^-) + C b 


154) 

(55) 

(56) 

* (57). 


The M r in text above is the sum of M 2 and M b which are the only moments which need to be 
considered in practical design. 


If — = 1, formulas (55) and (57) become 
r 0 


.V/2 = tcr 0 2 (0.2 + Ci + C2). 


(52) 


M b = ^ r o (C a + C b ). 


( 53 ) 






































486 


A TREATISE ON CONCRETE 


pounds per square foot, and r 0 in feet, the moments are in foot pounds 
per foot or inch pounds per inch. 

If the column head is enlarged so as to be comparatively thin at its 
circumference, a part of it is flexible and must be considered as a part 
of the slab so that the assumed line of support at which the slab may be 
considered as rigidly fixed is within the column head.* 

The assumed line of support should coincide with the line of maximum 
bending moment. Its location depends upon the dimension and design 
of the column head and must be chosen by judgment rather than by 
computation. For ordinary conditions, it seems reasonable to consider 
this line of maximum moment as located within the column head at a 
distance from the circumference equal to the thickness of the slab; the 
radius r 0 in such a case would be a length, t, smaller than the radius of 
the column head. 

The maximum stress will not be on this line of maximum bending 
moment because the strength is there increased by the greater thickness 
of concrete. The maximum stress, therefore, will be ordinarily at the 
circumference of the column head.f Hence, for computing the bending 
moment at line of maximum stress in slab, r = ro -f- t. (See Example 14, 
page 487.) 

As in a fixed or continuous beam, the top of slab at support is in 
tension, and the bottom in compression, i. e. the moment is negative. 

The thickness and reinforcement of the slab are found as in ordinary 
beam and slab design and illustrated in Example 14, page 487. The 
limiting thickness of slab is usually determined by the thickness re¬ 
quired near the column to resist the negative bending moment there. 
It is advisable, then, to make the slab near the support as thin as pos¬ 
sible by using a rich concrete and a larger amount of steel and by plac¬ 
ing some steel in the bottom of the slab for compression. 

It is common practice in flat slab floor construction to place the steel 
in the top of the slab in four layers, two diagonal and two rectangular. 
The authors advise, instead, placing only the two diagonal layers of 
steel in the top of the slab for tension, as shown in Fig. 152a, page 485 
and illustrated in the example, and the two rectangular layers in the 
bottom of the slab. By this plan the bottom steel assists in taking 
compression, and the centers of tension and compression are brought 
farther apart, thus increasing the values of d and jd for a given thick¬ 
ness of slab and therefore permitting a thinner slab for a given loading. 
Tests show that the steel may be distributed over the full diameter of 
the column head plus at least a distance equal to the thickness of the 
slab on each side of it. 

A value for compression in concrete, f c , higher than in beam construc¬ 
tion is permissible, and a lower value of n, because of the rich concrete 
mixture and because of the fact that the maximum stresses occur near 


*Even in ordinary beam and slab design, the line of support is customarily assumed within the 
structural support. 

fSince evolving this analysis, the actual stresses in the Minneapolis building tested by Mr. A. R. 
Lord and described before the National Association of Cement Users in December, 1910 , have been 
compared with the stresses computed by the above formulas and the results tend to confirm, from a 
practical standpoint, the correctness of our formulas and assumptions. 


REINFORCED CONCRETE DESIGN 


487 


the support, where the concrete bears on a larger area, and for this 
reason is able to stand, say, 15 per cent higher stresses than in the mid¬ 
dle of the beam. It is advisable, however, to fix a maximum stress of 
800 pounds per square inch even with a rich concrete of proportions 
say 1:1^:3. 

The slab between the circular plates may be considered as supported 
on all edges. From Fig. 152 it is evident that the largest deflection and 
the largest positive bending moment occur in the middle of the panel, and 
may be safely taken as those of a square plate supported on all edges, the 
side of which is the diagonal distance between the lines of inflection. 
This distance, l lf between lines of inflection may thus be taken as the 
span, and thickness and reinforcement at the middle computed very 

j2 

conservatively by the formula* M = ^ 1 . 

24 


EXAMPLE OF FLAT SLAB DESIGN 

Example 14: Design a flat slab to support a live load of 200 pounds per square 
foot; spacing of columns 17 by 17 feet; diameter of head 54 inches. Assume working 
stress in steel, f s = 16 000 pounds per square inch; in concrete at support, f c = 700 
+ * 5 % = 800 pounds per square inch; and Poisson’s ratio, g = 0.1, allowing for a 
rather rich concrete. 

Solution'. The slab will be considered as a flat circular plate fixed to column and 
supporting at its circumference the rest of floor, as outlined on page 483. The radius, 
ro, to line of maximum bending moment will be taken as the radius of the column 
head minus the thickness of slab, r0 = 2.25 —.67 = 1.58 feet, and the outer radius 
of plate, r 1, will be taken as the average distance of the points of inflection of the slab 
from centers of columns. The radius, r\, is thus one-fifth of the distance between lines 

of maximum bending moment plus r 0, hence, r \ minimum = ——A— r .58 = 4.35 

5 

feet, and ri maximum = —-1.58 = 5.75 feet, the average value of r\ is 


= 5.05 feet and the ratio of radii is ^ = 


5 05 
1-58 


= 3-2Q- 


Live load = 200 lb. per sq. ft., assumed dead load = 100 lb. per sq. ft., giving a 
total unit load, w, of 300 lb. per sq. ft. 

Area of slab is 17 by 17 = 289 sq. ft. and area of circular plate 5.05 2 X 3.14 = 80.1 
sq. ft.; hence, the difference of the two areas, 208.9 sq. ft., is the area of slab tributary 
to each column outside of assumed circular plate. The loading of this area is sup¬ 
ported around the circumference of the flat plate, and equals 208.9 X 300 =62 700 
lb. Dividing this value by the circumference of the outer edge of the plate gives the 
circumferential unit loading, q = 1980 lb. per lin. ft. 

Line of maximum stress is at circumference of column head hence r = 2.25 and 
ratio of r to r 0 = 1.42. 

From the corresponding constants in table on page 518, the bending moment at the 
circumference of column head is M = (300 X i.58 2 Xi. 89) + (1980 X 1.58 X 2.54) = 
9400 in. lb. per inch of circumference. This is a negative moment, the top of slab 
being in tension and the bottom in compression, as in any fixed or continuous member 
at the support. 

If steel is used only in top of slab, the depth, reinforcement, and thickness of slab 
may be determined from the ordinary slab formula, page 421, using the total M given 
above, after changing it to inch pounds per foot. If steel is used in both top and 
bottom, the required depth and reinforcement may be determined by formulas (18) and 
(20), page 428. In the present case, if% of steel will be placed diagonally in two 


*Tests of the Minneapolis building (see foot-note p. 486 ) show that stresses at middle of span are 
small so that t his formula is conservative. 







488 A TREATISE ON CONCRETE 


layers at top and 0.7% of steel rectangularly in two layers at bottom; hence, using 
formula (18), page 428, and table on page 517, withratioa = 0.15 ,d=-y- 


9400 


800 X 0.24 


= 7 inches, requiring a slab thickness of about 8 inches. 

The total amount of steel required in top of slab at column is ^4 v = 27 X 2 X 3.14 

X 7 X . 0137 = 16.3 sq. in. Each of the two layers is effective on both sides of column, 
hence each layer must have 16.3 -f- 4 = 4.08 sq. in. Total width of layer or band 
is taken as the diameter of column head plus twice the thickness of slab, or 70 in., 
and, using |-inch round bars, they would be placed sh in- apart At the bottom of 
slab at column, the ^-inch round bars would be placed 7 in. apart. 

Several trials must usually be made to determine the most economical relation of 
the amount of steel and concrete. It should be borne in mind that the increase of rein¬ 
forcement for a short length over the support decreases the thickness of entire slab, 
reducing the amount of material and at the same time the dead load and the moment. 
Hence, a larger percentage of steel than used in beam and slab design and the intro¬ 
ducing of steel at the bottom usually will prove economical. 

The diagonal distance,/1, between lines of inflection is 24 — 10.1 = 13.9 feet, and 
bending moment in middle of slab (see p. 487) is 

M = 3 °? . X i 3-9 2 __ 29000 in. lb. per foot of'width. The effective 

24 

depth of slab, d, as determined by the necessary depth at support is 8 — 1 = 7 in. 

Then, from page 418, C = •V—= 0.142. 

' 29000 

In Table n (p. 520), p — 0.0035 corresponds to C = 0.142, hence, 0.35 per cent of 
steel in each diagonal direction will be necessary, or ^-inch round rods 8 in. apart. 
In this case the rods would naturally be placed 7 in. apart as a matter of convenience. 


CONCRETE COLUMNS 


Columns of short length, essentially piers, the length of which is not 
more than six times the least lateral dimension, may be built of plain 
concrete with no reinforcement, provided the loading is central. Columns 
longer than this should be reinforced for safety in construction and also 
to guard against the possibility of eccentric loading and the danger of 
sudden failure. It is desirable to further limit the use of reinforced 
columns to a length of 15 diameters. 

Although concrete is especially adapted for sustaining compression, 
its compressive strength is so much lower than that of steel that in a 
building it is frequently difficult to keep the columns in the lower stories 
within the limits required by the uses for which the building is con¬ 
structed. 

To reduce the size of the column, four distinct methods are used either 
separately or in combination: 

(1) Rich proportions of concrete. 

(2) Vertical steel bars designed to assist in taking the compression. 

(3) Hooping or banding. 

(4) Structural steel shapes in combination with the concrete. 

These will be considered in the order given. 

While as a general proposition concrete in compression is always 
cheaper than steel, the limits of size of column frequently make steel 
reinforcement necessary not only to resist bending caused by eccentric 
loading or lateral pressure, but to take a part of the vertical compression 
load. 







REINFORCED CONCRETE DESIGN 


489 


Whatever the type of construction, the effective area to use in figuring 
the compression should usually be less than the total area to allow a certain 
thickness on the surface for fire protection. The Joint Committee recom¬ 
mends that the protective covering shall be taken to a depth of i^inch on all 
surfaces, since in a severe fire the concrete to this depth may be affected by 
the heat and its strength destroyed. A less thickness than this should be 
sufficient where the contents of a building are not especially inflammable, 
a decrease in the total diameter or width of a column of 1 to 2 inches 
being frequently a fair allowance when computing the effective area. 

The steel, however, should in ail cases be imbedded at least i\ to 2 inches, 
and when circular hooping is used to add strength and ductility the effective 
area must be taken as that within the hooping. 

Rich Proportions of Concrete. The compressive strength of concrete 
is approximately proportional to the amount of cement which it con¬ 
tains (see page 392), so that increasing the proportion of cement is an 
effective means of strengthening the column to permit smaller section. A 
rich concrete also has a higher modulus of elasticity and there is conse¬ 
quently less deformation under load. Besides this, a rich concrete works 
smoother in placing and makes it easier to produce a homogeneous column, 
provided the aggregates are properly graded. The strength of concrete 
for different mixtures is indicated on page 360, and working stresses are 
suggested on page 527. Before permitting the use of high column stresses 
in a structure, actual compressive tests should be made upon cylinders 8 
inches diameter by 16 inches high composed of the same materials to be 
used and mixed in the required proportions with the same wet consistency. 

Vertical Steel Bar Reinforcement. Tests of long columns made at the 
Watertown Arsenal,* the Massachusetts Institute of Technology,! and 
the University of Illinois,! indicate conclusively that vertical steel bars 
imbedded in concrete may be counted upon to take their portion of the 
loading. As a column takes its load, it is shortened in height, the concrete 
and steel, shortening equally because they are bonded together. The con- 

1 

crete, however, has so much lower strength that it receives its allowable 
load before the steel can reach its full working strength. Consequently, 
the working load upon the steel must be figured at a low value, which is 
determined by the amount of shortening it has undergone up to the point 
where the concrete is shortened so as to reach its working strength. Since, 
with a given load, the shortening or deformation is proportional to its 

* Tests of Metals, U. S. A., 1904, 1905, 1906, 1907. 

j- Transactions American Society of Civil Engineers, Vol. L, p. 487. 

J University of Illinois Bulletin 20, December 25, 1907. 


49 ° 


A TREATISE ON CONCRETE 


modulus of elasticity (see p. 529), the working stress in the steel must be 
the working stress in the concrete times the ratio of the moduli of elasticity 
of steel to concrete, as indicated below. 

Although tests indicate that if vertical steel is placed at least 2 inches from 
the surface of the column, the elastic limit of the steel may be reached with¬ 
out danger or buckling, it is nevertheless advisable in almost all cases to 
place occasiona horizontal loops around the steel spaced at distances apart 
not greater than the width of the column as an additional precaution against 
the buckling of the rods, and also for the purpose of keeping the bars in 
place during the pouring of the concrete. The size and location of such 
loops are discussed in connection with column design on page 624. 

Joints in the vertical steel when small diameter rods are used, say up to 
1J inch, may be provided for by lapping as indicated on page 464. Large 
diameter rods should have their ends planed true and butted with a sleeve 
around the joint, or should have some other posidve connection. In foot¬ 
ings where the length of imbedment is not sufficient to take all the stress, 
a horizontal bearing plate must be provided. 

Since the relative loading upon the steel and the concrete at any period 
is theoretically in direct proportion to the ratio of their moduli of elasticity 
at that period, and since full size column tests have borne out this assump¬ 
tion, the allowable loading, that is, the allowable unit pressure, is readily 
obtained as follows:* 


* From mechanics 


stress per square inch 
modulus of elasticity 


deformation 


/' / 

hence = deformation of steel and — = deformation of concrete. 
E. E. 


Since with perfect adhesion between concrete and steel all parts of the column must undergo the 
same deformation, 


r. h 

ir k ot 


The allowable stress in steel is therefore the allowable stress in the concrete times the ratio of 
elasticity. For practical purposes the total loading must be introduced. Since the total pressure 
in the column must be the sum of the pressure in the concrete plus the pressure in the steel, 

t A ~ fc A C + f't J 8 « f A ~fc A C +fc" A , 


and since A.= A —A. we have 

V o 


/ = /, 


[ 


A - A c 


-I- n 


] 


or since p = —_ we reach the result 
A 


f = f c f <4 “ P) + ”p] 






REINFORCED CONCRETE DESIGN 


491 


Let 


/ = allowable unit pressure upon the reinforced column, equal to the 

total load divided by the effective area. 
fc — allowable unit pressure upon the concrete of the column. 

U = allowable unit pressure upon the vertical steel in the column. 


n 

P 

A 

A 


= ~* = ratio of modulus of elasticity of steel to modulus of elasticity 
Pc 

of concrete. 

= load to be sustained by the column. 

= area of total effective* cross-section of column. 

= area of concrete in cross-section. 

= area of steel in cross-section. 

^4 

= —- = ratio of cross-section of steel to total cross-section of column. 


For determining the total allowable unit compression, / (which is the 
total load, P, divided by the effective area A) with fixed area of concrete 
and steel, we have 


/ = 


fc A e + fc n A > 


(59) 


In terms of the percentage of steel, 


/ =/ct I + O - l) p] 


(60) 


The percentage of steel to use to obtain total unit stresses when the com¬ 
pression on the concrete is limited to f c is 


P = 


f-fc 
fc O - x ) 


(61) 


and the effective cross-section of column is 


A = 


f c \ 1 + (w - 1) p] 


(62) 


P 

°r A = ~f 


( 63 ) 


To this area must be added the protective covering as indicated above. 


* See page 497. 





49 2 


A TREATISE ON CONCRETE 


The table below gives values of / for different stresses and different 
moduli of elasticity. 


Working Loads on Concrete Columns Reinforced With Longitudinal Rods 

{See p. 492) 


RATIO OF 

STEEL 

ALLOWABLE UNIT LOAD ON COLUMNS IN LB. PER SQ_. IN. 

P 

Ratio of Moduli, n 

= 10 

Ratio of Moduli, n = 15 Ratio 

of Moduli, ti 

= 20 

(0 

CO 

( 3 ) 

( 4 ) 

(5) 

(6) 

( 7 ) 

(8) (9) (-°) 

(■■) 

(12) 

03 ) 


fc = 

fc — 

I fc = 

fc = 

fc - 

fc = 

fc - fc “ fc = 

fc = 

fc = 

fc = 


45° 

55° 

650 

75 ° 

450 

55 ° 

650 75 ° 45 ° 

55 ° 

650 

750 

O.OI 

49° 

599 

708 

817 

513 

627 

74 i 855 535 

654 

773 

892 

0.02 

53 1 

649 

767 

885 

576 

704 

832 960 621 

759 

897 

io 35 

O.O3 

57 1 

698 

825 

952 

639 

781 

923 1065 706 

863 

1020 

1177 

O.O4 

612 

748 

884 

1020 

_ 

702 

_ 

858 

1014 1170 792 

968 

1144 

1320 


Note —Use column (6) ordinarily for first class 1:2:4 concrete. 


Examples on page 498 illustrate the use of these formulas. 

The table on p. 493 from tests by Mr. James E. Howard gives the relation 
of actual tests to theoretical computations based on a ratio of elasticity of 
15. It is noticeable that the actual strength is almost always more than the 
theoretical, and this is especially the case with the leaner mixtures because 
the modulus of elasticity of the leaner concrete is lower, and therefore the 
ratio of 15 is very conservative. 

An excellent analytical treatment of columns reinforced with vertical 
steel is given by Professor Talbot in one of his University Bulletins.* The 
problem is discussed briefly by one of the authors in a paper before the 
Boston Society of Civil Engineers.| 

The analysis of the action of combined compression and bending, such 
as is produced in columns loaded eccentrically, and the method of com¬ 
puting the reinforcement in such cases is treated in pages 560 to 574. 

Hooped or Banded Columns. Mr. A. Considere in France was the first 
to apply to reinforced concrete the principle that if a material is confined 
laterally, it will deform or shorten less under vertical loading, and there¬ 
fore can sustain a heavier load before it crushes. This is the principle 
involved in the hooped or banded column. It is carried out in practice by 
placing steel bands or spiral hooping within the column designed to resist 
the lateral deformation. 

* University of Illinois, Bulletin No. 12, Feb. 1, 1907. 

J Sanford E. Thompson in Journal Association Engineering Societies, June 1907, p. 316. 



























REINFORCED CONCRETE DESIGN 


493 


Tests at the Watertown Arsenal,* the University of Illinois')* and 
the University of Wisconsin,J 1906-1907, prove that while hooping or 
banding increases the crushing strength of the column, the deformation, 
that is, the shortening of the column, is so great at a comparatively early 
period in the loading that the safe strength cannot be based directly upon 
the breaking strength. 

A perfect fluid like water will transmit pressure equally in all directions. 
Concrete, on the other hand, under ordinary loading expands laterally a 
very small percentage of its vertical deformation or shortening (see p. 484); 
so that, even from a theoretical standpoint, the hoops should not come into 
play until the concrete has shortened so much that its elastic limit, or the 
period corresponding to this, has been passed. § 

Strength of Plain vs. Vertically Reinforced Concrete and Mortar Columns. 
Columns 12" x 12". Height 8 feet. Age of Mortar and Concrete 6 months 

Watertown Arsenal (see p. 492). 


PROPORTIONS 

Plain 

Concrete 

or 

Mortar 

Columns 

Actual 

Strength 

lb. per 
sq. in. 

REINFORCED.COLUMNS 

REFERENCE 

TO “TESTS OF 

metals” 

U. S. A. 

Reinforcement. 

Actual 
Strength 
lb. per 
sq. in. 

Computed 
Strength 
based on 
col. (4) 
and a ratio 
of n = 15 
lb. p.sq.in. 

Cement. 

Sand. 

-— 1 

Stone. 

Description. 

Ratio 
Area 
Steel to 
Area 
Column. 

(I) 

( 2 ) 

(3) 

(4) 

( 5 ) 

(6) 

( 7 ) 

(8) 

( 9 ) 

I 

2 

0 

3070 

8-f" round bars 

0.029 

4200 

4290 

I 9°5 P- 377 

I 

3 

0 

2380 

8-f" round bars 

0.029 

3840 

33 2 ° 

I 9°5 P- 377 

I 

4 

0 

1520 

8-1" round bars 

0.029 

3380 

2120 

I 9°5 P- 377 

I 

5 

0 

1080 

8-f" round bars 

0.029 

2810 

1510 

1905 P- 377 

I 

5 

0 

1080 

13-f" round bars 

0.046 

3900 

1780 

1905 P- 377 

I 

1 

2 * 

1720 

4-f " twisted bars 

0.014 

2890 

2060 

1904 p. 386 

I 

2 

3* 

1769 

4-f" twisted bars 

0.014 

2010 

2100 

1904 p. 386 

I 

2 

4 

1413 

4-0" 0.74" x 0.74" 









trussed bars 

0.014 

1900 

1689 

1906 p. 538 

I 

2 

4 * 

1710 

4-f" twisted bars 

0.014 

1990 

2050 

1904 p. 386 

I 

2 

41 

2400 

8-f" twisted bars 

0.029 

37OO 

3360 

1907 p. 242 

I 

3 

6 

145° 

8-f" corr. bars 

0.019 

2290 

1840 

1904 p. 379 







1 


1906 p. 535 


* to i$" pebbles. 
fAge 17 months 22 days. 


The action of the hooped column as established by tests on long columns 
is discussed by one of the authors as follows:|| 

* Tests of Metals, U. S. A., 1906. 

-j-University of Illinois. Bulletin No. 20, Dec. 15, 1907. 

{Transactions American Society for Testing Material, Vol. IX 1909. 

§ See discussion by Sanford E. Thompson in Journal Association Engineering Societies, July, 

1907, p. 320. The effect of lateral expansion based on the action of plain columns is here treated 
before the publication of the tests of hooped column which established the principle. 

|| Sanford E. Thompson in Transactions American Society of Civil Engineers, Vol. LXI, 

1908, p. 47. 






























A TREATISE ON CONCRETE 


494 

When a load is placed upon the top of any column, it causes vertical com¬ 
pression or deformation, with, at the same time, a lateral expansion.. The 
lateral expansion in concrete columns, as shown by tests upon plain and 
upon reinforced columns by Mr. J. E. Howard at the Watertown Arsenal* 
and by A. N. Talbot, M. Am. Soc. C. E., at the University, of Illinois,! 
is at first very small. Any stress produced in the steel hooping must be 
proportional to its deformation or stretching; hence, with small lateral 
expansion of the concrete, there can be but slight stress in the hoops, bor 
this reason, and also because of the initial shrinkage of the concrete, which 

the lateral expansion 
must first overcome 
scarcely any stress or 
pull comes upon the 
hoops until the concrete 
within them has reached 
a loading equal to the 
breaking load in plain 
concrete. As this load 
is approached, the mod¬ 
ulus of elasticity of the 
concrete becomes very 
much lower, and conse¬ 
quently both the verti¬ 
cal and lateral deforma¬ 
tions become much 
greater. Then, and not 
until then, does the 
lateral pressure begin 
to act appreciably upon 
the hoops. In other 
words, up to the very 
crushing strength of 
plain concrete, the value 
of the hooping is act¬ 
ually negligible. From 
then on, the reinforce¬ 
ment takes practically 
all the load, and a high 
ultimate strength may 
be attained, although 
coincident with great 
shortening of the 
column. 



Fig. 153. Deformation of a Hooped and of aPlain 
Column.f (See p. 494-) 


Even with the*concrete restrained within the hoops, the shell of concrete 
outside of them, which is necessary for fireproofing and for the protection 

* Tests of Metals, U. S. A., 1905, pp. 293-336. 

■}• Proceedings American Society for Testing Materials, Vol. VII, 1907, p. 382. 
t Columns 109 and 182 from Bulletin No. 20, University of Illinois, December 15, 1907. 
















































REINFORCED CONCRETE DESIGN 


495 


of the steel, begins to crack and peel at about the same load as that which 
will cause complete failure in unreinforced concrete. Professor Talbot, 
in fact, states as a general proposition that: “Cracking and peeling of the 
concrete appear at loads corresponding to the ultimate strength of the 
concrete.” 

Tests also indicate that the shortening of the column is so great that the 
elastic limit of any vertical steel rods is passed at a load but slightly greater 
than that corresponding to the crushing strength of plain concrete. 

The typical deformation of a column reinforced with spiral hooping as 
compared with a column having no reinforcement is shown by the curves 
Fig. 153. Although the ultimate strength of the hooped column shown is 
3700 pounds per square inch, it will be seen that at a load of 1800 pounds 
per square inch, the crushing strength of the plain column, the curve drops 
off very rapidly and the line produced back to the axis of ordinates at A 
agrees very closely with the crushing strength of the plain column. At 
2000 pounds per square inch the deformation per unit of length is 0.0017. 
At this deformation vertical steel in such a column would be stressed to 
51 000 pounds per square inch. In other words, at a load only 10% higher 
than that to be expected of a plain column, even steel of a high elastic 
limit would have reached its yield point. 

The entire subject is treated very fully by Professor Talbot in the descrip¬ 
tion of his tests in the Bulletin from which the diagram is taken. 

Quoting again from Mr. Thompson’s Discussion before the American 
Society of Civil Engineers: 

Tentative conclusions with regard to hooped column design at the present 
stage of tests may be summarized as follows: 

(1) Hooping, if properly applied, increases the ultimate breaking strength 
under a single loading to double or treble the breaking strength of a plain 
column. 

(2) The surface of concrete outside of the hooping will begin to crack 
at a loading corresponding to the breaking load of an unhooped column. 

(3) Hooping, if not continuous or rigid, will peel off with surface concrete 
so that the effective strength of the column will be no greater than a similar 
one of plain concrete. 

(4) The total vertical deformation of a hooped column is so great at the 
period of first external crack that any vertical steel, unless designed to carry 
the entire load, is stressed beyond its safe strength. 

(5) The ultimate breaking strength of a hooped column is no measure 
of its safe strength, and formulas based on the ultimate strength are useless. 

Notwithstanding these conclusions it must not be inferred that hooping 
is of no value. It does increase the crushing strength, and thus adds 



496 


A TREA TISE ON CONCRETE 


ductility to the column and permits of a somewhat higher unit stress upon 
the concrete. The hoops also appear practically to affect the shearing stress 
so that the column acts more like a cube than like a long prism, with con¬ 
sequently higher strength. The Joint Committee conclude: 

The general effect of bands or hoops is to increase greatly the “toughness” 
of the column and its ultimate strength, but hooping has little effect upon 
its behavior within the limit of elasticity. It thus renders the concrete a 
safer and more reliable material, and should permit the use of a somewhat 
higher working stress. The beneficial effects of “toughening” are ade¬ 
quately provided by a moderate amount of hooping, a larger amount serving 
mainly to increase the ultimate strength and the possible deformation before 
ultimate failure. 

The loadings suggested for use by the Joint Committee are referred to 
on page 527. 

A type of formula suggested by Considere for determining the ultimate 
strength of hooped columns is as follows: 

Let 

{ = ultimate unit pressure upon the reinforced column, equal to the 

total load divided by the effective area in pounds per square inch. 
f e = ultimate unit pressure upon the concrete of the column in pounds 
per square inch. 

p — ratio of sectional area of longitudinal reinforcement to the area of 
concrete core. 

p" — ratio of volume of steel hooping in a given height of column to the 
volume of the concrete core in this height. 


Then 


/ = i -5 fc + 2 400 p + 5100 p' (64) 

Professor Talbot suggests the following formulas for ultimate crushing 
strength: 

/ = fc + 6 5 000 P" (65) 

for columns reinforced with bands, and for those reinforced with spirals 

f =f c + 100 000 p. ( 66) 

The above formulas cannot be safely used, however, for computing 
the working strength of hooped columns. 


REINFORCED CONCRETE DESIGN 


497 


The Joint Committee suggest with reference to hooping: 

The effective area of the column shall be taken as the area within the 
protective covering (see page 489); or, in the case of hooped columns or 
columns reinforced with structural shapes, it shall be taken as the area 
within the hooping or structural shapes. 

The Joint Committee also specify that the hoops or bands should not be 
counted upon directly as adding to the strength of the column. They suggest: 

Where bands or hoops are used, the total amount of such reinforcement 
shall be not less than 1% of the volume of the column disclosed. The 
clear spacing of such bands or hoops shall not be greater than one-fourth 
the diameter of the enclosed column. Adequate means must be provided 
to hold bands or hoops in place so as to form a column, the core of which 
shall be straight and well centered. 

Hooping then may be considered not as adding to the working strength in 
proportion to the amount of steel in the hoops, but rather as increasing the 
toughness of the column and reducing the danger of sudden failure, so that a 
lower factor of safety is permissible. In practice, to gain the benefit of 
this, a higher working stress may be permitted in hooped columns when 
reinforced with steel bands or hoops the total volume of which in a given 
length of column is at least 1 per cent of the volume of concrete within the 
hooping. 

Adopting the Joint Committee recommendations: 

Columns with reinforcement of not less than 1 per cent in bands or hoops 
may be given a working stress 20 per cent higher than for plain concrete 
columns. If working stress in plain concrete is taken as 450 pounds per 
square inch, the hooped concrete maybe thus given 540 pounds per square 
inch. 

Columns reinforced with not less than 1 per cent and not more than 4 
per cent of longitudinal bars and with not less than 1 per cent in bands or 
hoops may be given a working stress 45 per cent higher than plain concrete 
columns. If the working stress in plain columns is taken as 450 pounds 
per square inch, the hooped and vertically reinforced column may be thus 
given 650 pounds per square inch plus the working value of the longitudinal 
rods as indicated on page 492. 


STRUCTURAL STEEL REINFORCEMENT 

If the structural steel is designed to take all the load and then is simply 
fireproofed with a concrete covering, it is not reinforced concrete. When 
the structural steel is designed so that it takes a load in combination with 


A TREATISE ON CONCRETE 


498 

the concrete it may be termed reinforcement. In this case the steel is 
figured in the same way as vertical bars and the stresses determined from 
formula (60), page 491. If, for example, the allowable stress on the con¬ 
crete is 450 pounds per square inch and a ratio of 15 is used, the steel can 
be figured only for a compressive stress of 6750 pounds per square inch. 

To utilize the full working strength of the steel, the plan has sometimes 
been followed of separating the structural steel core from the concrete so 
that they will work independently, and designing the columns in the lower 
stories so that the steel will take the entire weight of the upper stories while 
the concrete surrounding the steel supports the weight of the lower stories. 

Structural steel reinforcement is sometimes in the form of a cross in the 
center of the column, or, as in the case of the McGraw building,* channels 
connected by riveted latticing are placed and concrete poured within the 
reinforcement as well as providing a protective layer around it. Stresses for 
this type are suggested on page 528. 

Tests*)* of columns reinforced with structural steel shapes frequently 
show lower ultimate strength thaxi similar columns reinforced with the 
same quantity of steel in the form of vertical round bars. This probably 
is due in part to the difficulty in properly placing the concrete around 
the'Structural steel. 


COLUMN EXAMPLES. 

Example 15: What size of square column reinforced with 2 per cent of 
longitudinal bars without bands will be required to support a load of 94 000 
pounds? 

Solution: By paragraph (a), page 527, the allowable compression on 2000 
pounds concrete is limited to 450 pounds per square inch. For this allowable 
stress, using 2% of longitudinal reinforcement and a ratio of moduli of 
elasticity of 15, the area of column from formula (62), page 491, is 

94 000 

A __ --_-- 

450 (1 + 14x0.02) 

= 163 square inches, corresponding to 12.8 inches square. The denominator 
of this expression may be obtained directly from table on page 492. Allow¬ 
ing 2 inches for protective covering gives 14.8 inches, or, say, 15 inches square. 

Example 16: Find the diameter of a round column reinforced by 1 per 
cent of hooping only, designed to support a load of 120 000 pounds. Assume 
the allowable pressure on plain concrete as 450 pounds and a ratio of moduli 
of elasticity, n = 15. 

Solution: The allowable unit compression on hooped columns may be 
increased 20 per cent over that on plain concrete (see paragraph (b), page 527), 


♦William H. Burr, Transactions American Society of Civil Engineers, Vol. LX, 1908, p. 433. 
JM. O. Withey in Engineering Record, July 10, 1909, p. 41. 


REINFORCED CONCRETE DESIGN 


499 

hence / = 45°+ 20% = 540. The area of section from formula (63) is 

. 120 000 

A = —- 

54o 

= 222 square inches, giving an effective diameter of 16.8 inches. Adding 3 
inches for protective covering gives a total diameter of 20 inches. 

Example 17: What sectional area of vertical steel will be required for a 
square column limited to 36 inches diameter, which has to bear 1 000 000 
pounds with pressure in plain concrete limited to 450 pounds per square inch? 

Solution: By paragraph (c), page 528, in a column reinforced with vertical 
bars and 1% of bands or hoops, the allowable pressure on the concrete may 
be increased 45% over that on plain concrete, hence f c = 450 + 45% = 652 
pounds per square inch. Considering the area within hooping equal to 33 2 = 
1090 square inches as effective, the unit pressure from page 491, will be 

1 000 000 
' ~~ 1090 

= 918 pounds per square inch. Assume n =15, then from formula (61), 
page 49B 

918 — 652 
P ~ 14 x 652 

= 0.029, and area of steel, A = 1090 X 0.029 = 3 r -6 square inches. From 
table on page 507, it is found that 18 round rods inches diameter will give 
the required area. 

Example 18: What should be the area of a column 10 feet high supporting 
1 000 000 pounds, reinforced with 3.5 % of longitudinal reinforcement ana 
1 % of hooping for n = 15 and an allowable compression in plain concrete 
limited to 450 pounds? 

Solution: Since the column is reinforced with longitudinal and hooping 
reinforcement, the unit compression on concrete may be taken as f c = 450 
+ 45 % = 652 pounds per square inch (paragraph c, page 528). Then from 
formula (62), page 491, the column area is 

1 000 000 

a _ -—--— -.— 

652 (1 + 14 X 0.035) 

— 1030 square inches. The denominator of this expression may be ob¬ 
tained directly from table on page 492. 


REINFORCEMENT FOR TEMPERATURE AND SHRINKAGE 

STRESSES 

All masonry is subject to temperature cracks, but when they are distrib¬ 
uted in the many joints between bricks or stones they do not show so plainly 
as on the smooth surface of concrete. 

Expansion from a rise in temperature rarely causes trouble except at 
angles where the lengthening of the surface may produce a buckling or a 
sliding of one portion of the wall past the end of the other. In a building, 
the walls and floors are generally so well bonded together and free to move 






5°° 


A TREATISE ON CONCRETE 


as a unit, that no provision need be made for expansion. In a structure 
like a square reservoir, the effect of expansion must be taken into account 
in the design to prevent failure at the corners. 

Contraction is often more serious, although cracks are by no means neces¬ 
sarily dangerous. To prevent cracking due to the shrinkage of the concrete 
in hardening (see p. 287) or to the lowering of the temperature, reinforce¬ 
ment should be inserted or joints formed to localize the cracks. (See p. 
285.) 

Reinforcement properly placed distributes the contraction stresses so 
as to make the cracks very small, practically invisible, but it does not prevent 
them entirely. 

The steel must be sufficient in quantity, : n 1 should be of small diameter 
and placed as close as practicable to the surfaces to distribute the cracks 
and thus make them very fine. Deformed bars, that is, bars with irregular 
surfaces which provide a mechanical bond with the concrete, are more 
effective than smooth bars, and steel of high elastic limit also is advan¬ 
tageous. 

In practice, from to of 1% to to of I % ( a ratio of 0.002 to 0.004) of 
steel, based on the cross-section of the concrete, is commonly used as tem¬ 
perature or shrinkage reinforcement. 

The tensile strength of concrete is so low that a small change in tempera¬ 
ture will crack it. For example, the coefficient of expansion of concrete 
is 0.0000055 (see p. 287) and the modulus of elasticity is generally assumed 
as 2 000 000; therefore, the stress (see p. 404) per degree Fahrenheit is 
0.0000055 ^ 2 000 000 = 11 pounds per square inch, and a fall in tempera¬ 
ture of tt = 27 0 is sufficient to crack a concrete the tensile strength of 
which is 300 pounds per square inch. 

It is evident, and it has been proved by experience, that there is less 
cracking in concrete laid in cold than in warm weather. 

Longitudinal reinforcement is especially necessary in conduits which 
must be water-tight. 

Shrinkage cracks due to the hardening of the concrete may be prevented 
by keeping the concrete wet. (See p. 287.) 

It has been suggested by Mr. Charles M. Mills that the relation between 
the tensile strength of the concrete and the bond with the bars is an impor¬ 
tant factor in governing the size of the cracks, and the following analysis, 
based on his suggestions, gives a means of estimating the size and dis¬ 
tance apart of the cracks so as to form a basis for judgment as to the sizes 
and percentages of steel to use. 

The tensile stress in the steel at a crack tends to pull out the bars from 


REINFORCED CONCRETE DESIGN 


5oi 


the concrete, and referring to Fig. 154, the bond stress of the bar in the 
length ab must equal the tensile stress in the whole cross-section of the con¬ 
crete at b caused by the contraction of the concrete. 

Let 

v = distance apart of cracks. 

D — diameter of round bar or side of square bar. 
p = ratio of cross-section of steel to cross section of concrete. 

Then,* if, as is sufficiently accurate for practical purposes, the strength 
of concrete in tension is assumed to be equal to the bond between plain 
steel bars and concrete, the distance apart of cracks is 

D 

x = — for square or round bars. 

2 p 

The distance apart is inversely proportional to the unit bond*, so that a 
deformed bar having twice the bond strength would space the cracks 
one-haJf as far apart and allow them to be only one-half as wide. 



-)°/'7cA 0 

.0»X) W? y 


Fig. 154. Reinforcement for Temperature Stresses. ( See p. 501.) 


It is evident that the distance apart of the cracks is proportional to the 
diameter of the reinforcing bars, and inversely proportional to the percent¬ 
age of steel. 

From this formula is tabulated the estimated percentage of reinforcement 
for different spacing of cracks and different sizes of bars, assuming the 
bonding strength of the steel to the concrete to equal the tensile strength 
of the concrete. 


* In addition to above notation, let 
A c = area of section of concrete. 

A s = area of section of steel. 

0 — perimeter of steel bar. 

f' c — tensile stress in concrete. 


u — unit bond between plain steel and concrete. 
f s = unit tensile stress in steel. 

D = diameter of bar. 


Theri A c f c ' = \ uox, or x 
2 Ag A 


2 A fg 2 A £ * A g 

-. If f' r = u, x — -, and since p = — 

u 0 0 A r 


x = -. Also, 

Op 0 


D D 

- for both round and square bars, hence x — $ — 

4 * P 






















502 


A TREATISE ON CONCRETE 


Estimated Percentage of Reinforcement for Different Spacing of Cracks 


DISTANCE APART OF CRACKS WITH 


PLAIN BARS. 

DEFORMED BARS *. 

12 " 

8 " 

18 " 

12" 

24 " 

16 " 

36 " 

24 " 

48 " 

32 " 

0 0 

] 



% 

% 

% 

% 

% 

■% 


'r 

1.04 

0.70 

0.52 

0 • 35 

0.26 

0.21 


|// 

1.56 

I . 04 

00 

O 

0.52 

0 • 39 

O.3I 

Diameter of round or side of 

r 

2.08 

i -39 

I . 04 

0.69 

0.52 

O.4I 

square bar. .. 

¥' 

2.60 

1.74 

I.30 

0.87 

0.65 

0.52 


£ // 

3.12 

2.08 

I . 56 

1.04 

0.78 

O . 62 


V 

3 • 65 

2.44 

I . 82 

1.22 

0.91 

0 • 73 


{ T' 

4.17 

2.78 

2.08 

1 -39 

1.04 

0.83 


Note: To express the steel as the ratio of area of cross-section of steel to 
cross-section of concrete, divide the percentages by ioo; thus 1.04 becomes 
p = 0.0104. 


* Assuming the bond of deformed bars to be 50% greater than plain. 

The size of the crack is governed by the amount of shrinkage and for 
cracks due to temperature changes may be estimated as the product of 
the coefficient of contraction (0.0000055) by the number of degrees fall 
in temperature by the distance between cracks. 


Estimated Width of Cracks for Different Distances Apart 


WIDTH FOR DIFFERENT TEMPER¬ 
ATURE CHANGES. 

DISTANCE APART 

12" 

18 " 

24 " 86" 

00 

1 

60 " 




30° Fahr* .. 

O.0020 

O.OO33 
O.OO46 

0.0030 

0.0050 
0.0069 

O.0040 

O.0066 

O.OO92 

°.° o 59 

0.0099 
0.0139 

• 

0.0079 
0.0132 
0.0185 

0.0099 
0.0165 
0.0232 

qo° “ 

J . 

70 ° “ . 

/ . 


From this, if it can be determined how large a crack will be allowable, 
the corresponding spacing can be obtained. 

To avoid large cracks it may be necessary to use enough steel to prevent 
its passing its elastic limit. If the bars are continuous for such a length 
that the ends are practically immovable, as in a long retaining wall, a drop 

* 30° corresponds to a shrinkage of 0.017%; 5°° to 0.028%; 70° to 0.038%. 


















































REINFORCED CONCRETE DESIGN 


5°3 


in temperature, tending to shorten them, produces a tensile stress which 
is independent of the distance between the restrained ends. Assuming 
the coefficient of expansion of steel the same as concrete and the modulus 
of elasticity of steel as 30 000 000, this stress is 30 000 000 X 0.0000055 
= 165 pounds per square inch per degree of temperature, or for5o°Fahr. 
is 8250 pounds per square inch. This is well within the elastic limit of the 
steel and would not, of itself, cause the steel to take a permanent set. How¬ 
ever, since the concrete surrounding the steel will be continuous except at 
certain cracks, the stretch in the steel may be unevenly distributed and 
largely confined to the immediate vicinity of the cracks. If cracks occur 
while steel is unstressed, through the concrete shrinking, the steel tends to 
resist the shrinkage by tension at the crack and compression at the center of 
the block of concrete, and the tensile stress will be equal to the compressive 
and each equal to one-half the tensile strength of the concrete. This may be 
expressed by the following formula, using the foregoing notation:* 



Since the tensile stress in the concrete is liable to be low at the time 
shrinkage cracks are formed, it may be assumed, for illustration, as 20^ 
pounds per square inch making 



This represents the stress due to local cracks which is additional to ine 
temperature stresses above described. The total stress is, therefore, for 

^o° change of temperature 8250 + /' or 8250 + If the elastic limit' 

P 

of the steel is 40 000 pounds per square inch, and we must keep below th* 


40 000 = 8250 + 


100 

-and p = 0.0031 


For steel, the elastic limit of which is 50 000 pounds per square 


50 000 = 8250 + 


100 

and p 

P F 


0.002/ 


These values of p represent the lowest theoretical ratio 
section of steel to area of cross-section of concrete which can be used witn- 
out the steel passing its elastic limit at certain of the cracks when the ends 
are restrained or the length is so great that intermediate parts are practi¬ 
cally restrained. 


* 



a j\ ° r /« 


± t 

2 A 


fc hence f‘ t 



2 







504 


A TREATISE ON CONCRETE 


In view of the very slight stretch required to relieve the stress in the bars 
when the elastic limit is exceeded, and the probability of its distribution 
by the restraint to movement by the mass, it is not always essential to 
consider the elastic limit. 

SYSTEMS OF REINFORCEMENT 

One of the earliest recorded examples of the application of reinforced 
concrete is a boat of concrete and iron, built by Mr. L. J. Lambot in France, 
and shown at the Paris International Exhibition in 1855.* In 1861 Mr. 
Coignet began his investigations, and in 1866 Mr. Monier, to whom the 
invention of reinforced concrete is often attributed, applied the combination 
of concrete and iron to various structures, and laid the foundation for its 
future widespread applications. 

As long ago as 1872, Mr. W. E. Ward,f at Port Chester, N. Y., built a 
house entirely of concrete, reinforced with iron I-beams and round rods. 

The rapid development of reinforced concrete has resulted in the intro¬ 
duction of numerous systems, many of them covered by patents, for arrang¬ 
ing the metal in the concrete, or for special forms of metal. These systems 
are fully described in the various French works on reinforced concrete.ij; 

A few of the systems, representing both the arrangement and the form 
of the metal, are described below, and forms of metal extensively used in 
the United States are illustrated in Fig. 155. 

% 

Systems of Reinforcement 

Bonna. Metal of cruciform cross-section. 

Bertini. Girder Frame. Horizontal tension members with vertical stir¬ 
rups shrunk on to them. 

Chaudy and Degon. Cross rods passing under bearing rods, but looped 
up between them. 

Coignet. Round bars in top and bottom of beam connected by diagonal 
wire lacing. 

Columbian. Vertical steel plates with horizontal ribs. 

Cottacin. Round rods interlaced in the same manner as in wire netting. 

Cummings. Bars of different lengths having their ends bent to an 
incline and formed into a loop to resist internal stresses. 

Cup Bar. Special rolled section with longitudinal ribs connected at fre¬ 
quent intervals by cross ribs forming cup depressions. 

* Christo phe’s Beton Arme, 1902, p. 1. 

f Transactions American Society Mechanical Engineers, Vol. IV, p. 388. 

J See among others Christophe’s Beton Arme, 1902, pp. 10-71, and Morel’s Ciment Arme, 1902. 
pp. 88 to 152. 



Expanded Metal. 



Kahn Trussed Bar. 



Thacher Bulb Bar. 



Ransome Twisted Bar. 



Johnson Corrugated Bar. 



De Man Undulated Bar. 


Fig. 155.—Types of Reinforcing Steel. {See pp. 504 and 506 














































5°6 


A TREATISE ON CONCRETE 


De Man. Undulated Bars. (See Fig. 155.) 

Diamond Bar. Bars rolled round with parallel ribs passing along and 
around the bar forming diamond-shaped shoulders on its surface. 

Donath. Inverted T-beams or I-beams connected by horizontal diagonals 
of light, Hat metal on edge. 

Expanded Metal. Sheet steel, slit and expanded, so as to form a diamond 
mesh. (See Fig. 155, p. 505.) 

Ferroinclave. Sheet steel with inversely tapered corrugations to be cov¬ 
ered on both sides with concrete. 

Gabriel. Deformed tension members with trussing of hard drawn wire. 

Habrich and Busing. Flat metal twisted hot. 

Hennebique. A combination of alternate straight bars and bars with ends 
bent up at an angle, with vertical U-bars, or stirrups, of Hat iron passing 
around the straight bars and reaching nearly to the top of the beam. 

Herringbone Frame. Horizontal tension member with special attach¬ 
ments for stirrups. 

Holzer. Metal in form of I-beams. 

Hyatt. Flat plates or bars set on edge and pierced with holes through 
which pass small round rods to form the cross reinforcements. 

Johnson. Corrugated bars. (See Fig. 155, p. 505.) 

Kahn. Horizontal flanged bars with flanges sheared up at intervals. 
(See Fig. 155, p. 505.) 

Lock-Woven Steel Fabric. Steel wire mesh, locked at intersections. 

Lug Bars. Twisted bars with projecting lugs at intervals in the surface. 

Melan. Steel ribs, either I-beam or 4 angles latticed, imbedded in the 
concrete of the arch. 

Monier. Two series of round parallel bars at right angles to each other. 

Mushroom. Flat floor slabs supported by columns with enlarged heads. 

Parmley. Bars with bent ends, to place in the sides of a conduit or the 
haunches of an arch to resist tension. 

Rabitz. Various combinations employing galvanized wire. 

Ransome. Square steel rods twisted cold. (See Fig. 155, p. 505.) 

Roebling. Flat steel bars set on edge, clamped to supporting beams, and 
held in alignment by flat bar separators. 

Schuller. Like Monier System except rods are placed diagonally. 

Scofield. An oval bar with projecting shoulders. 

Thacher. Bulb bars. (See Fig. 155, p. 505.) 

Triangle Mesh. Wire mesh reinforcement with transverse metal placed 
diagonally. • 

Trussit. Expanded metal or herringbone lath bent to V-shaped section. 

Visintini. Beams of concrete, cored out so as to form lattice girders. 

Welded Wire Fabric. Wire mesh reinforcement with wires at right 
angles to each other and welded at intersections. 


REINFORCED CONCRETE DESIGN 


5°7 


Table i. areas, weights and circumferences of bars. 


Areas and 1 Veights of Square and Round Rods and Circumferences of Round Rods. 


One cubic foot weighs 490 lb. 


Ih 

<u 

T3 

O 

-d 


-a 

-a 


*2 




T3 

£ 

& . 
c/) 

^ c/} 


4 • 

to 

& * 
bjO 

"S 

tn 

« . 

t/j 

O 

W O 

cS • 

to 

& • 
to 

S 8 

. -c 

c C 

Square 
ire inche 

Round 
ire inche 

CJ fl 

u •*+ 
a a 

0 

S-e 

»-*-« O 

§4 
cr^ 
c/} 0 

0 

T3 d 

G O 

ss or Dial 
in inches. 

Square 

.re inche 

Round 

ire inche 

c!a 

QJ ^ 

i) a 
(3 0 
§4 

w 0 

O 

13 

• — 

W a 


3 

£4 

o4 

04 

03 

2 


£4 


0 ^ 

CJ . tn 

C 

^0 cr 

O c/> 

O & 


4-» <D 

4-* 1) 

<D 

a 

<4-1 O* 

O So 

O Cfl 

3^ 

<D 

4-. 0) 

0 

12 

H 

rf.g 

a; 

L 

ce.S 

<L> 

V 0 

4 

.SfO 

0) 

£ 

.Sfo 

0 

£ 

u 

13 

H 

cj.S 

<L> 

H 

< 

Area 

in 

•E § 

U 0 

Pi 

*>o 

OJ 

£ 

.SfO 

<u 

£ 

0 






2 

4.0000 

3 - i 4 i 6 

6.2832 

13.60 

10.68 

1 

A 

0.0039 

0.0031 

0.1963 

O.OI3 

0.010 

A 

4-2539 

3-34io 

6-4795 

14.46 

11.36 

i 

0.0156 

0.0123 

0.3927 

0.053 

0.042 

1 

4.5156 

3-5466 

6.6759 

15-35 

12.06 

16 

0.0352 

0.0276 

0.5890 

O.II9 

0.094 

A 

4.7852 

3-7583 

6.8722 

16.27 

12.78 


0.0625 

0.0491 

0.7854 

0.212 

0.167 

1 

5.0625 

3.9761 

7.0686 

17.22 

^•S 2 

5 

16 

0.0977 

0.0767 

0.9817 

o-333 

0.261 

5 

1 6 

5-3477 

4.2000 

7.2649 

18.19 

14.28 

§ 

0.1406 

0.1104 

1.1781 

0.478 

o-375 

I 

5.6406 

4-43 QI 

7-46I3 

19.18 

15-07 

T 6 

0.1914 

0.1503 

1-3744 

0.651 

0.511 

T6 

5-9414 

4.6664 

7-6576 

20.20 

15.86 

4 

0.2500 

0.1963 

1.5708 

0.850 

0.667 

h 

6.2500 

4.9087 

7.8540 

21.25 

16.69 

9 

1 6 

0.31-64 

0.2485 

1.7671 

1.076 

0.845 

A 

6.5664 

5- 1 5 72 

8.0503 

2 2-33 

17-53 

1 

0.3906 

0.3068 

1-9635 

1.328 

1.043 

1 

6.8906 

5-4II9 

8.2467 

23-43 

18.40 

ii 

0.4727 

°-37 12 

2.1598 

1.608 

1.262 

ii 

7.2227 

5.6727 

8.4430 

24.56 

19.29 

i 

0-5 6 25 

0.4418 

2.3562 

I-9I3 

1.502 

a 

4 

7-5625 

5-9396 

8.6394 

25.OO 

20.20 

13 

TS 

0.6602 

0.5185 

2-5525 

2.245 

1-763 

13 

1 6 

7.9102 

6.2126 

8.8357 

26.90 

21.12 

4 

0.7656 

0.6013 

2.7489 

2.603 

2.044 

I 

8.2656 

6.4918 

9.0321 

28.IO 

22.07 

15 

1 6 

1 

0.8789 

0.6903 

2.9452 

2.989 

2-347 

I 5 
T6 

8.6289 

6-777 1 

9.2284 

29-34 

23.04 

1.0000 

0.7854 

3- I 4 l6 

3.400 

2.670 

3 

9.0000 

7.0686 

9.424S 

30.60 

24.03 

tV 

1.1289 

0.8866 

3-3379 

3-838 

3.0:14 

1 

1 6 

9-3789 

7.3662 

9.621I 

3I.89 

25.04 

I 

1.2656 

0.9940 

3-5343 

4.303 

3-379 

h 

9.7656 

7.6699 

9-8I75 

33-20 

26.08 

3 

T 6 

1.4102 

i-i °75 

3-7306 

4-795 

3.766 

3 

1 6 

10.160 

7.9798 

IO.OI4 

34-55 

2 7- I 3 

1 

4 

1-5625 

1.2272 

3.9270 

5-312 

4.173 

1 

10.563 

8.2958 

10.210 

35-92 

28.20 

5 

lo 

1.7227 

1-353° 

4.1233 

5-857 

4.600 

5 

1 6 

10.973 

8.6179 

IO.407 

37-3i 

29.30 

1 

1.8906 

1.4849 

4-3 r 97 

6.428 

5-°49 

1 

H-39I 

8.9462 

IO.603 

38.73 

30.42 

16' 

2.0664 

1.6230 

4 - 5 i6 o 

7.026 

5-5 18 

A 

11.816 

9.2806 

IO.799 

40.18 

31.56 

4 

2.2500 

1.7671 

4-7 I2 4 

7.650 

6.008 

1 

12.250 

9.6211 

IO.996 

41.65 

32.71 

16 

2.4414 

I-9I75 

4.9087 

8.301 

6.520 

9 

1 6 

12.691 

9.9678 

II.I92 

43- T 4 

33-90 

5 

8 

2.6406 

2.0739 

5- I °5 I 

8.978 

7 -°5 1 

& 

8 

I 3- I 4 I 

10.321 

II.388 

44.68 

35-°9 

1 1 

1 6 

2.8477 

2.2365 

5-3 OI 4 

9.682 

7.604 

1 1 

I <? 

I3-598 

10.680 

II-585 

46.24 

36.3 1 

f 

3.0625 

24053 

5.4978 

10.41 

8.178 

a 

4 

14.063 

11.045 

II.781 

47.82 

37-5 6 

1 3 

1 6 

3.2852 

2.5802 

5.6941 

11.17 

8-773 

13 
IT 

14-535 

11.416 

11.977 

49.42 

38.81 

l 

3-5 I 5 6 

2.7612 

5.8905 

n-95 

9.388 

7 

8 

15.016 

n-793 

12.174 

5I-05 

40.10 

rf 

3-7539 

2.9483 

6.0868 

12 76 

10.02 

1 5 

1 6 

I5-504 

| 12.177 

1 

I2.370 

52-7 1 

' 

41.40 

1 










































5°^ 


A TREATISE ON CONCRETE 


BEAM AND SLAB TABLES 

Beam Tables. Tables 2,3, and 4, pages 509, 510 and 511, give the load¬ 
ing and reinforcement for beams, based on 1 inch of width under different 
conditions. For a beam 10 inches wide, for example, both the safe load per 
linear foot and the steel area will be ten times the values given in the tables. 

The tables are for rectangular beams but may be used for T-beams 
which have a depth 3 or 4 times the thickness of slab by taking the width 
of flange as the breadth, b. 

Table 2 is for a simply supported beam and is based on a working com¬ 
pressive stress in concrete of 500 pounds per square inch and in steel of 14 000 
pounds per square inch—lower values than are customarily used in con¬ 
struction, but required in many building laws. If the compression in con¬ 
crete is limited to 500 pounds, while 16 000 pounds is permitted in the 
steel, use the same loading but reduce the steel in the ratio of 16 to 14. 

Tables 3 and 4 are for ordinary design, approved by the authors and 
corresponding to recommendations of the joint Committee. All tables 
are based on a ratio of elasticity of n = 15. (See p. 408.) 

For other working stresses than those given, the loads may be multiplied 
by ratios of the values of the constant C in Table 10, page 519, since C is 
proportional to the load. 

The uses of the tables are illustrated in Examples 12 and 13. As high 
steel is not recommended for ordinary work on a small scale, no table is 
presented for safe loads for concrete reinforced with it. 

Slab Table. Table 5 is for slab design with different working stresses 
in the steel and concrete. Ordinarily, the series at the top of the second 

w p 

page of the table is used. Note that the values are based on- For 

10 

wl 7, 

—, generally used where the slabs are fully continuous over the supports, 
12 

add 20% to the loads, leaving the area of steel as given. For square slabs 
fully reinforced in both directions, the loads may be doubled, or if also 
fully continuous, they may be doubled and 20% added also. 

Table 6 is more convenient for review of beams already designed. It 
is computed by using formulas (7) and (8) on page 753, and selecting 
the lower value of M. The most economical ratio of steel for the limiting 
stresses is p = 0.0077. For ratios lower than this the safe loads on the 
slabs are governed by the tensile strength of the steel, while for larger 
ratios they are limited by the working strength of the concrete in compres¬ 
sion. 




REINFORCED CONCRETE DESIGN 


5°9 


O 

<0 

'' 3 - 


ft 3 

2 5 

c/D 

W 

A * 

W *• 

> 

»—i 

H 
< 

> 

Pi 
W 
c n 
ft 
O 
o 

<J 
« 

H 
X 
W 

Pi 

o 

pH 

C/D 

a 

c 
w 
m 5 

/-N O 

o 

W cq 


3 


£ 

-si 

to> 

£ 


O 

»o 


Pi 

o 

&< 

Pi 

0 

C/D 

>< 

i-l 

Pi 

a 

*—i 

C/D 

rt 

o 

ph 

w 

c/D 

A 


N 

w 

to-1 

pq 

H 


ON 

M 

vn 


« £ 

* H 

w c 

• °s 

^ o 


* 

o 


o 

4J 


1> 

G 

i /3 

b/D 

C 


co 

c3 

1) 

Mh 

CS 

i /3 

V 

J 2 


& 

o 

W“> 

TD 


<0 

CO 


o 


Q ^ 

*3 

CLO Lri 

£ ~ 

5 II 

Cj c 

to 

k 3 00 


£ 

to 


to 

to 

to 


to 


toO 

.£ 

"§ 

O 

o 

-1 

to 

0 


a 

o 

T3 

a> 

(/) 

PQ 


n: 

3 


3 

V 


V 

G 

rt 

</> 

toO 

_S 

’3 

3 

GO 

-T3 

d 

O 

•—H 

CJ 

to-*— 

CO 

11 

-C 


U-D 

(S 

-o 

r 3 


u. 

O 


(•pp; -rf aae'i — 

_• 

0 ip 0 

000 

000 

OOO 

000 

0 0 0 

000 

000 1 


CO CS 

i> w 0\ 

« 0 0 

cO co £n^ 

O NO VP 

d O nO 

to cs O 

OOO 


IJ° ^ 


O N O' *'• 

^ to to <N 

x^O GO 

CO Cs m 

O O w< 10 O CS 

Os CO CS 

coo 1 

rf H rf 



co O'to 

ttoOO O 

C4 d-NO 00 O cc 

d O r- 

d pc O 

NO O ON 

^uauioj^ ajtJg O 

,_s 



M 

M M M 

H cs cs 

CS CO CO 

rf tO vO 

00 cs to 

M M 




d - O tto 

CO co 

OnnO O 

NO M CO 

d to d 

O « d 

O CS H 

0 0 00 

* ^HLW 

G 

^ CS CO CO 

Tf rfcp 

ioo h 

r-NOO CO 

ON O O 

M CS CO 

rf to 

m rt tN 

xpuj 8UQ lUtJdjJ 

• 

ip 0 0 0 
cs . . . 

OOO 

OOO 

000 

0 H4 W 

M M M 

M M M 

CS CS Cl 

13 ui caay 

jaajg 

O' 

CQ 

^ O O O 

OOO 

odd 

OOO 

OOO 

OOO 

OOO 

OOO 





to to 

»o 






WS 'Ze 

Avojsq q^daQ -—.a 

^OOO 

O cs cs 

CS to to 

to to to 

to to O 

OOO 

OOO 

10 to to 

cs 

v 7 M M M 

M M M 

M W M 

M M M 

M M (S 

CS cs CS 

CS CS CS 

cs cs cs 





iO >0 

to to O 

OOO 

OOO 

OOO 

OOO 

OOO 

qaa^g 

^ • 

^OOO 
co . . . 

0 t- 

r^to 

VO to to 

to to O 

OOO 

000 

to to to 

01 indarr >2-— 

CS Tfto O 

t-' r^oo 

On O w 

CS CO rf 

to 0 

00 O P 

dvO 00 

CO Osto 






M H4 

M W M 

M M M 

w cs CS 

CS CS CS 

co CO rf 

•^ooq aBauiq jad 


^ Tf Tt-VP 

O O N 

00 OO On 

O O M 

M CS CO 

rf O In. 

On O to 

to OS rf 

9 P!AV P au I 

au 0 

£ 

cs • • • 

00 Os O 

M CS CO 

to O ^ 

OO On O 

M CO lO 

|n» 0 Cl 

CO rf w 

uinaq jo jipiaAY 


w 

H 

M M M 

M M M 

M M CS 

CS CS CS 

CS CO CO 

co rfto 



VO , 








\0 rf to 

( 


fQ 








rf O 00 










cox »n 

rf O CO 



0 







CO CO rf 

O00 H 



CO 








W 

* 








CO O 

tNLO rf 

PioO Oc 



10 






CO rf 

rf 10 vO 

O cs O 



N 








M M 

3 

oS 








M M CS 

d Ito O 

d O *p 


O 





CO 

rf to vO 

t -00 O 

rf O v O 

0) 


CS 







w 

HH CS CS 

« 










toto-4 











O 


O 




NO O 

d On to 

O NOs 

CS vO M 

On Pl d 







CS CO 

CO CO rf 

rf to O 

CO Os M 

*0 cs 0 

43 









M 

H cs cs 

M 


1 









• N 

01 


00 













W 

to O' co 

CO POO 

H CON 

H fN Tf 

OC tN tN 





CS 

CS CS CO 

CO rf rf 

to O N 

On O Pl 

tN rf cs 

bfi 

r* 









M W 

H cs CO 

.2 (N 
•O N 


t" 



0 CO 

co cs fN. 

CO 00 W4 

tN H«0 

P O On 

O I** cn 

3 


M 



H cs CS 

CS CO CO 

d d*p 

to fN .00 

O N CO 

O 

"S ^ 
cs g 









W M M 

HH cs co 

— 3 

D ^ 


vO 


O lO 

OS coo 

HO CS 

00 0-00 

VP O P* 

to to 

to CS rf 

'rt ^ 


M 


W M 

M cs cs 

CO CO rf 

Tf to to 

vo 00 as 

w co to 

CS w M 










M M M 

Cl CO rf 

^ . g 






















-3 S aa 


to 


m Tf 

«NO O 

O HCO 

to M O 

rf w M 

HH rf os 

O to M 

q g <d 


M 


M M M 

cs cs co 

co d d 

to O O 

tN O H 

CO to 

lO to In. 

7^8 








M 

M M M 

cs <0 rf 


V ^' 










3 0 0 

4- 

*t 

O 

COO O 

to O to 

M 00 to 

fO H tN 

to rf 

M 1^10 

COCO O 

0 -> 0 


M 


M M CS 

CS CO ^O 

d d>p 

O t'N 

00 0 « 

to tN O 

on O d 

7 to* >*- 

fl .e* +> 

PH 







W M 

M M CS 

CS rf to 












3 s» 2 
« 3 ^ 

3 










• H 

ro 

M 

to 00 CO 

On VP 0 

tN-tO rf 

CO fO CO 

00 M 1^ 

to to CO 

O cp r- 

rt •« to 

c: 

*H 

M 

M M CS 

CS CO Tt 

rf to vO 

r-co co 

Os CS rf 

tto O P0 

rf t^ CS 

to H © 

c3 







W M 

M CS CS 

CO rfsO 

0 3 a 

a 










»h d 

^ ^ c 

**r »w «*h 

GO 

CS 

Os CO 

r- m r-to 

Tf H IN 

VO to to 

0 f'N CO 

to CS CS 

to W Os 

O NO NO 

O 0 


M 

M 

w cs cs 

COTf i- 

to vO t-N 

00 O' 0 

H rf fN 

O rttN 

O ip cp 

£11 

C-. ' w/ 







M 

M M H 

CS CS CS 

rf to tN 










• 

cj ^ 


M 

0 ip 

HUD M 

O On NO 

vO N O' 

CS to CS 

t^ Osto 

rf t-N CS 

\C ho 

3 £ 


M 

W M 

CS CS CO 

p- -Nflp 

vO t^00 

O H CS 

POnO O 

rfGO co 

fNVC tN 

.a ^ 
a 4S. 







M M M 

M M CS 

CS CS CO 

rf 'O X) 











U Q 

O co 


0 

00 CO DO 

to M Q\ 

O Oc GO 

O COCO 

CO O' GO 

no vp 00 

to vO CS 

NO O 


M 

W M 

CS CO CO 

Tf LO VO 

00 On O 

cc p d 

no O d 

On d 0 

t" O 

/-N O 






w 

M M M 

W CS CS 

CS CO rf 

lO GO 











w ' 



O sO fO 

H 00 00 

OlNt 

Os to cs 

CS CS CO 

to coo 

to CO VO 


id 


O 

M M CS 

CO CO T* 

sO t^CO 

Os M CO 

to t^OO 

O VP O 

O cs 0 


0 s 

0 





M M 

M M M 

CS CS CO 

CO rf rf 
















COO Oc 

OS CO M 

VO COO 

tO vO CO 

COOO PV 

O to 00 

CS (S 


to*— 


00 

H cs CS 

CO rfvO 

P On O 

ci d-o 

Os H CO 

O cs co 

\C CO 


Cj 




M 

M M M 

H CS CS 

cs CO co 

rf to 


OQ 






















: os 



ttoVO 00 

to cp O 

Os woO 

d « 0 

M tO CO 

Os Oso 






H CS CO 

CP'OOO 

O cs CO 

vO Os cs 

ip 00 0 

CO M O 



H 





W M 

M M CS 

CS CS CO 

co rfto 






cpvO to 

OvvO On 

to to CO 

fO O O 

CS CO H 

cs 





VO 

cs co«o 

O 00 O 

CO O 00 

CS O O 

rf GO M 

0 






W 

M M M 

CS CS CO 

CO CO rf 

rf 






row *t 

H COh 

to rN. rf 

W rf M 

co co 






to 

cou-> 

O Cl to 

O CO tN 

CS tN CO 

om Os 







M M M 

M CS CS 

CO CO rf- 

rf to to 




-- - - 



\n so 

00 On O 

h « n •vj-vp no 

fNOO O 

0 p« d 

C NO 00 c 

NO (COO 

•ui«ag 


><; a 

M 

M M M 

W W M 

M M M 

CS CS Cl 

CS CS CO CO r* ■*- 


JO TfyddQ 


11 

1) 


1 ) 

Jd 

o 

C 

• H 

3 

• F* 

^3 

4-* 

03 

• H 

£ 

t-, 

43 


vo 

r» 


s 

G 

J3 

'o 

u 

'a, 


CO 

3 

d . 
O- w 
w — 

3 ° 
43 <« 
*■• -3 
— * 
0 8 * 
<0 T 3 
<U 

to 3 

d ^3 
3 *-> 
0 1 *-*— 

co o 

11 co 

-C <U 

4—> »-H 

_ C3 


~ cr 

—* CO 

PS . 

s t> 

o 43 

> 3 *-> 

4 -* 

* 0 
CL,_ 
O d 
>- 0 
Cl, o 


3 

43_ _ 

a g 
a S 

— G 

-3 d 

— 3 

rs -3 

£5 to*-< 

^3 -3 

4-» 

'a, ^ 
!5 >n 

3 3 

S m 

— 
a> d) 
_o <3 
— 
«— Cfl 

O^H 

43 © 

3 § 

*'3 

>N <u 

{3 


43 » to 
4J O 
co q- 
Lh ^ 

u 

I 

1) 

P3 

<L> 

4-* 

CO 
to*-» 

O 
jd 

4-> 

a* 


D 
u. 
Z3 

4-3 

M 

G 

i_ 

Cl, vc 

CD ** 

53 ^ 

3 •• 

d 

Cl, m 

co 

tj 3 

3 "O 
C d 
d u, 

co SuO 


too 

3 

^5 

u 

O 

C 

1) 

> 

’So 

n 

4-4 

1-4 

o 


T3 

D 

.h 

’3 

cr 

<D 


1-4 S ^ 

<u -5 cr 

-a ^ r 

G « d J3 

03 „ u 

^3 >to 
1) U 

jd i) 

T 5 ^ > c: 

a; 

T) d) ^ U 

S« O 


JC 

o 


o ^ 


3 

Cto 


p , H 

»2 

a£ ^ o 

s! a 

Ph <3 2 r* 

U) 'O g vO 


(D 


W5 


t3 

«S 

O 

»— 4 

<3 
M —1 
toj 
cn 

to 

O 


flJ J) 

43 43 - 0 

-M -(-> 

O O 


d 


toe 

o 


CO 

!-G 


cj 

(3 

toe 

<3 

1-. 

O 


W M 

’CJ T 3 
P cc! 
O O 


8 

d 


D 

11 


pH fa 


ccj 

-t-> +-> 3 

0 0-3 

H H H 


3 u_ 

_3 O 

d o 
> •£ 
d 

to 


— M d" vo 


to 

3 

Pi 


-3 

H 

* 









































































</5 


5 IC 


A TREATISE ON CONCRETE 




1 

i 

^3 

''j- 
* < 
N 


O O O O O O 


\ 

o o 


Ce9i -d MS') 
•aouB^sisag 
jo juauioj\[ ajsg 

-- rO 

G 

• X 

•t CM H 
^ H CM CO 

CM CM M 
covo CO 

10 sO 00 

CM rfvo 
covo co 

O <N t 

H M W 

VO 00 CM 

Os l^CO 

VO Os CM 

M M CM 

O-sO 

0 co 

SO Os M 

CM CM CO 

O O CM 
m rfto 
VO CO CM 

CO Tf to 

O O 00 
to CO O 

CM COVO 

sO t^OO 

OOO 

OC co O 

M O' *t 

CM SO CM 

M M CM 

*' 9 PIAV 
xpuj auo ureag 

a 

H 00 

fT> fO fO tJ- 
^OOO 

t O N 
VO sO O 
OOO 

VO IOO 

t^oO 00 

OOO 

vO ~+ CM 

O 0 w 

0 •-< M 

CS M 

M CM CO 

MMX 

Os t Os 
CO vo O 

M M M 

vo O O 
00 O w 

M CM CM 

00 t O 

VO O vO 

CM CO CO 

u utBajy |aa;g 

cr 

“ 

^000 

6 6 6 

boo 

OOO 

OOO 

boo 

OOO 

000 

•|"iS 


^000 

to »o 

O CM CM 

VO VO 

CM CM VO 

10 to to 

VO to O 

OOO 

OOO 

to VO VO 

Asopg ^dag 

w.S 

CM M M X 

M W M 

M W M 

M M M 

M M CM 

CM CM CM 

CM CM CM 

CM CM CM 

•jaajg 
oj xjjdag 

Si 

O O O 
co • • • 

N ■a-tn vO 
'—^ 

to to 

0 t>* t>» 

t^oO 

VO VO O 
t''* r^vo 

Os O w 

M M 

10 to VO 

CM CO Tf 
W H M 

l/UO O 

to so r>» 

M M M 

OOO 

00 O CM 
M CM CM 

OOO 

TtsO 00 

CM CM CM 

VO to VO 

CO CM-O 

CO co ^t 


o 

M 

10 

2. 

ob 


•joog JBaurj jad 

apiAV. 4 0U I 9U 0 
unjag ]o jtpSi^w 


^ t TfLO 
CM * • * 

N‘O'0 


O O N 

00 Os O 


00 CO Os 

x cm co 


O O m h n fO 

to vO n- 00 Os O 

MMX M M CM 




w COlO 

CM CM CM 


Os O H io Os Tf 

|N O w CO t M 
CM CO CO CO t VO 


3 

►si 

5i 

0 

c 

M 

u 



PQ 


00 

0 

PQ 



co 

to 

>» 

& 

to 

d 

X 

0 

J3 



0 


45 

45 

&0 
• X 



to 

5 

* ^ 

CQ 

45 

£ 





Wj 



H 

►-H 

6 

0 



a 


0 

^3 

S^ 


0 


0 

sO 

3 

c 


0 

0 , 

M 

II 

"y 

G 

E 

a 


Pi 

0 

? 

V 

•o 

• X 

0 

Vj 


Pi 

8 

oq 

v> 



C 

• H 


tH 

►0 

ft 

d 

VO 

vO 

0 

M 

O 

a 

H-l 

45 

s 

2 

/"-s 

<s> 

45 

MX 

O 

G 

0 

3 

45 

a 

O 

mL 

w 

6j0 

S 


0 

M 

v* 

CaO 

0 

0 

t*x 

C/5 

O 

to 

E 

rt 

41 

• X 

4> 

MX 

to 

tj 

M 


G 

03 


<to 

rv 

II 

PQ 

<0 

t; 


VO 

CO 


O 

CO 


vo 

CM 


Os 


CO 


o o 

O 


O O'VO 

O co 00 


00 Os 
rfrtn 


O CM VO 

r^oo Os 


so O W 
CO Qsto 
M M CM 


CM 00 O 
t 


sO O t 

to t^CO 


HO 0 N 

O M CO 


O CM M 
Os t^o 

H CM CO 


sO 



O ^3 

^3 


O 

a. 


O 

o 

p-l 

cd 

CJ 

g 


45 

<u 


45 

G* W. 
✓~N O 

9 ^ 

V-/ 

-o 

cQ 


CO 

13 

Eh 


"X3 

<3 _ 

-2 .c/ 3 . 

» 


<o 


s 

til 


a 

C3 

a 

go 


On 


00 


a 

<o 


■uiwag 
fo mdoQ 


-c g 





co Os 00 
•t ^tto 

SO ^ w 

so 1^00 

Os Os CM 

00 O CO 

X X 

C^IO Tf 

IOOO H 

X X CM 

sO sO 10 

O CM vO 

CO ^t VO 



VO O 
fO rt 

r^to Tf 

Tf to so 

CM CO M 

r^oo os 

00 HVO 

Os CM Tf 

X X 

Tf TfOO 

N O H 

►4 ft ft 

O CM so 

Tf cm 

CO TfVO 



cm 00 •d- 
CO co rf 

co W X 
to so 

O M O 

00 Ov O 

w 

Os Tf CO 

O COsO 

XXX 

Tf CO Tf 

O ft nO 

M ft ft 

000 

CM OS 

CO vo VO 


O 

CM 

vO co O 

CO rj-vo 

Os CO Os 

VO so 

WHO 

O O M 

M M 

CM M CM 

CM tO OO 

XXX 

t^so sO 
HVO Os 

CM CM CM 

Tf OS CM 

CM 00 00 
•tv 0 


VO CM 

CM CO 

w OvvO 
►r ►tvo 

r^oo O 
sO t> Os 

w vO -vf 

O M PI 

M M M 

00 O SO 

co O 

M X CM 

VO 00 Tf 

Tf 00 CO 

CM CM CO 

00 vo co 
l^sO 00 

t'O 00 


Os N 

CM CM CO 

SO SO Tfr 
rfto \0 

SO O CM 
t^CO O 

X 

\0 CM O 

w CO rf 

M M M 

t'* Tf tO 

to Os CO 

M X CM 

O 00 0 

00 CM 00 

CM CO CO 

Tf sO vo 
t to O 

VO hO 

X 

o s ! 

00 Tl- CO 
CM CO Tt 

COiO co 
10 sO 

VO HH vO 

OO O H 

M X 

CO M M 

co VO sO 

MMX 

O CM OS 
00 CM VO 

M CM CM 

OvO vO 

CM CO 

CO CO Tf 

too co 

CM sO to 

NO 00 M 

M 

sO CO 

M CM 

M 00 Os 
CO CO rf 

x rfvo 
sO t^OO 

HOOvO 

O 1-4 VO 

M W M 

10 to SO 

10 r^co 

XXX 

Os 00 CM 

O VO X 

CM CM CO 

ft ft VO 

Tf O 
to TfliO 

vo t^oo 

CM O CO 
NO fO 

X X 

CM OS 00 

W M CM 

t^sO 00 
CO Tf VO 

woo w 
t^oO O 

M 

Os CO O 

M COsO 

XXX 

CM sO 00 

00 O M 

M CM CM 

VO CM 

Tf O NO 

CM CO CO 

CM Tf 

CO H Os 
•t VO vo 

O CM 0 
VOOO N 

CO Hio 

X X 

•t CO CM 

W CM CO 

rf O 

•<frvo 

vo -a- 0 

00 O M 

W M 

0 0 

■'t'O 0\ 

M M tH 

Ow O 

M TJ-VO 
ft N N 

CM O sO 

Os SO CO 

CM CO •t 

00 O N 

X X O 

vo so 

CM NO Os 

X O sO 

O too 

XXX 

r^co O 

M CM 

cOvO •t 
vo sO 00 

cOsO Tf 

O CM *t 
WWW 

O Os Os 
Os CM 

M W CM 

CM sO O 
O Os M 

CM CM CO 

COsO 00 
10 CO CM 
CO Tfto 

00 Tf 

CM COVO 

so t^oo 

t CM X 

CM O NO 
cm CM 

w X CM 

CM TfOO 

CM CO rf 

SO O CO 

SO 00 0 

M 

00 so 00 

CM VO *>• 
XXX 

Otn to 

M TtOO 
WWW 

rf Os 

CM sO 00 
CO CO co 

Os cm 
CO covo 
Tf vo VO 

VO O vo“~ 
r> hio 

Os O 

X 

X X 

X 0 
to X 

X CM 

C50 CO h. 

CM TfrO 

Tf CM x 

00 O CO 

X X 

CM t^vO 
sO Os CM 

M M CM 

'O M 0\ 
>0 Hin 

Ct to co 

O' -t C4 
OvO On 
► t ^ 

CM CM Tf 
VO 00 CM 
VO sO 00 

CM CM sO 

00 VO CO 
Os M CO 

X X 

co 0 

X vo 

OssO 

M CM 

sO to O 
COiO 00 

OHO 
O HtN 

XXX 

W hvf 
HU) OS 
CM CM CM 

00 0 00 
'too 
*0 ■'t "t 

to vO CO 
fO O tf 
vn vO NO 

X OOO 

CM OS 

f^oo O 

X 

CM 

00 

CM 

M 


CO VO 0 

^■tsO 

M 

Os CM CM 
MfOO CO 
M M CM 

00 0 M 

00 vo 0 
c< <0 -a 

CO CM 

t^vo co 

MflO SO 

00 so sO 

CM CM 

t^oo 00 

CM CM sO 
00 H SO 
OS CM 'vt 

W X 



O OMO 

O VO 

M M 

^ CM Tf 

w sO co 
CM CM CO 

vo rt 
m 0 

•vtvo vo 

t"0 b 
00 O H 
<3 O 

Os 00 M 
•too sO 

O M CM 
XXX 

Tf 

X 

•t 

M 



vo >0 t'- 

00 O O 

M 

M CM CO 

XXX 

•vrvo vo 

MMX 

4^00 Os 

XXX 

O CM Tf 
CM CM CM 

sooo 0 

CM CM CO 

SO CM 00 

CO t t 


oj 

.d 

u 


C/5 4/ 

g 

2 tJ 

CL. 

C/5 Mx 

« ° 
d c /5 

*-* *G 
vx o 

w <u 

c/) *0 

45 

2 d 
G -w 
CT 

" - 


45 


<o 


C JS £ 

.S o 


3 

cr 

V) 


-C _ 

±3 * 

rs c 4) 

*•2-2 

*-• O 

JD O Z 

* n 

^2 c 

G. O 


2 Ji'’ tJ 

§ « O. M 


0 §J 
. 0 c 

-g B" £ 

• •—« G _■ 


O "H 

t- S 


a, 


vyi 


4) 

t. ” 

„ 2 - 
S « a. « 


45 

~ 

^3 S “ 

tfl 4 h 

■O 45 O 

’£ ?. A 


to 

4) 

C/5 

U5 

45 


fcuO 

G 

* 

o 

* 

c 

41 

> 

# *-* 
GJO 

45 

J3 


</5 

HO 

45 45 

g H3 

*2 
w & -a 


lx 

o 


m-« j__i —- 

>s O CU « g 

^ 3 ^^ -fis -g 

.. 03 Mx 
O -r CJ 45 



W T* CV3 

•H W'O c 

<J u u ~ 

15 CD (U 45 

S C? J3 ^3 ^3 

“ O o - 

O O U. Vh •“ 

o cn W .S 

^ O >a -o 

<D « J5 

i4_i <U O O 3 

“ 13 73 > 

U Wl X X 4) 

0 0 0 0^3 

ft! pH H H H 


« H w + 


VI 

W 

G 

S 

PS 


-a 

H 

* 












































































REINFORCED CONCRETE DESIGN 


5 £I 


• 

H 

& 

W 

u 

rt 

w 

p 

o 

fl 

H 

O 

& 

P 

W 

P 

to 

a 

w 

« 

P 

W 

H 

o 

Ph 

P 

c/3 

rt 

o 

fa 


c /5 

a 

< 

w 

PQ 

C/3 

P 

O 

P 

& 

•—i 

H 

P 

O 

u 

fa 

O 

c/3 


P 

W 

o 

fa 

« 

C/3 

P 


't 

w 

fa 

m 

H 


<0 

73 


<*> 

8 

o 


M 


5 


nS 

<v 

Im 

<3 

t> 


B 

nj 

oo 

tuQ 

c 


CO 

~C 

nJ 

O 


o 

1-1 


G 

u 


V/O 


QJ 

a, 

o 

N 

4—> 

u 

G 

H 3 

<D 


KS.iol 00 

O 3 I 2 


8 


<*> 

Nj 

o 

*8* 

•** 

<*> 


c 

o 

T 3 

4 J 

V) 

rt 

PQ 


u 

£ 


(XO 

8 

§ 

O 

fa) 

O 

CO 


('89Z, ’& 99 S) 

aou'B^sisa^j jo "7 

luauioj^ aj^g w d 

„o 0 o 

S't M 

Ov 

04.H « OO 

O 0 O 

04 01 M 

fOvo CO 

to VO oo 

0 o o 

04 TT ‘0 

CO to co 

O « Tf 

W H W 

O O 0 

tO 00 01 

On t^CO 

O On 01 

M w M 

o o o 

»fvO 

O to co 

NO O' w 

04 01 CO 

o o o 

nO O ci 

W Tf to 
to CO Cl 

CO Tf to 

OOO 
o o oo 
to CO O 

01 co»o 
vO t^oo 

121800 

169300 

224600 

^ 3pi ^ 

ipuj auQ uiWag ^ 
b ui T?ajy I9aig g 

H CO VO 
^ fO to Tj- 

^ O O O 
o 6 6 

^ O 
inO'O 

o o o 
odd 

to co Os 
t^oo 00 
o o o 

0 o o 

O t oi 

O' O m 

O H4 M 

o o o 

O' m 

H 01 CO 

M M M 

odd 

On Tf Os 
CO »o vO 

M M M 

o o o 

to O O 

CO O h 

H N 01 

odd 

00 Tf 0 

to O to 

04 CO CO 

OOO 

•jaa^g ^ . 

Avojag q^daQ w .5 

o o o 

CM . . . 

' M M M 

to to 
Own 

M M W 

to to 

01 04 to 

W H M 

to to to 

M M M 

to to O 

M M 01 

o o o 

01 Cl 04 

OOO 

04 01 01 

to to to 

C4 04 04 

•l^S ^ g 

o; q^daQ 

«° ° 0 
^ TflO VO 

to to 

O 

t^oO 

to to O 

O' 0.10 

On O m 

M W 

to to to 

01 CO Tf 

M M M 

mu' O 

to vC «** 

M M M 

o o o 

00 O 04 

H 01 01 

OOO 

Tf nO 00 

01 01 01 

10 to to 

co O' to 
co co Tf 

300 J jBaux^i jad 

9 P!A\. T l 0U I 9u O dS 
uiBag jo Jt[3iaA\.” 

/^s Tf TflO 
<M . . . 

Cl to vO t>» 

nO no r^> 

oo o o 

M 

00 00 On 

h 01 co 

M M M 

o o « 

to VO 

M M M 

H OI CO 

00 On O 

M M 04 

TfvO t' 

M CO tO 

04 C4 01 

o o 

|N O N 

01 CO CO 

lO O' Tf 

00 Tf w 

CO Tf tO 


to 

fO 







O CO 

to to 

COnO Tf 

00 HI to 

W M 


o 

ro 






0 On 

Tf 

00 00 On 
IOnO n 

COOO O 

M lO O 

H H N 

s 

cS 

0 

m 

«4-» 

o 

to 

n 





io O c» 

M> Tf Tf 

f'CO O 

Tfli") 

Tf CO Tf 
00 On H 

w 

COIN M 

NO Cl 0 

M Cl CO 

0 

N 




<5 M oo 

«0 Tj- Tf 

LO N O 
uiO'O 

Tf M O 
^ On m 

M 

M Tf CO 
CO to t'N 

M M M 

to to M 

tO tO t"N 

Cl CO Tf 

(*H 

—4 

bj3 

*3 

fe 

o 

M 



On CO 
01 CO 

On^O co 
CO Tf to 

O On to 
nOO N 

Ol H N 

00 O w 

M M 

to O CO 
Tf Cn» On 

M W M 

co co M 

00 O' 04 

C4 CO'O 

fcfi 

.S 

-3 M 

00 

w 



In N N 

04 CO CO 

Tf « On 
T f to to 

l ^\0 CO 
vO t ^00 

H 04 NO 

On m co 

M M 

Cl o O 

nO On C4 

M M 04 

to CO M 

M COCO 
co Tf 10 

3 w 

’o S 

s s 

3 

f »^«a 

^ O 

^•S ^ 

M 


rf 

04 

O vO 01 
CO co rt 

On 

rf to vO 

vO NO M 
t^OO On 

NvO n 
O oi to 

W W M 

H CO h 
00 M Tf 
H 01 04 

CO H Cl 
try 0*0 

CO TfvO 

VO 

M 


m r^. 

C4 01 

rf m 

fO Tf Tf 

\C to to 
to O 

to co 

00 On O 

M 

to 01 01 

M Tf 

M M M 

Tf O 00 
O 'tl' 
N N N 

00 Tf nO 

O' «o co 

CO to t'' 

Jh s S 

p ® o 
~ « p 
© ^ A 

to 

• M 

Kk 


O rf m 

w 01 co 

oo co 

co rfto 

co *f to 
vO r^oo 

O 

On m m 

M M 

M 01 NO 
cOnO On 

W M M 

co co 

CO tN H 

04 01 co 

fOO N 
to CO CO 

Tf NO CO 

GOO 

O ■» o 
^ < *— 

S -S’ -2 

■g Tf 
« M 
fa 

M 

cO 00 vO 

01 01 CO 

rf rf h 

T}-to VO 

Ol Tf tN 
t^oo ON 

HO Tf 
H 01 CO 
M M M 

O to Tf 
to 00 ci 
w M oi 

tN co cO 

vO H \0 

oi co to 

O CO HI 

Cl Cl NO 
to Jn On 

oj o 2 

a S ^ 

2 p a 

■«2 ^ p 

c 

• H 

G 2* 
ej 

a 

fO ON 

M M 

NO oi M 

01 CO 

M 01 M 

to O 

Tf 00 co 
00 On m 

H 

OnvO to 

01 TflO 

M M M 

Tf to O 

O' W NO 

H 01 01 

O CO M 
hO 01 

CO CO Tf 

Tf O to 

0 CO W 

NO 00 HI 

M 

^ ^ 

O _ 0 

O g a; 

§ s 

u 

CO 

N 

M 

OO fO 

M M 04 

M CO 00 
rO to 

O CO Tf 
VO i^co 

ONtO CO 
ON hh co 

M M 

Ol 01 04 

to r-oO 

M M M 

Tf Ol NO 
O to O 
01 04 co 

Tf t^lO 

NO Cl ON 

CO Tf Tf 

00 to CO 

0 CO 0 
tN. qn co 

ej « 

4) a 

C 2 " 50 

M r»o 

• —4 

J 

^ H— 

u Q 

M 

M 

M 0\ t>» 

M M 04 

f-to cO 

co to 

H h ON 
1^00 Os 

i^oo 

M COtO 
M M M 

O Tf fT. 

00 O w 
w N M 

Mi O Mi 
Tf O v O 
N Ml Mi 

Cl CO ON 
CO 0 oo 
Tf to to 

CO N tN 

Tf fN.tO 

CO HI to 

^ «0 

C, ^ 
o 

O 

w 

rf fO fO 
H 01 CO 

TftO O 
^tio 

vO tr> O 

00 O 04 
M M 

01 NO H 
Tf O O' 

M M M 

CO tN CO 
M TfvO 

04 01 01 

Tf Ml O 

Cf.'C rf 

C< Mi Tf 

CO Tf Ol 
04 « M 
to O t'' 

O CO Tf 

ci m cO 

O Tf CO 

M W W 

T 3 

3 j 

o 

hQ 

o 

00 c 0 O 

H W 't 

tO t'-’O 

to 'O co 

o oo 

O to "T 

W M M 

to T T '0 

tN O (O 

H 04 04 

O O Tf 

frO « 
M tO« 

Tf CN CO 
vO Tf Tf 
CO Tf to 

NO 00 O' 

Tf tO 

NO t^oo 

On hi 
to to 

Cl tN. 

M M 

0 ) 

<+* 

G. 

W 

00 

coo M 

01 fOio 

O to ON 
r^oO O 

M 

UI -TOO 

<OvO 00 

M M M 

04 On On 

04 to On 

01 04 04 

m O 

Tf CO M 
CO CO Tf 

OoO r~ 
vO -O 00 
Tf m \o 

66 O f0 

HO H 
00 On HI 
M 

Tf NO 

O M 
to C4 

M Cl 

o 3 

0 

H 


oo 

fO TfvO 

M M 01 
O M 

M W 

sO Tf to 

OH Tf 
H 01 01 

O co o 

On CO O' 
oi *0 co 

nO to nO 
Tf O CO 
TflO to 

M N 00 

O Tf O' 
O t'OO 

oo 

NO 

o 

M 



VO 

b to"*-* - 
TfO O 

Tf 04 CO 
04 tO O 
M M M 

© M 't 
tf » M 
« M O 

Tf O m 

OnO co 
CO Tfto 

r-oo O 

O OO Mi 
OO M 

00 0 <N 

M M N 

00 O w 

M M 




to 

00 "M-"ds 

lO O' PI 
M 

oo 6 o oo 

^ H o* 
w 01 N 

i3 © m 
^ MOO 
MO rf tT 

CC M"> TT 

T. vO >0 
1^0 M 

Tf O •"« 
Q'ty) 

00 o o 

M 

00 

r- 

w 

M 



•uiBaf 
jo ij^da 

S* A 

a v -'.s 

| to NO 

oo o> o 

M 

M n ro 

M M M 

Tf tO NO 
M W M 

r>*o 0 ^ 

M M M 

« C4 01 

<S M. Ml 

Ml Tf Tf 


t 


« O 

« -S 

cu a, 

M “ « 

« u TJ 

-g ^ ^ 

g *- JG 

c **- *-' 

_, ° *— 4 

G „ o 

• CO 

fll CO 

^3 £ <U 

3 3 § 

- 

•frjSjS 

o-N ^ *2 

JO O O 

4-> 4-» • 

gT j § 

6 g p 2 

3 O .2 M 

’o £ £ g 
o o g 

n . CL. tn> 

& o p -. 

Q_ l_, 

■a o- 

*3 ^ fj •• 

2 u <3 H* 

^ CO 

fl S3 c 'O 

S c a. 

_q .s « r 3 

- H S 

° « c 

rt «j ^ 

•S H £ 
“ s g 

>^**3 _ 2 

a °-tj . 

03 A 2 

S O.- - w 


u 


« > 
a> _, 

- 42 ^ 

i> w o 

P <+i " 

S ° ►, 

1/5 w a, 

T3 &. 

C +3 d 

^ «J 

-'O g 

"2 JJ 

S 43 -o 

co 5 cd 

a. o ~ 

Ifl V) 

Ui 

O ^3 
O uQ *-* 
W 05 P 

r) t3 
ctf «J 2 
0 0 3 

^ '<3 

■a *s > 

4 -» -M « 

O O -G 

HHH 


VO 


CO 

V 

CO 

M 

11 

H 

4-t 

CO 

tuO 

G 

15 

»- 

o 

G 

l> 

> 

‘So 

D 

JZ 


*n 

<u 

u. 

’3 

cr 

i> 


-G 

U 

IS 

f* 


G 

D 

u 

v- 

D 

a, 

t^« 

r-- 


r^ 

8 

6 


i> 

i> 

4-* 

CO 

U-* 

o 

.2 

*4-* 

ns 

u 

ns 

Vh 

O 

CO 

CO 
• •■— 
jC 

H 

* 


CO 

u 

•J 

D 

Pi 













































































512 


TABLE 5. USE FOR DESIGNING SLABS, IF FULLY CONTINUOUS, ADD 20% 

TO LOADS 


Safe Loadings per Square Foot and Reinforcement for Slabs for Various Working 
Stresses in Steel (f 8 ) and Concrete ( f c )• {See pp. 508 and 420.) 

Based on M = ^ For supported ends, (m = ~~ ^, deduct 20% from loads. For fully continuous, 

/ _ wl? \ 

{ M = — / ’ a dd 20%. For square slabs multiply by 2. Use same steel area always. 



Xi 

In 

u-« 

Total safe load ( w ) per square foot, including weight of slab. 
For safe live load deduct weight of slab in column (14). 

Cj 

ft 

- . 

"53 

■*-> 

•ji 

& 

O 

?ction 

foot 

+J 0> 

c 3 

0 c 

BB 
! 0.22 


C 

A 

Q, 


(See important foot-notes on opposite page.) 


cn O 

,0 

0 


S 9 
_ c 
.3 0 

t- c3 • 

— 

<L> O > 

m 

5 1/3 
a> 


V 

*0 

cj 

O 





Span in feet (Z) 






c V 
q rt 

to 3 

y k 
£ 

ft 

Q 

(d) 

•*-> 0 

Q 

(e) 

CG ° 

See j). 
75. 

21/ 


(h) 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

i5 

lb. 

in. 

in. 

sq. in. 

in.-lb. 















(14, 

(15 ) 

(16) 

j (17) 

(iS) 

00S 

OOOhl 

' 

3 

14/ 

24; 

36c 

92 

i5( 

231 

1 6< 
10E 
16] 

■ 7S 

11 i 

9c 

) 







32 

38 

45 

14 

2I 

2| 

a 

4 

a 

4 

0.130 
0. 167 
i O. 205 

2830 

4670 

6930 

II II 

4 

4 h 

5 

S07 

58 S 

768 

32( 

37* 

494 

22 e 
262 
34; 

i6( 

192 

25 

125 

14/ 

192 

IOC 

n( 

i 52 

8i 

9 1 
12 ; 

102 





51 
58 
64 

3l 

3^ 

4 

a 

4 

1 

1 

0.242 
0.260 
0.298 

975 o 
11320 
14780 

O 

10 § 

M 

O 

6 

7 

8 

1201 
x 729 
23S3 

772 

ill] 

i 5 is 

53d 

77i 

io5c 

39; 

565 

77c 

30c 

432 

588 

238 

342 

471 

192 
27 e 
37d 

15s 
225 
312 

134 

193 

262 

113 

163 

222 

143 

195 

123 

167 

77 

90 

103 

5 

6 

7 

1 

1 

1 

0.372 

0.446 

0.521 

23100 

33260 

45270 

II II 

St P, 


3081 

3898 

1971 

2495 

1365 

1733 

loot 

1273 

77c 

975 

608 

77c 

495 

62/ 

407 
515 

342 

433 

292 

369 

25 I 
318 

219 

277 

116 
128 

8 

9 

1 

1 

0.595 

0.670 

59140 

74840 

O 

O 

O 0 
tT 0 

M VO 

2* 

3 

3* 

195 
! 322 

480 

125 

207 

308 

87 

143 

214 

64 

io5 

i 57 

8c 
12 c 

95 







32 

38 

45 

li 

2i 

2! 

} 

2 

a 

4 

0. 176 
0.227 
0.277 

3760 

6190 

9230 

II II 

4 

4* 

5 

675 

784 

1023 

434 

S03 

657 

3°i 

349 

457 

221 

256 

334 

169 

196 

256 

134 
15 5 
203 

108 

125 

163 

104 

136 

114 

96 



51 
58 
64 

3l 

3* 

4 

a 

4 

1 

1 

0. 328 

0.353 

0.403 

12990 

i 5 o 7 o 

19680 

00 

0 

in 9 

M O 

1 || 

6 

7 

8 

1S99 

2303 

3134 

1027 

1479 

2013 

713 

1027 

1398 

523 

753 

1024 

400 
5 7 5 
783 

3i7 
456 
621 

255 
367 
5 00 

212 

3 o 5 

4i7 

' 178 
257 
349 

i5o 

217 

295 

132 

190 

259 

114 

163 

223 

77 

90 

103 

5 

6 

7 

1 

1 

1 

0.5 o 4 
0.6o5 
0. 706 

30750 

44280 

60270 

•I ll 

£ 0, 

9 

10 

4101 
5191 

2625 

332i 

1823 

2307 

1339 

1694 

1025 

1298 

810 

1025 

656 

830 

542 

686 

456 

577 

3 88 
491 

335 

424 

292 

369 

116 
128 

8 

9 

1 

1 

0.806 
0.907 

78720 

99630 

0 

0 

0 0 
■'t 0 

M I'¬ 
ll II 

2$ 

3 

3* 

246 

407 

604 

158 
261 
388 

110 
181 
269 

80 

133 

197 

102 
151 

81 

120 

96 






32 

38: 

4 5 

1? I 
2 i 
2! j 

a 

4 

1 

a 

4 

0.225 
0.289 
0. 353 

4730 

7830 

11620 

ll H 

•0 V 

|> 

4 

4* 

5 

85o 

986 

1293 

546 

633 

827 

379 

440 

574 

278 

322 

421 

2 12 
246 
322 

168 

19S 

255 

136 
x 5 7 
205 

113 

131 

171 

95 

IIC 

143 

93 

121 

106 


5 1 
58 
64 

3l ; 
3i 

4 

a 

4 

1 

1 

0.417 

0.449 

0. 514 

16350 

18960 

24770 

0 

w 

m 9 

M 0 

II II 

c P. 

6 

7 

8 

2012 

2898 

3945 

1292 

1861 

2334 

898 
1293 
1760 

658 

947 

1289 

5 o 3 

724 

986 

399 

574 

781 

321 

462 

629 

267 

384 

523 

224 

323 

440 

189 

273 

372 

166 

239 

326 

143 
2 0(, 
28l 

77! 

90 

103: 

5 

6 

7 

1 

1 

1 

0. 642 
0.770 
0. 899 

38700 

55730 

7586o 

9 

10 

5 161 
6534 

3303 

4181 

2294 

2904 

i685 

2133 

1290 

1633 

1019 

1290 

826 

1045 

682 

864 

573 

726 

489 

618 

421 

533 

367. 

464 1 

116 
128 

8 

9 

I 

I 

1.027 

1. 156 

99080 

125400 

00 S 

00091 

2 } 

3 

3i 

137 

226 

335 

87 

145 

2l5 

IOI 

149 

74 

109 

84 

66 







32 

38 

45 

14 

A 

2 ! 

a 

4 

a 

4 

i 

0 . io5 

0 . 135 

0 . i65 

2620 

434° 

6440 

11 II 

60 O 

4 

4* 

5 

47i 

546 

713 

303 
35 1 

4 58 

210 

244 

3x8 

i 54 

179 

233 

118 
i37 
178 

93 

108 

141 

75 

87 

114 

72 

95 

61 

80 




5 1 
58 

64 

3i 

3* 

4 

a 

4 

1 

1 

0. 195 ! 
0.210 

0. 240 

9060 
io510 
13720 

IT) 

O 

in 9 

H O 

i 1 

e p. 

6 

7 

8 

j - 

1115 
i6o5 
2186 

716 

1031 

1404 

498 

716 

975. 

364 

5 2 5: 

7i5 

279 

401 
5 4 6, 

221 

3i8 

433 

178 

256 

349 

148 

213 

290 

124 
179 
244 

io5 
i5 1 
206 

92 

133 
181 

114 

15 5 

77! 

90 

103 

5 

6 

7 

1 

• 1 

1 

0. 300 

0.360 | 
0.420 j 

21450 

30S80 

42040 

9 

10 

2860 

3619 

1831 

2317 

1271 

1609 

934 

1182 

715 
9 o 5 

565 

7x5 

457 

579 

378 

479 

318 

402 

271 

343 

233 

295 

201 

25 7 

116 
128; 

8 

9 

I 

I 

0.480 j 
0.540 

54910 

69500 

16000 

600 

2i 

3 

3} 

183 

303 

45 o 

117 

195 

289 

82 

135 

201 

99 

I47| 

112 

89 

72 






32 

38 

45 

1 ? 

2 1 

2| 

2 

2 

2 

0. 141 

0.181 
0.221 

3520 

.S830 

865o 

II II 

CO 

M—. 

< 

r-. 

4 

4* 

5 

632 

734 

958 

406 

47i 

6i5 

282 

327 

427 

207 

240 | 

313 

i58 

183 

239 

125 

145 

190 

IOI 

"7 

i 53 

84 

97 

127 

70 

82 

107 

90 

79 


51 
58 
64 

3i 

3i 

4 

3 

1 

1 

0.261 

0.281 

0. 322 

12160 

14110 
1S430 

vO 

O 

in 9 

M O 

II 11 

6 

7 

8 

1497 

21 56 
2935 

962 

1385 

i885 

668 

962 

1309 

489 

7o5! 

959 

374 

539 

734 

297 

427 

58i 

239^ 

344 

468 

199 

286 

389 

167 

240 

327 

141 

203 

277 

124 

178 

243 

106 

i 53 

209 

77 

90 

103 

5 

6 

7 j 

1 

1 

1 

0.402 
0.482 

0 . 563 

28800 

41470 

56450 

II II 

c a 

9 

10 

3840 

4860 

2458 

3111 

1707 

2160 

1 

1254 

i 587 

960 
1215 

759 

960 

614 

778 

5o8 

64?/ 

42" 

54 o 

364 

460! 

313 

397 

27 3 
346 

116 

12 8 j 

8 

9 j 

1 

1 

0.643 

0 . 724 

73740 

93320 
















































































































































TABLE 5 - Continued 


513 


o 

J 3 


-I* 

ej « 

o 

H 

(*) 

in. 


Total safe load ( w ) per square foot including weight of slab, 
l or safe live load deduct weight of slab column (i5) 
(See important footnotes.) 


Span in feet. ( l ) 


U 

<D 

a 

JO . 
c 3 -*-j 

"I 

« b 

S 

ho 5 . 
53 S3 


ID 

s 

to 

o 


a 

a> 

Q 

id ) 


£ 

_o 

4 ! 

^>-i 

nj 

a ai 

0) 

Q 

(e) 


1 a) 

4) g 
to O 


ci.Q 

C_2 . 

.« to 4J 

cS T 3 
u 
u 

83 a o 

g.2 § 
GO 


re 


c-g 

a> 
0 ) 
O 


£ 

o 

£ 


o 

c 

Cl 


sS 
02 

See p. 
753 

(M) 



4 

5 

6 

7 

8 

9 

1 0 

I I 

12 

13 

M 

iS 

lb. 

in. 

in. 

sq. in. 

in. lb. 


2 h 

206 



67 

52 

61 







32 

1? 

2 . 

0.162 

3952 


3 

340 

2l8 

151 

hi 

85 

54 






38 

2$- 

2 

0.208 

6536 

0 / 

0 

34 

509 

326 

226 

166 

127 

IOI 


67 





45 

2 3 
z 4 

2 

4 

0.254 

9770 

0 in 

►H VO 

4 

7 ii 

455 

3i6 

232 

178 

140 

114 

94 

79 

67 



51 

3 1 

3 

0.300 

13650 

II II 

44 

824 

528 

356 

269 

206 

163 

132 

109 

92 

78 

67 


58 

3 h 

1 

0323 

15830 

to w 

5 

1077 

690 

479 

352 

269 

213 

172 

142 

120 

102 

88 

77 

64 

4 

1 

o. 37 o 

20680 


6 

1683 

1077 

748 

550 

421 

332 

269 

223 

187 

159 

137 

120 

77 

5 

1 

0.462 

32310 

in 0 

7 

2423 

I 55 i 

1077 

791 

606 

479 

388 

320 

269 

229 

198 

172 

90 

6 

1 

0-554 

46520 

M O 

II II 

c a 

8 

3297 

2111 

1466 

1077 

824 

651 

528 

436 

366 

312 

269 

234 

103 

7 

1 

0.647 

63320 

9 

4308 

2758 

1915 

I 4 2 7 

1077 

851 

689 

570 

479 

408 

352 

306 

116 

8 

1 

0-739 

82720 


IO 

5454 

349 i 

2424 

1781 

1366 

1077 

873 

721 

606 

516 

445 

388 

128 

9 

1 

0.832 

104700 


2 4 

231 

148 

103 

75 









32 

if 

a 

1 

0. 183 

4440 


3 

382 

2 15 

170 

125 

95 

76 

61 






38 

2 f 

3 

4 

0. 235 

7340 

0 

0 

34 

567 

304 

253 

i85 

142 

112 

90 

75 

63 




45 

2 f 

a 

4 

0. 287 

10900 

O O 
vO O 

4 

797 

5 I 2 

356 

261 

199 

1 58 

127 

106 

89 

75 



5 1 

3 i 

3 

'4 

0. 339 

15330 

II II 

. «c O 

44 

925 

594 

4 i 3 

302 

231 

183 

148 

123 

103 

87 



58 

3 i 

1 

0 .365 

17:90 

5 

1209 

776 

539 

395 

372 

239 

193 

160 

135 

114 

IOO 


64 

4 

1 

0.418 

23230 

I> 

00 

6 

1887 

12 12 

842 

617 

472 

374 

301 

25 o 

210 

178 

1 56 

i 34 

77 

5 

1 

0.522 

36300 

0 

0 

7 

2719 

1746 

1213 

889 

679 

538 

434 

361 

303 

256 

2 2 5 

193 

90 

6 

1 

0.626 

52280 

10 • 
w 0 

8 

3699 

2390 

i 65 1 

I 209 

925 

732 

590 

491 

4 i 3 

349 

306 

263 

103 

7 

1 

0. 73 i 

7ii5o 

II II 

s; a 

9 

4840 

3098 

2 I 52 

i 58 i 

1210 

956 

774 

640 

538 

458 

395 

344 

I l6 

8 

1 

0. 835 

92940 


. IO 

6126 

3921 

2723 

2000 

1531 

12 10 

980 

810 

681 

58 o 

5 oo 

436 

128 

9 

1 

O. 940 

117600 


2 4 

118 

76 

53 










32 

if 

a 

4 

0. 071 

2270 


3 

195 

126 

87 

64 









38 

2 4 

a 

4 

O . 022 

376 o 

0 

0 

34 

290 

186 

129 

95 

72 








4 5 

2 f 

3 

4 

0.112 

5580 

O O 

O O 
<N IO 

II II 

4 

408 

262 

182 

133 

102 

81 







5 1 

3 4 

a 

4 

0.133 

785 o 

44 

474 

304 

211 

1 55 

118 

94 

76 






58 

3I 

1 

0.143 

9110 

II II 

00 

5 

619 

398 

276 

202 

i 55 

122 

99 

82 





64 

4 

1 

0.163 

11900 


6 

967 

621 

43 i 

316 

242 

192 

i 54 

128 

108 

91 

80 


77 

5 

1 

0.204 

18600 

0 

7 

1392 

894 

621 

4 55 

348 

286 

222 

i 85 

1 55 

131 

1 15 

99 

90 

6 

1 

0.245 

26780 

\r> 0 

M 6 

8 

1895 

1217 

846 

619 

474 

375 

302 

257 

211 

179 

i5? 

135 

103 

7 

1 

0.286 

36450 

II 

^ a 

9 

2480 

1587 

1102 

810 

620 

490 

397 

328 

276 

235 

202 

176 

I l6 

8 

1 

0.326 

47610 


10 

3139 

2009 

1395 

1025 

785 

620 

502 

4 i 5 

349 

297 

256 

223 

128 

9 

1 

0.367 

60260 


24 

161 

103 

72 

53 









32 

if 

3 

4 

0.099 

3100 


3 

267 

171 

119 

87 

67 








38 

2f 

a 

4 

0.127 

5 1 3 ° 

0 

0 

34 

396 

254 

177 

129 

99 

78 







4 5 

2 f 

3 

4 

0. 1 5 5 

7610 

= 200 

= 600 

4 

556 

357 

248 

182 

139 

no 

89 






5 1 

3 i 

f 

0.183 

10700 

44 

646 

41 5 

288 

2 I I 

l6l 

128 

103 

86 





58 

3 * 

1 

0. 197 

12420 

•5 O 

5 

844 

542 

376 

276 

2 I I 

167 

135 

I I 2 

94 

79 


4 

64 

4 

1 

0.226 

16220 

b* 

6 

1318 

846 

588 

431 

329 

261 

2 10 

175 

147 

124 

109 

94 

77 

5 

1 

0.282 

2535 o 

0 

7 

1898 

1219 

847 

620 

474 

376 

303 

252 

212 

179 

i 5 7 

133 

90 

6 

1 

0.338 

365oo 

10 . 

M O 

8 

2584 

i 659 

I I 52 

844 

646 

572 

412 

343 

288 

243 

214 

184 

103 

7 

1 

0.395 

49680 

n 11 

g a 

9 

3381 

2164 

l5o2 

1104 

8 4 5 

668 

541 

447 

376 

320 

276 

240 

116 

8 

1 

• 

0.451 

64900 


IO 

4279 

2738 

1901 

1397 

1070 

845 

684 

566 

475 

405 

349 

304 

128 

9 

1 

0. 5 o 8 

82140 


24 

202 

130 

90 

66 









32 

if 

3 

4 

0.126 

3890 


3 

334 

2 l 5 

149 

109 

83 








38 

2i 

3 

4 

0.162 

6430 

0 

0 

34 

497 

319 

221 

162 

124 

98 







45 

2 f 

f 

0. 198 

955 o 

0 0 

0 0 

M b- 
II II 

4 

44 

698 

810 

449 

520 

311 

361 

228 

265 

175 

202 

138 

160 

III 

129 

93 

107 

90 




5 1 
58 

3 f 

32 

a 

4 

1 

0. 234 
0.252 

13430 

i 558 o 

II II 

00 O 

5 

io 58 

679 

472 

346 

264 

210 

169 

140 

118 

100 

87 


64 

4 

1 

O. 288 

20350 

0 

vO 

6 

i 653 

1062 

737 

540 

413 

327 

264 

219 

184 

1 56 

137 

117 

77 

5 

1 

O.360 

31800 

0 

7 

238? 

1530 

1062 

778 

5 9 5 

472 

380 

316 

266 

224 

197 169 

90 

6 

I 

0.432 

45790 

in °. 

M O 

8 

3240 

2082 

1445 

io59 

810 

642 

5 1 7 

430 

361 

305 

268 

231 

103 

7 

1 

0. 5 04 

62330 

II II 

e a 

9 

4241 

27 i 5 

1 885 

1385 

1060 

838 

678 

56 i 

47 i 

402 

346 ! 302 

116 

8 

1 

0.576 

j 81420 

IO 

5368 

3435 

2386 

17S3 

1342 

1 060 

85 9 

710 

596 

5 o 8 

438 

1 382 

128 

9 

1 

0.648 

103030 


1 

) 


Rules, i. 

2. 

3 * 

4* 


For load for any width of slab multiply by width in feel. 

For area of cross-section of steel for any width of slab multiply column (18) by width in 
f C0 t. 

Total loads for other spans (0 and same depth of steel are inversely proportional to 
the squares of the spans. . 

Total loads for other depths of steel (d) and same span are proportional to the squares 

of the depths of steel. 


w 

Cfi 

p 


THESE ORDINARILY 























































































































Ratio of cross-section steel 
to beam above steel. 


514 

TABLE 6. USE FOR REVIEWING DESIGNS. IF FULLY CONTINUOUS 

ADD 20% TO LOADS. 


Safe Loads per Square Foot and Reinforcement for Slabs. Proportions 1:2:4. 

(See p. 508). 


Based on 

M = 

wP 

id 

For supported ends, | 

( wP 

, M ~T 

0 * O 

II II 

0 0 

•-1 1 

A A 

650 

1600 

n = 15 

For fully continuous. | 

/ wP 




For square slabs, | 

( wP 

( M = 20 


, deduct 20% from loads 
, add 20% to loads 
, multiply loads by 2. 


^ Ratio of cross-section steel 
'"i to beam above steel. 

5 ”? Total depth of slab. 

Total safe load ( w ) per square foot including weight of slab. 

For safe live load deduct weight of slab in column ( 15 ). 

(See important footnotes.) 

— Weight of slab per square 

| ? foot. 

S’S Depth to steel. 

5 ^ Depth below steel. 

4 

5 

6 

7 

Span in feet (/.) 

8 9 10 

11 

I 2 

13 

14 

1 5 




I 

i 











(i 5 ) 

(16) 

(17) 



3 

95 

60 

42 










38 


a 

4 



4 

198] 

125 

88 

64 

49 

39 







5 x 

34 

a 

4 



5 

300 

190 

133 

97 

74 

59 

48 , 






64 

4 

1 


6 

469I 

297 

207 

i 5 1 

116 

92 

74 1 






77 

5 

1 



7 

675 

428 

298 

218 

167 

132 

107 






90 

6 

1 



8 

919 

582 

406 

296 

227 

180 

146 

1 20 





103 

7 

1 



9 

I 201 

760 

531 

387 

296 

235 

190 

i 57 





I l6 

8 

1 



10 

1 5 19 

962 

671 

388 

375 

298 

241 

199 

167 




128 

9 

1 



3 

i 85 

1x7 

82 

60 

46 

36 

29 





. 

38 

2 4 

2 



4 

385 

244 

170 

124 

95 

76 

61 

5 o 





5 1 

34 

a 

4 



5 

§84 

37 o 

258 

188 

144 

114 

92 

77 

64 




64 

4 

1 


6 

913 

578 

403 

294 

225 

179 

144 

120 

100 




77 

5 

1 


7 

I 3 M 

832 

58 i 

423 

324 

257 

208 

172 

144 




90 

6 

1 



8 

1788 

ii 33 

790 

576 

441 

35 o 

283 

234 

196 

167 

145 

126 

103 

7 

1 



9 

2336 

1479 

1032 

752 

5 76 

4 58 

370 

306 

257 

219 

189 

164 

I l6 

8 

1 



10 

2957 

1873 

1307 

95-2 

730 

579 

468 

387 

325 

277 

239 

208 

128 

9 

1 



3 

272 

172 

120 

87 

67 

5 2 

43 

36 





38 

2^ 

i 



4 

567 

359 

25 o 

183 

140 

hi 

90 

74 

62 




5 1 

34 

1 



5 

858 

544 

379 

276 

2 12 

168 

136 

11 2 

94 




64 

4 

1 

c %. nnfi 

6 

1342 

85 o 

593 

432 

331 

263 

212 

176 

147 




77 

5 

1 



7 

1932 

1223 

854 

622 

477 

378 

306 

253 

212 




90 

6 

1 



8 

2630 

i 665 

1162 

847 

649 

515 

416 

345 

289 

246 

213 

i 85 

103 

7 

X 



9 

3435 

2175 

i 5 18 

1106 

848 

673 

544 

45 o 

377 

321 

278 

242 

116 

8 

I 



10 

4348 

2753 

1921 

1400 

1073 

852 

688 

570 

478 

407 

35 1 

306 

128 

9 

I 



3 

348 

220 

i 53 

112 

86 

68 

55 

46 





38 

24 

i 



4 

726 

460 

321 

234 

179 

142 

1 15 

95 

80 




51 

3l 

i 



5 

I X OO 

697 

486 

354 

271 

21 5 

174 

144 

121 




64 

4 

I 

0.008 

6 

1719 

108S 

760 

553 

424 

337 

272 

225 

189 




77 

5 

1 



7 

2475 

1 567 

1094 

797 611 

4 85 

39 5 

324 

272 

231 

20c 


90 

6 

1 



8 

3369 

2134 

1489 

io 85 

831 

660 

53 ; 

441 

370 

3 i 5 

272 

237 

103 

7 

1 



9 

4401 

2787 

1945 

I4i7 ( 1086 

862 

697! 577 

483 

412 

356 

310 

116 

8 

1 



1 c 

5570 

3327 

2461 

1793 1374 

1091 

882 73c 

612 

521 

45c 

392 

128 

9 

1 



3 

1 374 

237 

i 65 

120I 92 

75 

59 4 S 





38 

2 4 




4 

1 78 i 

494 

345 

25 i 19; 

1 5 ; 

124 102 

8d 




51 

3 i 

i 



5 

! Il82 

749 

5 22 

38] 

[ 292 

23: 

187 1 5 5 

13c 

> 



6 A 

4 

1 



t 

>i 1847 

117c 

8id 

59. 

456 

36: 

292 242 

20; 

175 

M< 

) 

7 * 

5 

1 

0.010 

l 

n 2660 1684 

1175 

8 5 < 

5 656 

5 2 

421 34 * 

$ 29: 

»| 24s 

21 

> 18* 

9 c 

) 6 

1 



1 O 3618 2 29 2 

I 

1 59 S 

116 

89: 

7 oc 

573 47 -: 

1 39 ’ 

1 33 S 

29 

2 25 ! 

10. 

} 7 

1 



I 9 4727 299; 

208? 

) 162 

2 I i6t 

92 < 

) 748' 61c 

> 5 it 

5 44 : 

38 

2 33 . 

5 x i< 

5 8 

1 



l 10, 5986 379c 

2645 192 

7 I 47 ‘ 

11 7 - 

2 948 78: 

4 65 

7 56 c 

1 

5 48 

4 42 

1 2 

5 9 

I 


0.120 
o. 144 
o. 168 


o. 192 
0.216 

o. 108 
o. i 56 
o. 192 

o. 240 
o. 288 
0.336 

0.384 

0.432 

0.162 
o. 234 
o. 288 

o. 360 
0.432 
o. 5 04 

0.576 
o. 648 

0.216 
o. 312 
0.384 

o. 480 
0.576 
o. 672 

o. 768 
0.864 

0.270 

0.390 

0.480 


o. 600 
0.720 
o. 840 

o. 960 
1.080 


o 





m 


See 
p. 753 
(M) 

in. lb. 


(19) 

1800 

3760 

5702 

8910 
12830 
17460 

22810 

28870 

35 io 
7324 
11100 

17340 

24970 

3398o 

44380 

56 i 8 o 

5 160 
10770 
16310 

25490 

36700 

49960 

65200 

82600 

6610 

13790 

20900 

32660 

47020 

64000 

83600 

io 58 oo 

7100 

14820 

2246.0 

33090 

5 o 52 o 

68750 

89800 
113700 


* Percentages of steel are values in this column multiplied by 100. 

Compression in concrete under tabular loads with the different percentages of steel: 

Ratio of steel. 0.002 0.004 0.006 0.008 0.010 

Compression in concrete, lb. per sq. in. 370 5 oo 610 65 o 65 o 

Role*, x. For load for any width of slab multiply by width in feet. 

2 ‘ £. or ^ r , ea j* cross-section of steel for any width of slab multiply column (18) by width in feet. 
3. Total loads for other spans (1) and same depth of steel are inversely proportional to the 
squares of the spans. 

4 * 4 e ptb*of Steel (d) and same span are proportional to the squares of the 







































































































5 I 5 

TABLE 7. CINDER CONCRETE SLABS 

A ratio of elasticity of n = 33 is used in the table below, although it is 
permissible to design with a ratio of 15 in very conservative practice. 

The loads for slabs with a ratio of steel of 0.002 are limited by the work¬ 
ing strength of the steel, and the values with the higher ratios by the work¬ 
ing strength of the cinder concrete. 

It is noticeable that less steel can be used economically for a given thick¬ 
ness of slab than with broken stone or gravel concrete, because the strength 
of the slab is more apt to be limited by the strength of the cinder concrete 
than by the strength of the steel. 


Safe Loading and Reinforcement for CINDER CONCRETE SLABS One Foot in Width. 
Proportions 1 : 2 % : 5 . Mild Steel. (See p. 5 1 5 ). 

72 

Based on M = f c = or < 225, = or < 14 000, ?i = 3o 


”3 










* 




v • 


Total safe load ( w l ) per square foot including 



13 

0 ) 

G 0 ) 

ii aJ 


6 


weight of slab 







fl 0 

0 ) rt 

§ * L 

G 

For safe 

live load deduct weight 

of slab in 

a 

<v 

0 > 

CO 


a g 

■Jg r 

a 4 


column 

( 12 ). 




"2 o' 

CG 

£ 

s ° 

? cn 

gj !- 

0 c 3 

(See important 

foot-notes.) 



.5 8 

c n d- 

O 

JO 

13 

G 0 
o'* - 

.5 v 

<D £ 

& * 

G ” 








O 

,G 

43 

cj § 

U -, 

oB 

o-° 

30 

03 


4 

Span in 

5 6 

Feet (Z) 

7 8 

9 

10 

x) fl 

43 3 

• 3 - 

£ 

a 

<D 

Q 

(d) 

£ 

a 

0 

O 

(e) 

3 0 

* 3 X 5 

rt _G 

^ (fl 

+■> © 

CQ 

CO 0 

(See p. 
753 .) 

(Mr) 

3 )* 

in. 








ib. 

in. 

in. 

1 

sq.in. 

in. lb. 










(10) 

(11) 

( X 2) 

(13) 

(14) 


2 i 

48 

31 

35 





24 

ii 

2 1 

4 | 

O. 042 

920 


3 

70 

5 i 

26 




29 

2 * 

5 

4 

0. o 54 

1520 


3 i 

119 

76 

53 

39 




34 

2* 

3 

4 

0.066 

2280 


4 

166 

xo6 

74 

5 4 

41 



39 

34 

3 

4 | 

0.078 

3180 

0.002 

4 i 

192 

123 

85 

63 

48 



43 

3} 

I 

0.084 

3690 


5 

25 1 

161 

112 

82 

63 

5 o 


48 

4 

I 

0.096 

4S20 


6 

392 

25 1 

i 74 

128 

98 

78 

63 

58 

5 

I 

0.120 

7530 


7 

565 

361 

25 I 

184 

141 

112 

90 

68 

6 

I 

0. 144 

10840 


l 8 

768 

492 

341 

35 1 

192 

i 52 

123 

77 

7 

I 

0.168 

14750 


2 \ 

76 

48 

34 

25 




24 

t2 

1 4 

3 

4 ' 

0.084 

1460 


3 

125 

80 

56 

41 

31 



29 

2* 

2 

4 

0.108 

2400 


34 

187 

120 

83 

61 

47 

37 


34 

2! 

3 

4 

0.132 

3390 


4 

261 

167 

1x6 

85 

65 

5 a 

42 

39 

3 V 

3 

0. i 56 

5020 

0.004 

44 

3°3 

194 

135 

99 

76 

60 

48 

43 


1 

0. 168 

5820 

5 

396 

253 

176 

129 

99 

78 

63 

48 

4 

I 

0. 192 

7600 


6 

619 

396 

275 

202 

1 5 5 

122 

99 

58 

5 

I 

0. 240 

11880 


7 

891 

570 

396 

291 

223 

176 

143 

68 

6 

I 

0. 288 

17110 


l 8 

1213 

776 

539 

396 

303 

240 

194 

77 

7 

1 

0. 336 

23290 


2 \ 

86 

55 

38 

28 




24 

if 

3 

4 

0. 126 

1640 


3 

141 

90 

63 

46 

35 



29 

2 \ 

3 

4 

0. 162 

2710 


34 

211 

135 

94 

69 

53 

42 

34 

34 

2 4 

4 

0. 198 

4o5o 


4 

295 

189 

131 

96 

74 

58 

47 

39 

3 f 

f 

0.234 

566 o 

0.006 

> 4J 

342 

219 

152 

112 

85 

68 

55 

43 

3 h 

1 

0.252 

6570 

5 ' 

44 7 

286 

199 

146 

112 

88 

72 

48 

4 

1 

O. 288 

858 o 


6 

698 

447 

310 

228 

175 

138 

I I 2 

58 

5 

I 

O. 360 

13400 


I 7 

too5 

64 3 

447 

328 

25 1 

199 

161 

68 

6 

I 

0.432 

19300 


l 8 

1368 

876 

j 608 

'447 

342 

270 

219 

77 

I 

7 

1 

0 . 5o4 

26270 


* Percentages of steel are values in this column multiplied by ioo. 


Rules, i. For load for any width of slab multiply by width in feet. 

2. For area of cross-section of steel for any width of slab multiply 

column (13) by width in feet. 

3. Total loads for other spans (e) and same depth of steel are inversely 

proportional to the squares of the spans. 

4. Total loads for other depths of steel (d) and same span are propor¬ 

tional to the squares of the depths of steel. 






















































1.5 p p' = P p' = 0.5 p p' = 0.25 p 


TABLE 8. USE FOR BEAMS WITH STEEL IN TOP AND BOTTOM 


Constants for Determining Depth of Beam. Moment of Resistance, and Fiber Stresses for 
Different Percentages of Steel. [See p. 428 .] (See Example on page 470 .) 

Ratio of Elasticity of Steel to Concrete, n = 15 . 


Depth of beam 


Fiber stresses, 


I M ~ _ 

= * /-or 

\bfcCc 


fc = 


M 


Ccb d 2 


> fs = 


I M 

\b f, C, 

C, b d- ■ h 


whichever is greater 

M 

~ C\bd? 


Moment of resistance, M — fc^c & or fa^gb ^ 2 > whichever is less. 

Rule i. To determine Depth of Beam: 

Assume p, ratio of tension steel, and p' ratio compression steel. 

Assume a, ratio depth of steel in compression to depth in tension. 

Locate these values in table and find C c and C s corresponding. 

Substitute values C c and C s in formulas for depth, d (above.) 

Accept the larger value as depth from compressed surface of beam to center tension steel. 
Rule 2 . To determine Fiber Stresses and Moment of Resistance in a given beam: 

Compute p and p' and a. 

Locate these values in table and find required constants. 

Substitute values in formulas above and obtain required stresses or moment of resistance. 
Rule 3 . To determine Depth of Haunch at support of a beam or girder. 

Decide tentatively amount of steel in tension and compression. 

Assume a trial depth of haunch. 

Determine by Rule 2 the fiber stresses. 

If stresses are not as required, assume new depth of haunch and re-compute. 

(See Example 6 , page 470.) 

Rule 4 . To interpolate values of any C when required ratio of p to p' is given in table: 

Example: Given a = 0.15, p = 0.012, p' = 0.008. Then p' — 0.5 p, and interpolating 

in this group between p = 0. 1 , p' = .005 and p = .015, p' = .0075. gives C c = .23 and C s -= 
0.0103, 

Rule 5. To interpolate values of any C when required ratio of p to p' is not given in table. 

Example: Given a = 0.1, p = 0.013, p' = 0.009. Then p' = 0.69 p, which lies between 
groups p' = 0.5 p; and p' — p. 

Find by interpolation in group p' = 0.5 p; for p = 0.013, p' = 0.0065, C c = .24 and C s 
0.0114. 

and in group p' = p; for p = 0.013 and p' = 0.013; C = .29 and G T S = .0115. 

Interpolate between the two above values and find for p = 0.013 and p' = 0.09, C c = 0.26 
and C s = 0.0114. 

p = Ratio Cross Section of Steel in Tension to Concrete above it. 
p'= Ratio Cross Section of Steel in Compression to Concrete. 
k = Ratio Depth of Neutral Axis to Depth of Tension Steel. 

C c , C s , C' s = Constants in formulas above. 


p 

p' 

k | 

C 

c 

^ s 

° 8 

P 

P ' 

k 

CC l 


C ' 

0 s 

».o 5 = Ratio of Depth of Steel 

in Compression 

a =0.1 = Ratio of Depth of Steel in Compres- 


to Depth of Steel in 

Tension. 



sion 

to Depth of Steel in Tension 

0. oo 5 

O .00125 

0. 307 

O. 

i 5 

0.0046 

0.0121 

0. oo 5 

O .00125 

0. 310 

0. i 5 

0.0046 

0.0148 

O. OI 

O .0025 

0. 394 

O. 

20 

0.0088 

0.0154 

O. OI 

0 .0025 

0. 398 

0. 20 

0.0088 

0.0175 

0. oi 5 

0.00375 

0. 45 o 

O. 

24 

0.0130 

0.0179 

0. oi 5 

0.00375 

0.454 

0. 23; 

0. 0129 

0.0199 

0. 02 

0. oo 5 

0. 490 

0. 

27 

O.0172 

0.0199 

0. 02 

0. oo 5 

0. 494 

0. 26 

0.0170 

O. 02 19 

O. 025 

0.00625 

0.52 1 

0. 

30 

0.0214 

0.0218 

O. 025 

0.00625 

0. 526 

O. 291 

0.02 10 

0.0235 

0. 03 

0.0075 

0. 546 

0. 

32 

0.0266 

0.0234 

0. 03 

0.0075 

0. 55 1 

0. 31 

0 .0250 

0.0250 

0. 035 

0.00875 

0. 566 

O. 

34 

0.0298 

O .0250 

0. 035 

0.00875 

0.571 

0. 33 

0.0290 

0.0265 

0. 04 

O. OI 

0. 583 

0. 

36 

0.0342 

0.0265 

0. 04 

0. 01 

0. 589 

0. 35 

0.0330 

0.0280 

0. oo 5 

O .0025 

0. 296 

O. 

16 

0.0046 

0.0131 

0. oo 5 

O .0025 

0. 299 

0. 16 

0.0045 

0. 01 58 

O. OI 

0. oo 5 

0. 373 

O. 

22 

0. 0090 

0.0174 

0. 01 

0. oo 5 

0. 381 

0.21 

0.0088 

0.0192 

0. oi 5 

0.0075 

0. 420 

O. 

28 

0.0134 

O.0210 

0. oi 5 

0.0075 

0. 428 

0. 26 

0.0131 

0.0227 

0. 02 

O. OI 

0. 454 

0. 

32 

0.0178 

O.0240 

0. 02 

0. 01 

0. 462 

0. 30 , 

0.0174 

0. 0256 

O. 025 

O. 0125 

0. 480 

0. 

36 

0.0222 

O.0269 

O. 025 

0.0125 

0. 488 

0. 34 

0. 02I 5 

0.0284 

0. 03 

0. oi 5 

0. 499 

0. 

40 

0.0266 

O.0296 

0. 03 

0. oi 5 

0. 5 o 9 

0. 38 

0. 0258 

0.0312 

0. 035 

0.0175 

0. 5 1 5 

0. 

44 

0.0310 

O. 0323 

0. 035 

0.0175 

0. 524 

0.41 

0.0301 

O .0339 

0. 04 

0. 02 

0. 528 

0. 

48 

0.0355 

O .0350 

0. 04 

0. 02 

0. 539 

0 44 

0 0343 

0 .0356 

O 

O 

O 

Gn 

0. oo 5 

0. 274 

0. 

18 

0.0046 

O .0149 

0. oo 5 

0. oo 5 

0. 284 

0. 17, 

0.0045 

0.0176 

O. OI 

O. OI 

0. 336 

0. 

27 

0.0092 

O.0212 

O. OI 

0. 01 

O. 349 

0. 2 5 

0.0089 

0.0232 

0. oi 5 

0. oi 5 

0. 372 

0. 

35 

0.0138 

O.0266 

0. oi 5 

0. oi 5 

0. 386 

0. 32 

0.0133 

0.0285 

0. 02 

0. 02 

0. 395 

0. 

42 

0.0184 

O.0320 

0. 02 

O. 02 

O. 410 

0. 3 » 

0.0177 

0337 

O. 025 

O. 025 

0.412 

0. 

49 

0.0230 

O .0373 

O. 025 

0. 025 

O. 428 

0. 44 

0.0221 

0.0381 

0. 03 

0. 03 

0. 425 

O. 

56 

0.0275 

O.O423 

0. 03 

0.03 

0. 442 

0. 5 o 

0.0265 

0.0411 

0. 035 

0. 035 

0. 435 

0. 

63 

0.0322 

O .0473 

0. 035 

0. 035 

0.452 

0. 56 

0.0309 

0.0481 

0. 04 

O. 04 

0. 443 

O. 

70 

0.0368 

0.0523 

O. 04 

0. 04 

O. 461 

0. 62 

0.0353 

0.0503 

0. oo 5 

0.0075 

0. 256 

0. 

20 

0.0046 

0.0168 

0. oo 5 

0.0075 

0. 268 

0. 18 

0.0045 

0.0197 

O. OI 

0. oi 5 

0. 305 

0. 

32 

0.0093 

O. 025 1 

0. 01 

0. oi 5 

O. 322 

0. 27 

0.0090 

0.0276 

0 oi 5 

O .0225 

0. 33 i 

O. 

42 

O.0140 

0.0330 

0. 01 5 

0 .0225 

0.350 0.371 

0.0134 

0.0348 

0. 02 

0.03 

0. 349 

0. 

i>2 

0.0186 

0.0404 

0. 02 

0.03 

O. 369 

0. 46 

0.0178 

0.0417 

U"> 

w 

O 

6 

0.037S 

0. 361 

0. 

62 

0.0232 

0.0476 

0.025 

0.0375 

O. 382 

0. 54 

0.0222 

0.0489 

0.03 

0. 045 

0. 369 

0. 

72 

0.0280 

0.o 55 o 

0. 03 

0. 045 

O. 392 

0. 62 

0.0267 

0.0454 

0.035 

O. of >25 

0. 376 

0. 

81 

0.0326 

0.062 5 

0. 035 

0.o 525 

0. 399 

0. 70 

0.0312 

0.0626 

0.04 

0. 06 

0. 381 

0. 

91 

O .0372 

0.0699 

0. 04 

0. 06 

0. 4 o 5 

0. 78 

0.0357 

0.0651 





















































1.5 p p' = P p' = 0.5p p' = 0.25 p ® p'= l.o p p' = p p' = 0.5 p p' = 0.25 p 


TABLE 8.—Continued. 

o a ^.° £ ross Section of Steel in Tension to Concrete above it. 
? — ™ a I-° £ ross Section of Steel in Compression to Concrete. 

* “ Ra £,° Dep * h of Neut f aI Axis ^ Depth of Tension Steel, 
t'c Cg. C s — Constants in formulas above. 


517 


o. 01 


o. 02 


o. 03 
o. 035 ; 
o. 04 

o. oo 5 
o. 01 
o. oi 5 

O. 02 

O. 025 
o. 03 
O. 035 
o. 04 

o. oo 5 
o. 01 
o. oi 5 

O. 02 

O. 025 
O. 03 
O. 035 
o. 04 

o. oo 5 
o. 01 
o. oi 5 
o. 02 

O. 025 
O. 03 
O. 035 
o. 04 


p' 

k 

C c \ 

! 

c s 

C i 

0 s 

P 

V ' 

k 

C e 

( s 

nr 

0 s 

atio of Depth of Steel in Compression 
Depth of Steel in Tension. 

o^=0.2 = Ratio of Depth of Steel in Compres¬ 
sion to Depth of Steel in Tension. 

O.00X25 

0.312 

0. i5 

0.0044 

0. 0189 

0. oo5 

0.00125 

0. 313 

0. 14 

0.0044 

0.0272 

O.0025 

0. 402 

0. 19 

0.0086 

0.0206 

0. 01 

0.0025 

0. 404 

0. 18 

0.0086 

0.0243 

0.00375 

0. 458 

0. 23 

0.0127 

0. 0223 

0. oi5 

0.00375 

0. 460 

0.22 

0.0x26 

0.0202 

0. oo5 

0. 499 

O. 25 

O.Ol67 

0.0240 

0. 02 

0. oo5 

0. 503 

O. 24 

0.oi65 

0.0272 

0.00625 

0. 530 

0. 28 

0.0207 

0. 0257 

O. 025 

0.00625 

0. 535 

0. 27 

0. 0204 1 

0.0284 

0.0075 

o.555 

0. 30 

0.0247 

0. 0273 

0. 03 

0.0075 

0. 56o 

0. 29 

0.0243 

0.0297 

0.00875 

0. 577 

0. 32 

0.02S6 

0. 0285 

0. 035 

0.00875 

0. 582 

0. 31 

0.0282 

0.0309 

O. OIO 

0. 595 

0. 33 

O.0326 

0. 0297 

0. 04 

0. OIO 

0. 600 

O. 32 

0.0320 

0.0320 

0.0025 

0. 304 

0. i5 

0.0044 

O.0202 

0. oo5 

0.0025 

0. 309 

0. 15 

0.OC44 

0.0279 

0. oo5 

0. 386 

O 21 

0.0087 

0.0226 

0. 01 

0. oo5 

0. 392 

0. 20 

0.0086 

0.0272 

0.0075 

0. 435 

0 5 

0.0128 

0.0254 

0. oi5 

0.0075 

0. 442 

0. 24 

0.0126 

0.0291 

0. 01 

0.471 

0. i. 

0.0169 

0.0279 

0. 02 

0. 01 

0.479 

0. 27 

0.ox66 

O. OJ I 2 

0.0125 

0. 496 

0. 32 

0.0210 

0.0306 

0. 025 

0.0125 

0. 506 

0. 30 

0.0206 

0.0331 

0. oi5 

0. 518 

0. 35 

0.025I 

0.0328 

0.03 

0. oi5 

0. 527 

0. 31 

0.0245 

0.0354 

0.0175 

0. 535 

0. 38 

0.0292 

0.0353 

0. 035 

0.0175 

0. 544 

0. 36 

0.0284 

0.0378 

0. 02 

0. 549 

0.41 

0.0333 

0.0376 

0. 04 

0. 02 

0. 559 

0. 38 

0.0323 

0.0397 

0. oo5 

0. 292 

0. 16 

0.0044 

O.0222 

0. oo5 

0. oo5 

0. 299 

0.16 

O.0044 

0.0313 

0. 01 

0. 360 

0.23 0.0087 

0.0265 

0. 01 

0. ox 

0. 371 

0. 22 

0.0086 

0.0314 

0. oi5 

0. 398 

0.29 0. 0129 

0.0313 

0. oi5 

0. oi5 

0. 411 

0. 27 

0.0126 

0.0352 

0. 02 

0. 425 0. 35 0. 0x71 

0.0357 

0. 02 

0. 02 

0. 439 

0. 32 

0.0166 

0.0390 

O. 025 

0. 444 

0. 40 

0.0213 

0.0402 

0. 025 

O. 025 

0. 460 

0. 36 

0.0206 

0.0428 

0. 03 

0.458 0.45 

0.0255 

0.0446 

0. 03 

0. 03 

0. 475 

0. 41 

0.0246 

0.0470 

0. 035 

0. 469 

1 0. 5o 0. 0297 

0.0490 

0. 035 

0. 035 

0. 487 

0. 45 

0.0286 

0.o511 

0. 04 

0. 479 

0. 551 0. 0338 

0.o 528 

0. 04 

0. 04 

0.497 

0. 49 

0.0326 

0.o551 

0.0075 

0. 280! 0. 17 0. 0045 

0.0247 

0. oo5 

0.0075 

0. 292 

0. 16 

0.0044 

0.0339 

0. oi5 

0. 338 0. 26 0. 0087 

0.0306 

0. ox 

0. 015 

O. 353 

0. 23 

0.0086 

0.0389 

0.0235 

0-369 0.33 0.0129 

0.0373 

0. oi5 

0.0235 

0. 386 

0. 30 0.0126 

0.0416 

0. 03 

0. 389 

0. 40 

0.0x71 

0.0439 

0. 02 

0. 03 

0. 409 

0. 36 

0.0166 

0.0464 

0.0375 

0. 403 

0.47 0.02X3 

0.o5o5 

O. 025 

0.0375 

0. 424 

0. 42 

0.0206 

0.0531 

0. 045 

0.414 

0. 54 

! 0.0256 

0.o 569 

0. 03 

0. 045 

0.436 

0. 48 

0.0246 

0.0592 

0.o 525 

O. 422 

0.61 0.0298 

0.0635 

0. 035 

0.o 525 

0.444 

0. 54 

0.0286 

0.0653 

0. 06 

0. 429 

0.68 0.0340 

0.0697 

0. 04 

0. 06 

0. 452 

0. 59 

0.0326 

0.0709 


= 0.25 = Ratio of Depth of Steel in Compression 
to Depth of Steel in Tension. 


0. oo 5 

0.00125 

0. 3x6 

0. 15 0.0045 

0.0458 

0. oo5 

0.00125 

0.318 

0. 14 

0. 01 

0.0025 

0. 408 

0.19 0.0086 

0.0320 

0. 01 

0.0025 

0. 411 

0. 18 

0. ox5 

0.00375 

0. 465 

0.22 0.0126 

0.0311 

0. oi5 

0 

0 

0 

00 

-4 

Cn 

0. 468 

0.21 

0. 02 

0. oo5 

0. 5 o 7 

0.24, 0.0164 

0.0315 

0. 02 

0. oo5 

0. 511 

0. 23 

O. 025 

0.00625 

0. 539 

0. 26 0.0202 

0.0321 

O. 025 

0.00625 

0. 544 

0.25 

0.03 

0.0075 

0. 565 

0. 28, 0. 0240 

0.0332 

0. 03 

0.0075 

0.571 

0.27 

0. 035 

0.00875 

0. 588 

0.30 0.0278 

0.0338 

0. 035 

O 

0 

0 

00 

04 

0. 592 

0. 29 

0. 04 

0. OIO 

0. 606 

0.31 0.0316 

0.0349 

0. 04 

0. OIO 

0. 611 

0. 30 

0. oo5 

0.0025 

0. 314 

0. iSj 0. 0045 

0.0476 

0. oo5 

0.0025 

0. 320 

0. i5 

0. ox 

0. oo5 

0. 398 

0. 19 0.oo85 

0.0347 

0. 01 

0. oo5 

0. 404 

0. 19 

0. oi5 

0.0075 

0. 45 o 

0.2 3 0.0125 

0.0342 

0. oi5 

0.0075 

0.456 

0.22 

0. 02 

0. 01 

0. 487 

0. 26 0.0164 

0.0354 

0. 02 

0. ox 

0. 495 

0.25 

r 

0. 025 

0.0125 

0. 514 

0.29 0.0202 

0.0373 

O. 025 

0.0125 

0. 522 

0. 27 

0.03 

0. oi5 

0. 537 

0.32 0.0240 

0.0386 

0. 03 

0. oi5 

0. 546 

0. 29 

0. 035 

0.0175 

o.556 

0.34 0.0278 

0.0404 

0. 035 

LO 

I- 

M 

O 

6 

0.564 

0.31 

. 0. 04 

0. 02 

0. 570 

0.36 090315 

0.0422 

0. 04 

0.02 

0. 58o 

0. 33 

0. 003 

0. oo5 

0. 308 

0. i5 0.0045 

0.o 523 

0. oo5 

0. oo5 

0. 317 

0. 14 

O. OI 

0. 01 

0. 382 

0. 20 0.oo85 

0.0386 

0. 01 

0. 01 

0. 393 

0. 19 

0. oi5 

0. 0x5 

0. 425 

0.25 0.0124 

0.0406 

0. oi5 

0. oi5 

0. 438 0.23 

0. 02 

0. 02 

0. 454 

0.29 0. 0162 

0.0435 

0. 02 

0. 02 

0.468 

0. 27 

0. 025 

0. 025 

0. 475 

0.33 0.0200 

0.0466 

O. 025 

O. 025 

0. 490 

0.31 

0. 03 

0. 03 

0. 491 

0.37 0.0238 0.o5o4 

0. 03 

0. 03 

0. 5 o 7 

0. 34 

0. 035 

0. 035 

0. 504 

0.41 0.0276 0.0542 

0. 035 

0. 035 

0.52 1 

0. 37 

. 0.04 

0. 04 

0. 515 

0.44 0.0314 

0.0277 

0. 04 

0. 04 

0. 532 

0. 40 

0. oo5 

0.0075 

0. 304 

0.15 0. 0044 

vC 

vr > 

Q 

0 

0. oo5 

0.0075 

0. 313 

0. 14 

0. 01 

0. OT 5 

0. 369 

0.22 0. 0084 

0.0446 

0. 01 

0. oi5 

0. 384 

0. 20 

0. 015 

0.0225 

0. 404 

0.27 0.0123 

0.0475 

0. oi5 

0.0225 

0.422 

0.25 

0. 02 

0.03 

0.428 

0.32 0. 0161 

0.o5i9 

0. 02 

0.03 

0.447 

0. 30 

0. 025 

0.0375 

0.444 

0.37 0.0199 

0.0576 

O. 025 

0.0375 

0. 464 

0. 34 

0. 03 

0. 045 

0. 4’7 

0.42 0.0237 

0.0623 

0. 03 

; 0.045 

0. 478 

0. 38 

0.035 

0.o525 

0. 466 

0.47 0.0275 

0.0681 

0. 035 

o.o 525 

0.490 0.42 

. 0. 04 

0. 06 

0. 473 

0.5 2 0. 0313 

0.0732 

0. 04 

0. 06 

0. 497 

0. 40 


a = 0.3 = Ratio of Depth of Steel in Compres¬ 
sion to Depth of Steel in Tension. 


o. 0045 o.1687 
0.0086 0.0455 
0.0125 0.0395 
0.0163 0.0377 

0.0201 0.0375 
0.0238 0.0376 
0.0275 0.0382 
0.0311 0.0389 

o.0045 o.1 5 1 5 
o.oo 85 | 0.0489 
0.0124 1 0.0433 
o.oi62 1 0.0423 


o. oi99 s 
o. 0236; 
o.0272 
o. 03081 

o. 0044^ 
o. 0084; 
o.0123 
o.0160 


o.0429 
o. 0434 
o.0448 
o.0463 

o.1790 
o.o 55 o 
o.0499 
o o 5 o 7 


0.0197! 0.0529 
0.0233 o.o 556 
0.0269 o.o 585 
0.0305 0.06x6 


o.0044 
o.0084 
0.0122 
o.0159 

o.0195 
o.0231 
o.0266 
o.0301 


o.2360 
o.0614 
o. o 574 
o. 0595 

0.0635 
c.0694 
o.0722 
o.0770 


















































































5i8 


USE THIS TABLE ORDINARILY 

TABLE 9 . FLAT SLABS SUPPORTED ON COLUMNS 

Data for Computing Bending Moments. (See p. 485) See Example 14, p. 487. 

Rule. To find bending moment In a flat plate loaded uniformly and supported on columns, 
or other fixed supports: 

Assume radius of support, r 0 , within column head, where bending moment is a maximum 
(see p. 485 ). 

Determine radius of surface assumed to act as a fixed circular plate, r x , (for a floor take this 
as 3- diagonal distance between lines of maximum bending moment plus radius, r 0 , of support) 
(See Fig. 152 a, p. 485 ). 

Radius r, used in table below, is radius to any point where bending moment is required. For 
critical section, r is radius of column head. 

Compute load per linear foot, q , around circumference of plate having radius, r x . (See p. 485 .) 

Take for w the live plus dead load per square foot of slab. 

Then moment causing radial fiber stress at any distance r (see table below), from centre of 
column is: 

M r = wrf C + qr Q C e 

Use Mr to find required depth of slab and amount of steel at edge of column head from 
ordinary beam or slab formulas. (See Example 14 , p. 487 .) 

Note that if w is in lb. per sq. ft., q in lb. per foot of length, and ro in ft., the moment will be 
in ft.-lb. per foot of width or in in.-lb. per inch of width of circumference having a radius r . 

Table below is computed from values on opposite page which should be used direct when 
Poisson’s ratio is other than 0.1. 

Values of constants C 5 and C e based on Poisson's ratio of 0.1. 


fi 


f 

Values of 

'o 



1.0 

i. i 

1.2 

1-3 

1.4 

i -5 

1.6 

i -7 

1.8 

1-9 

2.0 

CONSTANTS C h 

1.4 

0.10 

0.06 

0.03 

O.OI 

O.OI 

0.02 

0.04 

0.06 

0.09 

0.13 

0.17 

1.6 

0.24 

0.16 

0.10 

0.06 

0.03 

0.02 

0.02 

0.02 

0.04 

0.07 

O . IO 

1.8 

0.4S 

0.31 

0.22 

0.14 

0.09 

0.05 

0.03 

0.02 

0.02 

0.03 

0.05 

2.0 

0.72 

0.54 

o .39 

0.28 

0.20 

0.13 

0.08 

0.05 

0.03 

0.02 

0.02 

2.2 

1.08 

0.83 

0.63 

0.48 

0-35 

0.25 

0.18 

0.12 

0.08 

0.05 

0.03 

2.4 

1-52 

i-19 

0-93 

0.72 

O.56 

0.42 

0.31 

0.23 

0.16 

0.11 

0.07 

2.6 

2.04 

1.63 

1.30 

1.03 

O.82 

0.O4 

0.50 

0.38 

0.28 

0.20 

0.14 

2.8 

2.66 

2.15 

1.74 

1.41 

I .14 

0.91 

0.73 

0-57 

0-45 

o -34 

0.25 

3-0 

3.37 

2-75 

2.25 

1.85 

1.52 

1.24 

I .OI 

0.82 

0.66 

0.52 

0.40 

32 

4.17 

3-43 

2.84 

2.36 

I .96 

1.63 

1 -35 

1.11 

0.91 

0.74 

0-59 

3-4 

5.06 

4.19 

3-49 

2-93 

2.46 

2.07 

1-74 

i -45 

1.21 

1.00 

0.82 

3-6 

6.05 

5 04 

4-23 

3-57 

3-0 3 

2-57 

2.18 

1.84 

1.56 

1 .31 

1.09 

3.8 

715 

5-98 

5 05 

4 - 3 ° 

3-67 

3-14 

2.69 

2.30 

1.96 

1.67 

I.42 

4.0 

8.3s 

7.02 

5 96 

5 -oq 

4-37 

3-76 

3-25 

2.80 

2.41 

2.08 

1.78 

4-5 

11.77 

9.98 

8-55 

7.38 

6.41 

5-6o 

4.89 

4.28 

3-75 

3-29 

2.88 

5 -o 

15-99 

13-65 

H -79 

10.27 

9.00 

7-93 

7.01 

6.22 

5-53 

4.91 

4-37 


CONSTANTS C e 


14 

0 • 53 

0.36 

0.22 

0.10 

0.00 

— O.OQ 

—0.17 

—0.24 

—0.30 

—0.36 

—0.42 

1.6 

0.87 

0.66 

0.48 

0-33 

0.21 

O . IO 

0.00 

-0.09 

—0.17 

—0.24 

—0.30 

1.8 

1-25 

0.99 

0.77 

0.60 

0.44 

0-31 

0.20 

0.09 

0.00 

—0.09 

-0.16 

2.0 

1.66 

i -35 

1.10 

0.89 

0.71 

o -55 

0.42 

0 30 

0.19 

0.09 

0.00 

2.2 

2. TO 

1 73 

1.44 

1.19 

0.99 

0.81 

0.65 

0.52 

o -39 

0.28 

0.18 

2-4 

2-55 

2-lj 

1.79 

1-52 

1.28 

1.08 

0.00 

0-75 

0.61 

0.48 

0-37 

2.6 

3 03 

2.56 

2.17 

1.86 

i -59 

i -37 

1.17 

I .oc 

0.84 

0.70 

0.58 

2.8 

3-51 

2.98 

2.56 

2.21 

1.91 

1.66 

1.44 

1-25 

1.08 

0-93 

0.76 

3 -o 

4.02 

3-43 

2.96 

2-57 

2.25 

1.97 

1-73 

1.52 

1-34 

I -17 

1.02 

3-2 

4-54 

3-89 

3 38 

2-95 

2.60 

2.29 

2.03 

1.80 

1.60 

1.42 

1 .25 

3-4 

5-07 

4-36 

3-80 

3-34 

2-95 

2.62 

2.33 

2.08 

1.86 

1.67 

1.49 

3-6 

5.60 

4-83 

4.22 

3-72 

3-30 

2-95 

2.64 

2-37 

2.14 

1.92 

i -73 

3-8 

6.17 

5-34 

4.68 

4.14 

3-69 

3 - 3 i 

2.98 

2.69 

2-43 

2.21 

2.00 

4.0 

6-73 

5-84 

5-13 

4-55 

4.07 

3-66 

3-30 

2.99 

2.72 

2.48 

2.26 

4-5 

8.12 

7.07 

6.23 

5-55 

4.98 

4-50 

4-09 

3-73 

3-41 

3-13 

2.87 

5-0 

9.72 

8.50 

7-54 

6-75 

6.10 

5-55 

5 ■ 08 

4.66 

4-30 

3-98 

3-69 

























































5i8a 

Da,tu lor Determining Bending Moments for Flat Slabs Supported on Columns 

for Various Values of Poisson's Ratio. 

Rule . Proceed as indicated on opposite page, except using sum of moments M2 and M 



f ormulas (54) and (56) (p. 485) for M x and M a for circumferential fiber stresses are not. usually required. 


If r = 

II 

C'J 

V* 

wr 0 2 (0.2 

+ Ci -f- C 2) 

(52) 

and M fr 

= qr 0 


+ C b ) 

(S 3 ) 

Poisson’s 
ra t io 

g 

Ratio 
outer to 
inner 
radius 
fi _ 

r o 

Constants 

in formulas (52) to (57), 

pages 485 and 518a 


For uniformly distributed loading 

For circumferential loading 

Ci 

C 2 

c, 

c 4 

C a 

Cb 

c c 

1 

Q 


1.4 

0.21 

—0.31 

1 

. 21 

0.14 

O 

• 5 7 

— O 

.04 

1-73 

0 61 


1 . 6 

0-35 

—0.30 

I 

• 58 

0 . 29 

O 

.78 

O 

. 10 

1.98 

0.84 


1.8 

0.52 

—0.27 

2 

. OO 

0.48 

I 

. 00 

0 

. 26 

2.23 

1.09 


2.0 

0.74 

— 0.21 

2 

• 47 

0.72 

1 

.24 

O 

• 44 

2-47 

1.36 


2 . 2 

1.00 

—0.11 

2 

.99 

1.01 

I 

.48 

0 

.63 

2.72 

1 . 64 


2.4 

1.31 

0.02 

3 

• 56 

1-35 

1 

.74 

O 

.83 

2-97 

1.93 


2 . 6 

1.67 

0.19 

4 

.18 

i -75 

2 

.01 

1 

.04 

3.21 

2 . 24 

0.075 

2.8 

2.08 

O.4O 

4 

.85 

2 . 21 

2 

• 29 

I 

. 26 

3 46 

2.55 


30 

2-55 

O . 64 

5 

• 56 

2.72 

2 

• 57 

I 

.48 

3 - 7 i 

2.87 


3-2 

3.06 

0-93 

6 

■ 33 

3.30 

2 

.86 

1 

• 72 

3.96 

3-20 


3-4 

3-63 

I . 26 

7 

• 15 

3-93 

3 

• 15 

1 

.96 

4 . 20 

3-53 


3-6 

4-25 

I .64 

8 

.OI 

4 63 

3 

•45 

2 

.21 

4-45 

3-87 


3-8 

4-94 

2.06 

8 

■ 93 

5 - 4 ° 

3 

.76 

2 

• 47 

4.70 

4.22 


4.0 

5-67 

2-53 

9 

.89 

6.23 

4 

.06 

2 

• 72 

495 

4-57 


4-5 

7-77 

3-90 

12 

• 52 

8.58 

4 

.86 

3 

.40 

5-56 

5-48 


5-0 

10.25 

5-59 

15 

• 45 

IT - 37 

5 

• 67 

4 

.09 

6.18 

6.40 


1-4 

0.21 

— 0.31 

I 

.24 

O . 14 

0 

• 55 

—0 

.02 

1.77 

0.61 


1.6 

0-34 

—0.30 

I 

.62 

O . 28 

0 

•75 

O 

12 

2.02 

0.84 


1.8 

o- 5 i 

—0.26 

2 

•05 

0 47 

0 

• 97 

0 

.28 

2 . 28 

1.09 


2.0 

0.72 

—0.19 

2 

• 53 

0.71 

1 

20 

O 

.46 

2-53 

1.36 


2 . 2 

097 

—0.09 

3 

.06 

1.00 

1 

44 

0 

.66 

2 . 78 

1.65 


2.4 

1.27 

0.05 

3 

.64 

1 -34 

1 

69 

0 

86 

3 04 

1.94 


2 . 6 

1 . 62 

0.22 

4 

.28 

i -75 

1 

95 

I 

08 

3-29 

2.25 

0.10 

2 . 8 

2.02 

0.44 

4 

.96 

2 . 20 

2 

.21 

I 

30 

3-54 

2.56 


3-0 

2.47 

0 . 70 

5 

.69 

2.72 

2 

48 

I 

54 

3-80 

2 . 89 


32 

2.97 

I .OO 

6 

.48 

3 • 30 

2 

76 

I 

78 

4-05 

3-22 


3-4 

3.52 

1-34 

7 

•31 

3-94 

3 

05 

2 

02 

4-30 

3-55 


3-6 

4.12 

1-73 

8 

20 

4-65 

3 

33 

2 

27 

4-55 

3 89 


3-8 

4.78 

2.17 

9 

13 

5-42 

3 

63 

2 

54 

4.81 

4-25 

* 

4.0 

5-50 

2.65 

10 

12 

6 . 26 

3 

93 

2 

80 

5 06 

4.60 


4 5 

7.52 

4.05 

12 

80 

8.61 

4 

71 

3 

41 

5.70 

5-53 


5-0 

9-95 

5-84 

15 

80 

11.46 

5 

5 ° 

4 

22 

6-33 

6.47 


1 • 4 

0 . 20 

-0.30 

1 

3 ° 

0.12 

0 

52 

0 

01 

1.85 

0.60 


1 . 6 

0.32 

—0.28 

1 

69 

0.26 

0 

71 

0 

16 

2.12 

0 . 84 


1.8 

0.48 

—0.24 

2 

14 

0.45 

0 

91 

0 

33 

2.38 

1.09 


2.0 

0.67 

—0.16 

2 

65 

0 . 69 

1 

12 

0 

52 

2.65 

1 37 


2 . 2 

0.91 

—0.05 

3 

20 

0.98 

I 

34 

0 

72 

2.91 

165 


2.4 

1 . 20 

O.II 

3 

81 

1.33 

1 

58 

0 

93 

3.17 

i -95 


2.6 

1-52 

0.30 

4 

47 

1-73 

1 

82 

I 

16 

3-44 

2.26 

0.15 

2.8 

1.90 

0.53 

5 - 

18 

2.20 

2 

06 

I 

39 

3-70 

2.58 


30 

2.32 

0.81 

5 

95 

2.72 

2 

32 

1. 

64 

3-97 

2.91 


3-2 

2.78 

1 .13 

6. 

77 

3-31 

2 

58 

I . 

89 

4 23 

3-25 


3-4 

3 - 3 ° 

t • 5 ° 

7 ■ 

65 

395 

2 

84 

2. 

14 

4-50 

3 59 


3-6 

3-87 

1.92 

8. 

57 

4.67 

3 - 

11 

2. 

41 

4.76 

3-94 


3-8 

4.48 

2.38 

9 . 

55 

5-45 

3 - 

38 

2. 

68 

5 03 

4.29 


4.0 

5 16 

2.91 

10. 

58 

6.31 

3 - 

66 

2 

96 

5-29 

4 66 


4-5 

7.06 

4.42 

13 - 

40 

8.72 

4 - 

38 

3 - 

66 

5 96 

5 ■ 57 


5-0 

9-32 

6.30 

I 6 . 

52 

11.60 

5 • 

12 1 

4 - 

42 

6 . 61 

6.53 


Note —All values are plus unless otherwise indicated. 





















































SL'Sb 

TABLE 9a. NUMBER OF STIRRUPS IN UNIFORMLY LOADED BEAM 

lb 

Number of stirrups, N = ~ \ Z ~ (See Example 20 below). 

5 A s C n 

N s = number of stirrups in each end of beam. b = breadth of web of beam in inches. 

jd — distance from center of compression to center of horizontal reinforcement. (See p. 45 °-) 
l — span of beam in feet. v = total shearing unit stress at end of beam in lb. per sq. in. 

»' = allowable shearing unit stress (or diagonal tension) in concrete alone in lb. per sq. in. 

A s = cross-sectional area of vertical stirrup in sq. in. (In a U-stirrup, sum of areas of two legs.) 
f s = allowable unit tensile stress in the stirrup in lb. per sq. in. C n = constant. 


Values of Constant Cn for Finding Number of Stirrups in Each End of Beam. 


V 

f s = 12 000 

f 3 = 14 000 

/ s = 16 000 

/ s =i8 000 


v'=o 

40 

60 

80 

t/ = o 

40 

60 

80 

x>' = o 

40 

60 

80 

0 

II 

40 

60 

80 

70 

57 

311 

2800 


67 

363 

3267 


76 

415 

3733 


86 

467 

4200 


75 

53 

245 

1333 


62 

286 

1556 


7 i 

327 

1778 


80 

367 

2000 


80 

50 

200 

800 


58 

233 

933 


67 

267 

1067 


75 

300 

1200 


85 

47 

l68 

544 


55 

ig6 

635 


63 

224 

725 


7 i 

252 

816 

* 

go 

44 

144 

400 

3600 

52 

168 

467 

4200 

59 

ig2 

533 

4800 

67 

216 

600 

5400 

05 

42 

126 

3io 

i68g 

49 

147 

3^2 

1970 

56 

168 

414 

2252 

63 

188 

4 b 5 

2 533 

100 

40 

III 

250 

1000 

47 

130 

2g2 

1167 

53 

148 

333 

1333 

60 

167 

375 

1500 

105 

38 

99 

207 

672 

44 

116 

242 

784 

51 

133 

277 

8g6 

57 

149 

3 ii 

1008 

110 

36 

90 

176 

48 g 

42 

105 

205 

570 

48 

120 

235 

652 

55 

135 

264 

733 

115 

35 

82 

152 

376 

41 

95 

177 

438 

46 

iog 

203 

501 

52 

123 

228 

563 

120 

33 

75 

1.33 

300 

39 

88 

156 

350 

44 

100 

178 

400 

50 

113 

200 

450 

125 

32 

69 

118 

247 

37 

81 

138 

288 

43 

92 

158 

32 g 

48 

104 

178 

370 

130 

31 

64 

106 

208 

36 

75 

124 

243 

4 i 

86 

142 

277 

46 

96 

159 

312 

140 

29 

56 

88 

156 

33 

65 

102 

182 

38 

75 

117 

207 

43 

84 

13 1 

233 

150 

27 

50 

74 

122 

3 i 

58 

86 

i 43 

36 

66 

99 

163 

40 

74 

irx 

184 

160 

25 

44 

64 

100 

29 

52 

7 5 

117 

33 

59 

85 

133 

38 

67 

96 

150 

1 7 ° 

24 

40 

56 

84 

27 

47 

66 

98 

31 

54 

75 

112 

35 

60 

84 

126 

180 

22 

37 

50 

72 

26 

43 

58 

84 

30 

49 

67 

g6 

33 

55 

75 

108 


TABLE 9b. LOCATION OF VERTICAL STIRRUPS IN BEAM WITH 

UNIFORM LOADING 

Rule. Find distance of each stirrup from end of beam by multiplying l lt (obtained from formula) by 
values from Table gb, selected by reading along horizontal line opposite proper value of A T S< 


Values of Constant -Ci for Ftiding Distance of Each Stirrup From End o f Beam. 



EXAMPLE FOR NUMBER AND LOCATION OF STIRRUPS 

Example 20: Given: l = 24 ft.; total load = 2400 lb. per lin. ft.; b = 12 ";jd = 21"; v' = 40 lb. 
persq. in.;/ 5 = 16000. Use x 7 6 -inch square twisted U-stirrups, i.c., A s =0.383. 


Solution: Shearing unit stress at end of beam, v = ——L = 115 lb. per sq. in. 

2 X 12 X 21 

from Table ga, opposite v — 115, under f s = 16000, with v' = 40, we find C n = iog. 

T '— ~ —- = 6.g. Therefore use 7 stirrups in each end of beam. 

A s ( -n 0 . 383 X 1^9 


Taking values 
Hence, N s _ 


1 o locate stirrups, we find /, = ^-= gq inches. Take values from Table gb oppo¬ 

site = 7, and, multiplying each value by (1 =gq, distance of each stirrup from end of beam will give: 
1st stirrup, 3.5"; 2d, 10.8", 3rd, 18.7"; 4 th, 27.8"; 5th, 38.1"; 6th, 51.x"; 7 th, 70.3". 































































































TABLE io. TABLE FOR CONSTANT C FOR BEAMS 

Data for Determining Depth of Beam, Moment of Resistance and Reinforcement 


To be used, in formulas for Depth of rectangular beam or slab d = C I M 

V * 

and in formulas for Moment of Resistance M = 

(See pp. 418 and 754.) 

Based on dimensions in inches and moments in inch-pounds. 


katio OF moduli of steel to Ratio of Moduli ot Steel to 

concreie m = 10 Concrete n = 15 


Item 

+3 

bO 

G 

u 

gl 

O O 

/. 

lb. per 
sq. in. 

r* 

M 

□ 

<D <1> 

IT 2 C 

O 
fcfi C 
c 0 
£0 
t- 

0 0 
£ 
f c 

lb. per 
sq. in. 

Ratio Depth of Neu- 
^ tral Axis to Depth 
of Steel. 

Ratio of Moment 
^ Arm to Depth of 

steel (1 -1) 

>53 Ratio Area of Steel to 
Beam Above Steel. 

^ Safe Working Value 
of Constant C. 

Ratio Depth of Neu- 
^ tral Axis to Depth 
of Steel. 

Ratio of Moment 

v>. Arm to Depth of 

Steel, / k \ 

Ratio Area of Steel 

^ to Beam Above 
Steel. 

0 Safe Working Value 
of Constant C. 

I 

12000 

5 oo 

! 0.294 

0.902 

0.0061 

0.123 

0.3S4 

0.872 

0.0080 

0.109 

2 


55 o 

i 0.314 

0.L95 

0.0072 

0.114 

0.407 

0.864 

0.0093 

0.102 

3 


600 

0-333 

0.889 

0.0083 

0. 106 

| 0.428 

0.857 

0.0107 

0.095 

4 


65 o 

o. 35 1 

0.883 

0.0095 

0.100 

I 0 448 

0. 85 1 

0.0121 

0.090 

5 


700 

0. 368 

0.877 

0.0108 

0.094 

0.467 

0.844 

0.0136 

0.085 

6 


75 o 

0.3S4 

0. S72 

0.0120 

0. 089 

0.484 

0.839 

0.oi 5 1 

0.081 

7 


800 

I 0.400 

0.867 

0.0133 

0.08 5 

j 0. 5 oi 

0-833 

0.0167 

0.077 

8 

14000 

5 00 

0.263 

0.912 

0.0047 

0.129 

0.348 

0.884 

0.0062 

0.114 

9 


55 o 

[ 0.2S1 | 

0.906 

0.oo 55 

0.120 

0. 372 

0.876 

0.0073 

0.106 

IO 


600 

0.299 j 

0.900 

0.0064 

0. 111 

0.392 

0. 869 

0.0084 

0.099 

11 


65 o 

0.318 

0.894 

0.0074 

0.104 

0.409 

0. 861 

0.0095 

0.093 

I 2 


700 

0. 333 

0. 889 

0.0083 

0. 098 

0.428 

0. 857 

0.0107 

0.088 

13 


75 o 

o- 348 

0.884 

0.000 3 

0. 093 

0.446 

0. 85 1 

0.0120 

0.083 

14 


800 

0. 364 

0.879 

0.0104 

0.088 

0.462 

0.846 

0.0132 

0.080 

15 

16000 

5 oo | 

0. 238 

0. 921 

0.0037 

0.135 

0.319 

0.894 

0.oo 5 o 

0.118 

16 


55 o ; 

0.256 

0.915 

0.0044 

O. 125 

0. 339 

0.887 

0.oo 58 

0. no 

17 


600 I 

0.272 

0.909 

0.oo 5 1 

0. 116 

70.35S r S 

0.881 

0.0067 

0.103 

18 


65 o 1 

0.288 ' 

0.904 

0.oo 58 

0.109 | 

0.378 

0.874 

0.0077 

0.096 

19 


700 j 

0- 304 

0.899 

0.0067 

0.102 I 

0-397 

0.868 

0.0087 

0.091 

20 


75 o 

0.319 

0. 894 

0.0075 

0.096 

o- 4 t 4 

0. 862 

0.0097 j 

0.086 

2 I 


800 J 

0-333 

0. 889 

0.0083 

0.092 

0.429 

0.857 

0.0107 

0.083 

22 

20000 | 

5 oo [ 

0. 200 

0-933 

O .0025 

0.146 l 

0.272 

0.909 

0.0034 

0.127 

23 


55 o I 

0.217 

0.928 

0.0030 

0-134 

0.292 

0.903 

0.0040 1 

0.118 

24 


600 

0.232 

0.923 

0.0035 

0.124 I 

0.311 ; 

0.896 

0.0047 

0.109 

25 


65 o j 

0. 246 

0.918 

0.0040 

o. 11 7 

0.32S 

0.891 

0.0053 

0.103 

26 


700 

0.259 

0.914 

0.0045 

0. 110 

0.344 

o .885 

0.0060 ; 

0.097 

27 


75 o 

0.272 

0.909 

o.oo 5 i 

0.104 

0.349 

0.880 

0.0067 

0.092 

28 


800 

0. 285 

0. 905 

0.0057 

0.098 I 

0.374 

0.875 

0.0075 

0.087 

29 

24000 

5 00 I 

0.172 

0-943 

0.0018 

0. i 57 

0.240 

0.920 

O .0025 

0.135 

30 


55 o 1 

0. i 85 

0.938 

0.0021 

0.145 j 

0.256 

0.915 

0.0029 

0.125 

31 


6oo 

0.200 

0-933 

0.0025 

! 

0.134 

0.272 | 

0.909 

0.0034 

0.116 

32 


65 o j 

0.213 

0.929 

0.0029 

0.124 

0.288 

0.904 

0.0039 

0.109 

33 


700 

0.226 

0.925 

0.0033 

0.117 j 

0.303 

0.899 

0.0044 

0.105 

34 


75 o j 

0.238 

0.921 

0.003/ 

O . I I I f 

0. 319 

0.894 

0.oo 5 o | 

0.096 

35 | 


800 | 

O. 25 1 

0.916 

0.0042 

0. io 5 

0.334 | 

0.889 

o.oo 56 

0.092 


Note—F or intermediate stresses, interpolate. 
























































5 2 ° 


A TREATISE ON CONCRETE 


TABLE ii. DATA FOR DETERMINING DEPTH OF RECTANGULAR BEAM 
OR SLAB OR MOMENT OF RESISTANCE FOR DIFFERENT PERCENT¬ 
AGES OF STEEL. 


Ratio of elasticity, n = 15. 

Rule 1. To find depth of beam or slab for a given percentage of steel: 

On line with the given percentage, select the higher value of C. This, 
substituted in formula 



(see p. 418), gives the smallest permissible depth. Thus for 0.004 steel ratio 
the value of C. from column (9) must be used instead of from column (6) 
because the latter would stress the steel to 23 700 pounds, which would not 
be allowable. It is evident also that the ratio of steel is too low for econ¬ 
omy, because concrete is stressed only to 440 pounds. 

Rule 2. To find amount of steel for a given beam or slab and given load¬ 
ing with stress in concrete limited to 650 pounds per square inch and stress 
in steel to 16 000 pounds per square inch: 

bd 2 

Compute value of C from formula M = (see p. 754)- Locate this 

value either in column (6) or (9), whichever satisfies the allowed stresses, 
and find the corresponding value of p in the first column. Thus, if C — 
0.097, it mus t be located in column (9) instead of column (6), because the 
latter would give a higher stress in steel than is allowable. The desired ratio 
of steel is therefore 0.0077. If C = 0.088, it must be located in column 
(6) because column (9) would give too high a stress in concrete. 


Ratio area of steel to 
beam above steel. 

Ratio depth of neu¬ 
tral axis to depth 
of steel. 

Ratio moment arm 
to depth of steel. 

Working compressive 
strength of concrete 
Lb. per sq. in. 

Maximum fibre stress 
in steel correspond¬ 
ing to f c = 650 

Constant in formula 

d =c 

0 

see page 418 

Working tensile 
strength of steel 

Lb.per sq. in. 

Maximum fiber stress 
in concrete corre¬ 
sponding to /„ 

= 16000 

Constant in formula 

d=cVy 

0 

seepage 418 

V 

k 

3 

fc 

fs 

c 

fs 

fc 

c 

(1) 

(2) 

( 3 ) 

( 4 ) 

( 5 ) 

(6) 

( 7 ) 

(8) 

( 9 ) 

O . 002 

O.217 

0.928 

650 

32900 

0.124 

16000 

290 

0.183 

O . OO3 

0.258 

O.914 

650 

28000 

0.114 

I 6000 

370 

0.151 

O . 004 

0.292 

0.903 

650 

23700 

0.108 

16000 

440 

0.132 

0.005 

0.320 

0.893 

650 

20800 

0.104 

I 6000 

500 

0.118 

O . 006 

0-344 

0.885 

650 

18600 

0.100 

I 6000 

560 

0.108 

O . OO7 

°- 3 6 5 

0.878 

650 

16900 

0.008 

16000 

610 

0. IOI 

\ro . 008 

0.384 

0.872 

650 

15600 

0.096 

I 6000 

670 

0.095 

0.009 

0.402 

0.866 

650 

14500 

0.094 

16000 

720 

0.089 

0.010 

0.418 

0.861 

650 

13600 

0.092 

16000 

'760 

0.085 

0.012 

0.446 

0.851 

650 

12 100 

0.090 

16000 

860 

0.078 

0.014 

0 • 47 1 

0.843 

650 

11000 

0.088 

I 6000 

9 5 ° 

0.072 

0.010 

0-493 

0.836 

650 

10000 

0.086 

16000 

1040 

0.068 

0.018 

0.513 

0.829 

650 

9300 

0.085 

16000 

1120 

0.065 

0.020 

0 • 53 1 

0.823 

650 

8600 

0.084 

16000 

1210 

0.061 






































REINFORCED CONCRETE DESIGN 


5 21 




TABLE 12. PROPORTIONAL DEPTHS OF NEUTRAL AXIS 

The table below gives the proportional depths of the neutral axis calcu¬ 
lated from formula (6) on page 420 for various percentages of steel and 
moduli of elasticity. Its use is not advised for ordinary calculations of 
moments of resistance and dimensions of beams or slabs, because it presents 
no means of determining, without further calculation, the stress in the 
steel or the concrete, and therefore is liable to lead to uneconomical design. 
Its principal use is for determining the moment of resistance, and conse¬ 
quently the safe loading for beams already built. 


Proportional Depth 0} Neutral Axis below top of Beam for different per cents of 
Steel and various assumptions of Elasticity. (See p. 310.) 


' of area of steel 
ea of cross-section ^ 
am above steel. 

k 

Ratio of depth of neutral axis to depth of center of steel below most compressed surface of beam. 

E s 

Ratios of Modulus of Elasticity of Steel to Modulus of Concrete in Compression, 

Ec 

- _ n 

O U V 

o 3 0 u-t 
PC°o 

6 

75 

10 

12 

15 

20 

30 

35 

40 

0.001 

0.10 

0.115 

0.132 

0.143 

0.158 

0.181 

0.217 

O.232 

0.246 

0.002 

0.184 

O.159 

O.181 

0.196 

0.217 

0.246 

0.292 

O.311 

0.328 

O.OO3 

°- I 73 

O.191 

O.217 

°- 2 35 

00 

10 

6 

0.292 

0-344 

°-3 6 5 

0.384 

O.OO4 

0.196 

O.217 

0.246 

0.266 

0.292 

0.328 

0.384 

0.420 

0.428 

O.OO5 

0.217 

O.239 

O.270 

0.292 

0.320 

0.35^ 

0.418 

0.442 

0.464 

0.006 

°- 2 35 

O.258 

O.292 

0.314 

0.344 

0.384 

0.446 

0-47 1 

°-493 

0.007 

0.251 

0.276 

O.311 

°-334 

0.365 

0.407 

0-47 1 

0-497 

0 -5i9 

0.008 

0.266 

O.292 

0.328 

°-353 

0.384 

0.428 

0-493 

0.519 

0.412 

O.OO9 

0.279 

0.306 

0.344 

0.369 

0.402 

0.446 

0.513 

0 -539 

0.562 

0.010 

0.292 

O.320 

O.358 

0.384 

0.418 

0.463 

o.53i 

0-557 

0.584 

0.012 

°-3 1 5 

0-344 

0.384 

0.402 

0.446 

0-493 

0.562 

0.588 

0.611 

O.OI4 

°-334 

0.364 

O.407 

0.436 

0-47 1 

°.5 T 9 

0.588 

0.614 

0.638 

O.Ol6 

°-353 

0.384 

0.428 

0.457 

0-493 

0.542 

0.611 

0.637 

0.660 

O.Ol8 

0.369 

O.402 

0.446 

0.476 

0.513 

0.562 

0.631 

0.657 

0.680 

0.020 

0.384 

0.418 

0.463 

0-493 

°"53 I 

0.580 

0.649 

0.675 

0.697 

O.O3O 

O.O4O 

O.O5O 

0.446 

0-493 

0.531 

0.483 

0.531 

0.^69 

0.531 

0.580 

O.618 

0.562 
0.611 
0.649 

0-599 

0.649 

0.686 

0.649 

0.697 

0-73 2 
























5 22 


A TREATISE ON CONCRETE 


DIAGRAM i. 


BENDING MOMENTS FOR DIFFERENT SPANS AND LOADS. 



o 












































































































































































































































































































































































































































REINFORCED CONCRETE DESIGN 


5 2 3 


DIAGRAM 2 . BENDING MOMENTS FOR DIFFERENT SPANS AND LOADS, 



io 






















































































































































































































































































































































































































































I 

200 

100 

5000 

S00 

800 

700 

600 

500 

400 

300 

200 

100 

4000 

900 

800 

700 

600 

500 

COO 

300 

200 

100 

3000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

2000 

900 

800 

700 

600 

500 

400 

300 

200 

100 

1000 

900 

800 

700 

600 

500 

400 

300 


A TREATISE ON CONCRETE 


BENDING MOMENTS FOR DIFFERENT SPANS AND LOADS. 

wl 2 


M = 


12 



10 II 12 13 14 15 16 17 18 19 20 21 22 21 24 25 20 27 28 29 3U 31 32 33 34 35 36 37 38 39 40 

vPAN Or £3CAM IN FEET 

































































































































































































































































































































































































































































































525 


DIAGRAM No. 4. CURVESFOR DESIGN OFT-BEAMS 

To find minimum depth 

To find area of steel for any depth. 

To find total compression in flange. 



DIAGRAM 4. CURVES FOR DESIGN OF T-BEAMS. 525 

Notation: 526 

f c — working compression in concrete in lb. per sq. in. 

f 8 = working tension in steel in lb. per sq. in. 

b = breadth of flange in inches. 

t = thickness of flange in inches. 

d = depth of steel in T-beam in inches. 

t 

jd = moment arm, approximately equal to d - - • 

k = ratio of depth of neutral axis to depth of steel. 

Diagram is made from formulas (14) to (19), pages 755 and 756. 

Curves at left, of Moment Arm, are applicable to all conditions. 

Curves at right may be used for any combination of stresses having k as 
given in diagram. For other stresses find value of k in Table 10, page 
519, and interpolate between the curves. 

T 0 Determine Minimum Depth of a T-beam Consistent with a \\ or king 
Compression in Concrete. Enter Diagram 4 at top with value specified for 
maximum working compression f c in concrete times bt, which is assumed 
breadth of flange of T-beam, times thickness of slab. Follow this line 
down vertically until it intersects the slant line representing the previously 
assumed relation ot thickness of slab to depth of steel. From point of inter¬ 
section of these two lines follow horizontal line across, the diagram to the 
left till it intersects a vertical line corresponding to required moment in 
inch-pounds read from bottom of diagram. This will give minimum value 
of jd, the distance between center of gravity of steel and center of compres¬ 
sion in concrete. The depth from surface of beam to steel is d = jd + \t. 

If assumed relation between d and t does not correspond to actual, repeat 
the operation. 

No smaller depth than the minimum can be used. Larger depths than 
the minimum are usually economical (see pp. 424, 425). 

To Determine Area of Steel in a T-beam Consistent with a Working Ten¬ 
sion in the Steel. Enter diagram at bottom of page with bending moment 
in inch-pounds and follow this line vertically upwards till it intersects slant 
line jd, which is the distance between the center of the steel and center of 
compression of the concrete and is approximately equal to d - \t. From 
intersection of these two lines follow norizontal line to left and read off 
directly the area of steel required in square inches corresponding to the speci¬ 
fied working stress in the steel. 

( r 2 kd-t u \ 

To Determine Total Compression in Flange of a T-beam [f c ^ bt j 

Enter table at bottom with moment in inch-pounds, follow this line up 
vertically till it intersects slant line jd. From point of intersection follow the 
horizontal line to the right hand column of figures, which will give the total 

compression in the flange of a I -beam. 

To Determine Maximum Fiber Stress f c . Determine total compression as 

above. Equate this value to f c — &• Assume a value for k and com¬ 

pute f c . Determine value of f s . Refer to Table 10, page 519, and see if 
value of k corresponds to f c and f 8 . If not, select a new k and recompute. 




VALUES OF MAXIMUM WORKING COMPRESSION TIMES AREA OF FLANGE (f bt) USE FOR FINDING MINIMUM DEPTH 



TOTAL COMPRESSION IN FLANGE OF T-BEAM (f. bt) See P .755. 




































































































































































































































































































































































































































































































































































































































\ 


REINFORCED CONCRETE DESIGN 


5=7 


WORKING STRESSES IN REINFORCED CONCRETE 

The Joint Committee on Concrete and Reinforced Concrete, 1909, recom¬ 
mend working stresses as follows:* 

General Assumptions. The following working stresses are recommended 
for static loads. Proper allowances for vibration and impact are to be 
added to live loads where necessary to produce an equivalent static load 
before applying the unit stresses in proportioning parts. 

In selecting the permissible working stress to be allowed on concrete, we 
should be guided by the working stresses usually allowed for other materials 
of construction, so that all structures of the same class but composed of 
different materials may have approximately the same degree of safety. 

The stresses for concrete are proposed for concrete composed of one part 
Portland cement and six parts aggregate, capable of developing an average 
compressive strength of 2 000 pounds per square inch at twenty-eight days 
when tested in cylinders 8 inches in diameter and 16 inches long, under 
laboratory conditions of manufacture and storage, using the same con¬ 
sistency as is used in the field. In considering the factors recommended 
with relation to this strength, it is to be borne in mind that the strength at 
twenty-eight days is by no means the ultimate which will be developed 
at a longer period, and therefore they do not correspond with the real factor 
of safety. On concretes in which the material of the aggregate is inferior, 
all stresses should be proportionally reduced, and similar reduction should 
be made when leaner mixes are to be employed. On the other hand, if, 
with the best quality of aggregates, the richness is increased, an increase 
may be made in all worldng stresses proportional to the increase in com¬ 
pressive strength at twenty-eight days, but this increase shall not exceed 
25 per cent. 

Bearing.-}- For compression on surface of concrete larger than loaded 
area. 

32.5 per cent of compressive strength at twenty-eight days, or 650 pounds 
per square inch on 2 000 pound concrete. 

Columns, (a) Plain columns or piers whose length does not exceed 
twelve diameters, 

22J per cent of compressive strength at twenty-eight days, or 450 

pounds per square inch on 2000 pound concrete. 

(b) Columns with reinforcement of bands or hoops ,J 
27 per cent of compressive, strength at 28 days, or 540 pounds per square 
inch on 2000 pound concrete. 

Vertical steel reinforcement 8100 pounds per square inch. 


* The form in which these are given corresponds with the 1909 Report of the Reinforced Concrete 
Committee of the National Association of Cement Users. 

f For beams and girders built into pockets in concrete walls, the lower compressive stress of 450 
pounds per square inch should not be exceeded. 

+ The amount of band or hoop reinforcement must be at least 1 per cent of the volume of the 
column enclosed, and clear spacing of the bands or hoops not greater than one-fourth the diameter 
of the enclosed column. 


A TREATISE ON CONCRETE 


528 

(c) Columns reinforced with not less than 1% and not more than 4% 
of longitudinal bars and with bands or hoops spaced not greater than one- 
fourth the diameter of the enclosed column, 

3 2 i% of compressive strength at 28 days, or 650 pounds per square 
inch on 2000 pound concrete. 

Vertical steel reinforcement, 9750 pounds per square inch. 

(d) Columns reinforced with structural steel column units which thor¬ 
oughly encase the core, 

32%% of compressive strength at 28 days, or 650 pounds per square 
inch on 2000 pound concrete.* 

Vertical steel, 9750 pounds per square inch. 

Compression in Extreme Fiber. For extreme fiber stress of beams 
calculated for constant modulus of elasticity, 

32.5 per cent of the compressive strength at twenty-eight days, or 650 
pounds per square inch for 2000 pound concrete. 

Adjacent to the support of continuous beams, stresses 15 per cent greater 
may be allowed. 

Shear. Pure shearing stresses uncombined with compression or tension, 
6 per cent of compressive strength at twenty-eight days, or 120 pounds 
per square inch for 2000 pound concrete. 

Diagonal Tension. In beams where diagonal tension is taken by con¬ 
crete, the vertical shearing stresses should not exceed 

2 per cent of compressive strength at twenty-eight days, or 40 pounds 
per square inch for 2000 pound concrete. 

Bond for Plain Bars. Bonding stress between concrete and plain rein¬ 
forcing bars, 

4 per cent of compressive strength at twenty-eight days, or 80 pounds 
per square inch for 2000 pound concrete. 

For drawn wire. 

2 per cent, or 40 pounds on 2000 pound concrete. 

Bond for Deformed Bars.f Bonding stress between concrete and de¬ 
formed bars may be assumed to vary with the character of the bar from 

5 per cent to 7^ per cent of the compressive strength of the concrete 
at 28 days, or from 

100 to 150 pounds per square inch for 2000 pound concrete. 


* Lower stresses than these should be used unless the concrete is very carefully proportioned 
and placed. The authors recommend 500 lb. per sq. in. in general practice. 

j-No recommendation for deformed bars is given in the report of the Joint Committee; the 
values given are those suggested by the Reinforced Concrete Committee of the National Asso 
ciation of Cement Users. 


reinforced concrete design 


5 2 9 

Reinforcement. The tensile stress in steel should not exceed 16 ooo 
pounds per square inch.* The compressive stress in reinforcing steel 
should not exceed 16 ooo pounds per square inch, or fifteen times the work¬ 
ing compressive stress in the concrete. 

Modulus of Elasticity. It is recommended that in all computations the 
modulus of elasticity of concrete be assumed as y 1 ^ that of steel; that is, 
that a ratio of fifteen be employed. 


t 

b 

b' 

d 

P 

P' 

fc 

fa 

/ 

f a 

f 

n 


k 

kd 


z 

M 

Mb 

Mr 

M 2 

M b 

V 

V 

u 

o 

lo 

A 

A s 

w 

<7 

i 

r 

l 


STANDARD NOTATION^ 


thickness of slab, i.e., thickness of T-flange. 
breadth of beam; in a T-beam, breadth of T-flange. 
breadth of stem of T-Beam. r 

depth from surface of beam to center of tension steel. 

ratio of cross-section of steel in tension to cross-section of beam above 
this steel. 

ratio of cross-section of steel in compression to cross-section of beam 
above the steel in tension. 

unit compressive stress in outside fiber of concrete, 
unit tensile stress, or pull, in steel. 

unit compressive stress in steel, 
average unit compression in a column. 


E s 

E c 


Ratio of modulus of elasticity of steel in tension to modulus of 


elasticity of concrete in compression. 

= ratio of depth of neutral axis to depth of steel in tension. 

= distance from outside compressive surface to neutral axis in beam in 
which the depth to steel in tension is d. 

= ratio of lever arm of resisting couple to depth d. 

=' arm of resisting couple. 

= depth from surface of beam to center of compression. 

— moment of resistance or bending moment in general. 

= bending moment. 

= resisting moment. 

= bending moment in a flat slab causing radial fibre stress for loading 
distributed along the edge of the fixed plate. 

= bending moment in a flat slab causing radial fibre stress for loading 
uniformly distributed over the plate. 

= total shear. 

= unit shear. 

= unit working shear. 

= unit bond. 

= circumference of one bar. 

= total circumference of all bars in a beam. 

= total area. 

= area of steel. 

= unit loading for uniformly distributed load. 

= unit loading for circumferential loading. 

= diameter of bar. 

= ratio unit cost of steel to unit cost of concrete. 

= span of beam. 


*If the steel has a high elastic limit and is of the exceptional quality called for by the sytuin- 
cations on page 38, the authors would frequently permit a stress as high as 20000 pounds per 
square inch. , 

tSuhstantially as adopted by the Joint Committee on Concrete and Reinfoiced Concrete and 
as used in this Treatise. 


A TREATISE ON CONCRETE 


53° 


ll — longer span of a rectangular slab. 
l s — shorter span of a rectangular slab. 

M = bending moment of longer beam. 

M f — bending moment of shorter beam. 

a = denominator in bending moment formula M 

m = number of bars at the center of beam. 
m ] — number of bars to be bent. 

C = constant from Table io, p. 519. 

Cc.Cs, C s , = constant from Table 8, p. 516. 

C v C. 2 ,C a ,Cb- — constant from Table 9, p. 518. 

C s ,Cb = constant from Table on p. 454. 
r 0 — inner radius of flat plates in feet. 


w l 2 
a 


COMMON FORMULAS. 


Rectangular beam: 


Depth of steel, d = C 
Tension in steel, f s = 


l M 
\T> 

M 

A s j d 


Reference 
to Page 

418 


420 


Unit shear, v = ^ 

Ratio span to depth not l — a 
requiring stirrups, d > 1.74 C 2 v 


447 ! 
456 


Steel area, A 8 = pbd 


Compression in concrete, 
2 M 

bd' 2 jk 


Unit bond, u = 


V 

jd I o 


Reference 
to Page 

418 


420 


457 


T-Beam: 


Horizontal steel, A 8 — 


M 


f id 


' s 


(approx.) 


426 


Area required by shear, b' ^ d - - ) > 


/\ V 

o 

424 


Economical depth, d 

Length of haunch, x 
(approx.) 


t IrM 

2 “ \ f 8 b' 42 5 

l Mb - Mr 

5 Mb 

430 


Depth of neutral axis, 

2 nd As + 

kd = - . - 

2 n A s -f : 

Moment arm, 

jd = d - z 

Tension in steel, 

/ -Ji 

' 5 ~ Ajd 


755 


3 kd — 2 t t 
2 kd — t 3 


755 


Compression in concrete. 

, Mka 

,c ^ bt 0 kd - \t)jd 


7 55 


756 


756 
















REINFORCED CONCRETE DESIGN 


53* 


Beam with Steel in Top and Bottom: 
Moment, M = f c bd 2 C c 1 which ever is 
or =f s bd*C 8 l larger 428 


M 


Tension in steel, f s — ppj T c 


428 


Flat Plates 
Radial loading, 

Max. M 2 = wr 0 2 (0.2 + Ci + C 2 ) 4S6 


M 


Compression in concrete, f c = bdFC 


M 


Compression in steel, /'= 428 


Circumferential loading, 
Max Mb = qr 0 (C a + Cb) 


486 


Column: 

f - fc 

Ratio steel, p = x -c 

y fc (n - 1) 


49 1 


Area column, A = j-7—r-7— -r- , 491 

fc [1 + (n - 1) p] ^ 

Stirrups: 


2 sF 


Average unit load, 

j =f =fc[i + (n - 1) p] 


3 Asfsjd 


Area of stirrups, A g = — 449 Spacing of stirrups, 5 — 2 y 

Distance from sup- \ V 'bjd 
port where no x = - — -- 


stirrups needed 


45i 


Max. distance 

from support = 2 _ & 

where rods 1 2 \ 2 \ a 

may be bent, 

Diameter vertical stirrup . — A s — 1 

for square or round bar, ' l < G s d 454 For other shapes, — <- C&d 

Diameter inclined stirrup . — — 1 

for square or round bar, 1 < 454 | For other shapes, — < - Cbd 


8 m 
m 


491 


45 ° 

459 

454 

454 


Distribution of slab load to supporting beams: 


For longer beam 

2 / 1 (hV 

1 431 


For shorter beam, 

Ms = I (k wlZ) 


4 3 * 















Fig. 156. Walnut Lane Bridge, Philadelphia. 








A 


RCHES 


533 


• CHAPTER XXII 

ARCHES* 

BY FRANK P. McKIBBEN 

The treatment of arch design by what is termed the elastic theory, although 
generally considered a complicated problem, as a matter of fact is easily 
handled by one who is familiar with elementary mechanics and with the 
principles of reinforced concrete beam design. The process is necessarily 
somewhat lengthy, involving extended operations in simple arithmetic, but 
by following the analysis presented in the following pages it can be readily 
understood. It is doubtful whether in the whole category of the design of 
structures there is a prettier application of mechanics and mathematics 
than the design of a reinforced concrete arch bridge. 

While in a volume of this size it is impossible to present all phases of the 
subject, the underlying principles are treated in sufficient detail and with 
a discussion thorough enough to permit an engineer to safely design an arch. 

Following a brief historical introduction discussing the use of concrete 
versus steel construction, the different forms of arches are reviewed with 
suggestions for design; the loading for different conditions is scheduled 
(p. 541); the outer forces are analyzed, including the effect of temperature 
(p. 553); the method of procedure to be followed in arch design is taken up 
in a practical example item by item (p. 574); allowable unit stresses are 
r uggested (p. 583); the design of abutments is outlined (p. 583); and a 
few illustrations of existing bridges are presented. 

Girder bridges are not treated specifically in this chapter, but they may 
be readily designed by applying the principles of reinforced concrete beam 
and slab construction as treated in Chapter XXI on Reinforced Concrete. 

The treatment of conduit or sewer arches which are so deeply imbedded 
as to require computations for earth pressure is referred to on page 693. 

Perhaps the most interesting feature of the present chapter is the com¬ 
plete analysis of a typical arch which is presented on page 574. The steps 
to be followed are outlined consecutively and the mathematical processes 
indicated in full. 

The formulas for distribution of stress given on page 560 apply not only 
to arch design but also to column and beam design where there is eccentric 

♦The authors are indebted to Prof. McKibben for this chapter, which has been especially pre¬ 
pared by him for this treatise. 


534 


A TREATISE ON CONCRETE 


loading or thrust in place of or in addition to the ordinary loads. To facili¬ 
tate the understanding of the formulas, a departure is made from the usual 
notation schedule, which must necessarily be several pages away from the 
work, by placing in addition, at the bottom of each page, a brief definition 
of all the symbols used on that page. 

CONCRETE VERSUS STEEL BRIDGES 

Reinforced concrete, either as arch or girder spans, is being used not only 
in preference to steel trusses or steel girders, where the stone arch is too 
expensive to be considered, but the concrete bridge is frequently replacing 
the old steel structure. The reasons generally conceded for this wide¬ 
spread growth may be briefly stated as: (i) greater durability; (2) less 
cost of maintenance; (3) less vibration and less noise; (4) more aesthetic 
effects. 

The relative first cost for concrete and steel depends upon the local con¬ 
ditions. In many places a concrete bridge can be built for less than a first- 
class steel span, although it cannot so readily compete with the flimsy trussed 
spans frequently seen. The concrete may be laid with less skilled labor 
than the steel bridge, but since the concrete structure is built on the spot, 
while the steel is prepared in an established shop, even more careful super¬ 
vision and inspection are necessary with the concrete. The foundations for 
a concrete arch are frequently more expensive than concrete abutments 
for a steel truss because of the greater area required to take the thrust, while 
on the other hand, in rock or other hard material, a less quantity of concrete 
may be required for the arch abutments. This part of the design may often 
be the determining feature from the economical standpoint. 

The most serious objection to steel, especially for highway bridges, lies 
in the fact that unprotected it cannot resist for a great length of time the 
oxidation due to air, water and locomotive gases, and unless properly cared 
for and frequently painted, it rusts badly. The examination by the author 
of this chapter of approximately 600 highway bridges carrying electric 
railways proves that frequently these bridges are not properly maintained, 
many of them receiving little or no attention for years at a time, so that the 
structures are often badly corroded, and in fact, cases are on record where 
subordinate members of steel bridges have rusted away completely in less 
than fifteen years. 

In a concrete bridge the steel is effectively prevented from rusting by the 
concrete in which it is imbedded (see p. 327), so that, when properly designed 
and built no repairs whatever should be required, and no limit can be placed 
upon the life of the bridge. 


ARCHES 


535 


Concrete is strongest in compression, and is therefore eminently suit¬ 
able for use in arch spans where the stresses are largely compressive. The 
mass of the concrete and the quantity of earth filling or ballast over the 
arch so deaden the impact due to traffic that in many cases no impact 
allowance need be made, while at the same time the noise and vibration 
which occur in steel spans are avoided. 


USE OF STEEL REINFORCEMENT 

The use of steel reinforcement in a concrete arch is desirable but not 
absolutely necessary, as it is possible to construct a concrete arch like the 
Walnut Lane Bridge in Philadelphia (see pp. 532 and 592) with the 
concrete laid in blocks, each block forming a voussoir like the stones in a 
masonry arch. At the same time under ordinary conditions, while the intro¬ 
duction of steel does not, with the present knowledge of concrete arch design, 
permit great diminution in section, it does give considerable added strength 
at comparatively low cost and may prevent the formation of cracks in the 
concrete and take tension caused by any unforeseen action of the arch, 
such as settlement of foundations, improper allowance for temperature or 
shrinkage of the concrete while hardening. 

The area of the cross section of the longitudinal steel bars in solid arch 
rings is to a certain extent arbitrary. Good practice sanctions to i \ % 
of the ring at the crown and the exact quantity to use must first be selected 
by judgment, and then tested by the computation and revised if necessary. 

As in column design (see p. 489), it is impossible to stress the steel in 
compression to an amount ordinarily proper in structural steel work, 
because in so doing the deformation would be so great as to overstress 
the concrete. The actual compressive stress in the steel, therefore, can 
never be greater than the working stress in the concrete multiplied by the 
ratio of the modulus of elasticity of steel to that of concrete. Under ordi¬ 
nary conditions this limit on the steel may be taken as 7500 pounds per 
square inch. 

Since the beginning of this century there has been a remarkable development 
in methods of construction and in our knowledge of the principles of rein¬ 
forced concrete arch bridges, but even yet engineers incline to employ a 
somewhat excessive quantity of concrete in the solid rings of ordinary high¬ 
way concrete arches. This is frequently out of proportion to the quantity of 
material used in a reinforced concrete ribbed arch or a steel arch. Improve¬ 
ments in arch design evidently lie, as is indicated in subsequent pages, in 
the substitution of comparatively narrow ribs for solid arches and in the 


536 


A TREATISE ON CONCRETE 


use of hollow abutments with earth filling in place of solid concrete abut¬ 
ments. This will considerably reduce the cost of reinforced concrete arches. 

HISTORY OF CONCRETE ARCH BRIDGES 

In the development of concrete bridges it is natural that the arch rather 
than the beam should have been the first type of bridge to be constructed. 
It was a comparatively short step from the stone voussoir arch to the con¬ 
crete voussoir or to the monolithic arch. One finds therefore many concrete 
arch bridges, and, until recently, few beam bridges, although for short spans 
beam bridges are now being constructed in considerable numbers, both 
in this country and abroad. 

The first plain concrete arch of any importance was built in Europe in 
1869 and is known as the Grand Maitre bridge at Fontainebleu Forest. 
It has a maximum span of 115.8 feet and carries the aqueduct of the Paris 
waterworks from Vanne. The first plain concrete arch in the United States 
was constructed in 1871 by John C. Goodridge in Prospect Park, Brook¬ 
lyn, and has a span of 31 feet. The earliest reinforced concrete arch in 
Europe of which there is a well defined record was built in Copenhagen, 
Denmark, in 1879, with a span of 71.7 feet. It is probable, however, that 
Jean Monier of Paris was the inventor of the reinforced concrete arch and 
that he built some bridges before the dates mentioned. In the United States 
the first reinforced concrete arch on record was erected in 1889, with a 
span of 35 feet, by Ernest L. Ransome at Golden Gate Park in San Francisco. 

When these structures are compared with the 233 feet span of the Walnut 
Lane Bridge in Philadelphia, which in 1908 was, with perhaps one excep¬ 
tion, the longest plain concrete arch in existence, with the 230 feet, 3-hinge 
Griinwald Arch at Munich, Bavaria, or still more sharply with the Hudson 
Memorial design for an arch across the Spuyten Duyvil Creek with a span 
of 703 feet, a wonderful development is observed. 

Although in a very few cases concrete bridges built during this develop¬ 
ment have failed, every such failure can be traced to a direct disregard of 
well known principles of design or construction. Moreover, as a matter 
of fact, accidents to concrete arches have been much fewer than the failures 
of wrought iron or steel bridges during the corresponding period of metal 
bridge development. 


CLASSIFICATION OF ARCHES 

Arches in general may be classified with reference to the material of which 
they are made, the arrangement of the spandrels and arch rings, or the 


ARCHES 


537 


number of hinges. Reinforced concrete arches may be divided as to the 
arrangement of the reinforcement into three groups: the Monier, Melan 
and Wiinsch types. I he Monier arch in its developed form is the type most 
commonly used in the United States. This system of reinforcement was 
invented by Jean Monier about the year 1876. As first devised, a wire net¬ 
ting was imbedded in the concrete near the soffit, but later two nettings 
were used, one near the soffit, and the other imbedded in the concrete near 
the extradosal surface. Wire netting of small mesh with wires of equal 
size in both directions obviously is not well suited for use in an arch and 
considerable improvement was soon effected in this type by making the 
longitudinal bars of the reinforcement heavier than the transverse. 

In the usual design a layer of longitudinal bars is imbedded near the 
intrados and an equal number near the extrados, the bars of the two layers 
being connected with small bars or stirrups. Transverse bars, at right 
angles to the longitudinal, form with them a netting both in the top and 
bottom of the arch. They serve to prevent cracks in the concrete and dis¬ 
tribute the loads laterally. These cross bars also act with the stirrups in 
holding the longitudinal bars in place during construction. 

The principal longitudinal bars are designed to carry tension due to the 
bending moment and to assist the concrete in compression caused by the 
thrust and the bending moment. 

Melan Type. This system was invented by Joseph Melan of Brunn, 
Austria, in 1892. The reinforcement consists of curved steel ribs imbedded 
in the concrete and extending from abutment to abutment. For short spans 
the ribs are simply curved I-beams and for long spans each rib is made of 
two angles near the extrados latticed to two angles near the intrados. The 
built-up ribs thus formed are usually deeper at the springings than at the 
crown of the arch. The principal function of the lattice bars is to hold the 
angles in position when the latter are stressed, and to make a unit which 
is easy to handle during erection. By far the most important function of 
steel reinforcement is to carry bending moment, and the steel in the Melan 
type can be easily placed and kept in position during erection so as to fix 
positively its location in the finished structure. The material in the lattice 
bars of the ribs or in the webs of the I-beams is not economically placed. 
The first Melan arch in the United States, of 30 feet span, was erected at 
Rock Rapids, Iowa, in 1894, and many other bridges have since been built 
of this system. 

Wunsch Type. Comparatively few bridges have been constructed on 
this system. The arch, which was invented by Robert Wunsch of Budapest, 
Hungary, in 1884, has a horizontal extrados and a curved intrados and the 


53 « 


A TREATISE ON CONCRETE 


reinforcement of the arch ring consists of steel ribs spaced from to 
2 feet apart, with a horizontal upper member placed near the extrados 
and a curved lower member near the intrados. The two members are con¬ 
nected at each abutment to a vertical member imbedded in the concrete. 
The bridge at Sarajevo in Bosnia, of 83 feet span, is one of the largest built 
of the Wiinsch system. 

ARRANGEMENT OF SPANDRELS AND RINGS 

The spandrel, which is the space between the roadway surface and the 
top or extrados of the arch ring, may be treated in one of two ways, first, 
it may be entirely filled with earth or with concrete which carries the road¬ 
way; or, second, it may be left more or less open, and the roadway sup¬ 
ported upon a deck carried on a series of transverse walls, longitudinal 
walls, or columns resting upon the arch ring. 

Filled Spandrels. In this form of construction the earth or concrete 
filling rests directly upon the arch ring, and is held in place laterally by 
retaining walls which also rest upon the arch ring. As the depth of these 
walls, unless they are of reinforced design, increases from the crown to 
the springing, their thickness, designed to resist the earth pressure, also 
increases until at the abutments the spandrels may be largely filled with 
the concrete composing the side walls. 

If the side walls simply rest upon the arch ring, a crack is liable to form 
at the junction of ring and wall due to the deflection of the arch ring from 
the weight of the earth upon it. On the other hand, if the ring and wall 
are connected by sufficient steel to prevent the formation of this crack, 
indeterminate stresses are set up which are undesirable and which may 
result in transferring the crack to another place. This danger may be 
obviated by building the spandrel walls as gravity walls, leaving a vertical 
expansion joint at each junction of spandrel and wing walls and at some 
intermediate point between this joint and the crown. 

Another plan is to build thinner reinforced side walls as vertical slabs 
tied together, with the lateral pressure resisted by reinforced cross walls 
The principal objections to the use of solid fillings are as follows: (1) They 
increase the weight of the superstructure, and consequently thicker arch 
rings and larger foundations are required. (2) Unless the earth filling is 
carefully compacted by rolling, tamping or wetting, it will sink and allow 
the roadway to settle with it. (3) It is difficult to make the side walls and 
the arch ring act in unison, and unsightly cracks may be formed. Filled 
spandrels may be therefore limited properly to bridges with solid arch 


ARCHES 


539 


rings of short span, say not over 80 feet, or to those having a rise of less than 
yq the span, where the cost of form construction prohibits an open design. 

Open Spandrels. The objections just mentioned to the use of filled 
spandrels are of such importance that during the last few years the use of 
open spandrels in the larger structures has made rapid progress. In addi¬ 
tion to being lighter, the open spandrel construction facilitates inspection 
and lends itself to more pleasing architectural treatment. It permits indeed 
a treatment peculiar to concrete, which does not follow the type of design 
used for so many centuries in stone arch bridges. With open spandrels the 
roadway may be laid upon small arches or upon I-beams carried by trans¬ 
verse or longitudinal walls which in turn rest upon the arch ring; or it may 
be laid with reinforced concrete beam and slab construction, making a floor 
similar to those used in reinforced concrete buildings. The beams in this 
case are placed longitudinally with the roadway, and rest upon transverse 
walls. 

Upon the adoption of the open spandrel it was soon seen that considerable 
material was wasted in the transverse walls and in the solid arch rings. The 
next step, therefore, was to reduce the walls to columns and the ring to a series 
of longitudinal ribs spaced similarly to the ribs of a steel arch. In some 
cases these ribs are very wide, in fact, are really two independent arch rings 
as in the Walnut Lane bridge, Philadelphia,* and in other cases the ribs 
are narrow as in the Rock Creek bridge on Ross Drive in the District of 
Columbia.! 


HINGES 

The use of hinges in concrete arches is by no means of recent origin. As 
early as 1873, an arch was constructed near Erlach, Germany, with three 
asphalt “joints” and many others with hinges have been built since then. 
The chief object of the hinge in the arch rings or ribs is to render the 
structure more nearly determinate. 

Although two or even one hinge can be used, three hinges offer the advan- • 
tage of definitely fixing the pressure line throughout the ring so that it 
can be easily and accurately located. Except for the friction of the hinges, 
the stresses are practically independent of changes of temperature 01 of 
any reasonable settlement of the foundations. On the other hand, the 
hinges are often an expensive detail. It is sometimes claimed also that thiee- 
hinged arches are not so rigid as fixed arches, but because of their great 
weight this criticism does not appear to be well founded. 

*Scc p. 502. 
fSee p. 590. 


540 


A TREATISE ON CONCRETE 


In the design of a hinged structure the moment is usually assumed to be 
zero at the hinge. This assumption is not strictly correct because as the 
structure deforms under its load it tends to rotate about its hinges and 
this produces friction at the hinge due to the thrust acting thereon. 

The design of the hinge is a most important feature. One of the most 
instructive failures in arch construction was that of the Maximilian Bridge 
at Munich, a three-hinged voussoir masonry arch of two spans, each 144.3 
feet, when during construction, both spans of the bridge slipped off the 
hinges at the springings and dropped about 12 inches. This failure was 
due to an error in the design of the hinges. The bearing surfaces of the 
hinges were not given sufficient curvature, and the friction which was relied 
upon to prevent slipping of the two parts composing each hinge was reduced 
to a minimum by the use of a lubricant, which gave a low coefficient of 
friction. 

Three-hinged construction is best suited to arches of small rise where 
the center line of the rib can be made to fit closely the line of pressure 
resulting in small bending moments. Arches with one or two hinges are 
more indeterminate than three-hinged arches and have practically all of 
the disadvantages of both the fixed and the three-hinged types. 

SHAPE OF THE ARCH RING 

For hingeless arches the intrados should be either three-centered, five- 
centered or elliptical, while, if desired, the extrados may be the arc of a circle 
so placed as to give greater depth to the arch ring at the springings than at 
the crown. A segmental arch, that is an arch formed by the segment 
of a single circle cannot often be used to advantage, for it seldom can be 
made to fit the line of pressure. While many arches are elliptical in 
form, the three-centered intrados is perhaps the most common and it is 
pleasing to the eye, easily constructed and gives an economical design. 

Ribs with three hinges should be deepest at sections nearly midway 
between the crown and spring hinges, decreasing in depth toward the hinges, 
since sections near the hinges take only thrust and shear with practically 
no moment, while the intermediate sections resist a moment in addition to 
the thrust and shear. 

THICKNESS OF RING AT CROWN 

The next step in the design of an arch after deciding on the shape of the 
intrados is to choose a trial thickness of the ring at the crown and at the 
springing. The choice may be made by judgment based on experience or 


A RCHES 


54i 


with the aid of one of the various empirical formulas in use. Since the 
crown thickness depends not only on the amount of thrust but also upon 
the bending moment, which varies greatly in a given arch due to the varying 
positions of the live load, it is difficult and in fact impossible to devise a 
rational formula for its determination. 

The thickness of the arch ring should vary with the shape of the arch, 
with the span, rise, amount of filling over the ring, the amount of live load 
and the material of which the arch is made, and while there is no formula 
that will apply even approximately in all cases, the formula by Mr. F. F. 
Weld* gives fairly correct results in ordinary cases. It is as follows: 

Let 

h — crown thickness in inches. 

L = clear span in feet. 

w = live load in pounds per square foot, uniformly distributed. 
w f = weight of fill at crown in pounds per square foot. 

Then 

7 /— L w w f 

h — i L + — + + * (1) 

10 200 400 

Obviously the thickness for a hingeless arch should increase from the 
crown to the springing. The radial thickness of the ring at any section 
is frequently made equal to the thickness at the crown multiplied by the secant 
of the angle which the radial section makes with the vertical. For a 3- 
centered intrados and an extrados formed by the arc of a circle, these trial 
curves may be at the quarter points a distance apart of ij to ij times the 
crown thickness and at the springings 2 to 3 times the crown thickness. 

These empirical rules should be used only in preliminary study and 
never for the final design. The true shape of the ring and the thickness at 
different sections must be fixed by computation based on the line of pres¬ 
sure as described in the pages which follow. 


LIVE LOADS FOR HIGHWAY BRIDGES 

For highway bridges the kind and magnitude of the live load depend 
upon the location of the structure. Each location should be studied and 
the live load chosen to fit the requirements. The following classification 
is sufficient for stone or concrete arches and may also be applied to beam 
and slab construction. 


*Engineering Record, Nov. 4, 1905, p. 529. 




A TREATISE ON CONCRETE 


542 

City Bridges. For floors of city or other bridges carrying heavy traffic, 
three types of loads are recommended as follows: 

1. A uniform live load of 100 pounds per square foot on sidewalks and 
roadways. 

2. On each street railway track, one 8-wheel electric car having a wheel 
spacing of 5, 15, 5 feet between centers of wheels along one rail; each wheel 
carrying 12,500 pounds. The car is assumed to cover an area 9 feet wide 
by 40 feet long. 

3. One wagon weighing 20,000 pounds on each of two axles 12 feet apart. 

In applying these loads to find the maximum stress in the floor, either 

of the loads mentioned, or that combination of any of the above loads 
which produces the maximum stress, should be used. If the uniform 
load is used simultaneously with either of the concentrated loads, the former 
should cover only that part of the roadway not covered by the latter. 

For arch rings or ribs having a span of 100 feet or less, a uniform load of 
1800 pounds per linear foot of each railway track together with a uniform 
load of 100 pounds per square foot of remaining area of roadway and side¬ 
walks. 

For spans of 200 feet or more, a uniform load of 1200 pounds per linear 
foot of each railway track together with a uniform load of 80 pounds per 
square foot of remaining area of roadway and sidewalks. 

The load on each track should be assumed to cover a width of 9 feet, 
thus giving 200 pounds per square foot under the track for spans of 100 feet 
or less and 133 pounds per square foot for spans over 200 feet in length. 

For spans between 100 and 200 feet, the loads are to be taken proportion¬ 
ally. 

Suburban, Town or Heavy Country Bridges. For floors of suburban, 
town, or heavy country bridges, the same uniform load and electric car 
load as for floors of city bridges but with wagon weighing 10,000 pounds 
on each of two axles 10 feet apart. 

For arch rings or ribs having a span of 100 feet or less, a uniform load of 
1800 pounds per linear foot of each track, together with a uniform load of 
80 pounds per square foot of remaining area of roadway and sidewalks. 

For spans of 200 feet or more the' values corresponding to the above are 
1200 pounds per linear foot of each track and 60 pounds per square foot of 
remaining area. 

The load on each track should be assumed to cover a width of 9 feet. 

For spans between 100 and 200 feet, the loads are to be taken propor¬ 
tionally between the limits stated. 

Light Country Bridges. For floors of light country bridges, sub- 


ARCHES 


543 


jected to light highway or electric railway traffic, on each track one 8-wheel 
electric car carrying 9000 pounds on each wheel, or one wagon weighing 
6000 pounds on each of two axles 10 feet apart. These two loads should be 
assumed to act together where necessary to produce the maximum stress 
in the floor. 

For arch rings or ribs having a span of 100 feet or less, a uniform load of 
1200 pounds per linear foot of each track, together with a uniform load of 
80 pounds per square foot of remaining area of roadway. 

For spans of 200 feet or more, the values corresponding are 1000 pounds 
per linear foot of each track, and 50 pounds per square foot of remaining 
area. 

For spans between 100 and 200 feet the loads are proportional between 
the limits stated. 

It is customary to see that the design is sufficient to carry a steam road 
roller. The heaviest roller usually specified weighs 30,000 pounds, 12,000 
pounds on the front roller, which has a width of 4 feet, and 9000 pounds 
on each of the two rear rollers, each of the latter having a width of 20 inches. 
The axles are taken as n feet apart and the two rear wheels as 5 feet 
center to center. 

LIVE LOADS FOR RAILROAD BRIDGES 

For railroad bridges the loading depends upon the location of the line, 
and hence the future traffic which may be expected. Two consolidated 
locomotives, with 25 000 pounds on each driving wheel, followed by 5000 
pounds per foot of each track, is a common loading. An alternate plnn 
quite generally followed for the rings of stone or concrete arches where the 
filling is of sufficient thickness to distribute the concentrated loads over 
a considerable area of arch ring is to use 5000 pounds per foot of track 
with no concentrated load. This load of 5000 pounds per foot of track 
is equivalent to about 625 pounds per square foot of horizontal area. These 
values are satisfactory for spans, say, over 80 feet in length. 

Generally speaking, the shorter the span the greater should be the 
assumed uniform load, and hence for spans of, say, 80 feet or less, a uniform 
load of 1000 pounds per square foot is frequently adopted, this being 
approximately equivalent to the heaviest locomotive loadings. 

A concentrated load on top of a fill is generally assumed to be distrib¬ 
uted downward at angles of 45 0 . The top of the distributing slope may 
be taken from the ends of the ties. Wheel loads may be taken as dis¬ 
tributed over 3 feet of length of surface of fill and at 45 0 angles through 
the filling. 


544 


A TREATISE ON CONCRETE 


DEAD LOADS AND EARTH PRESSURE 

With open spandrels having columns or transverse walls, the dead loads 
act vertically upon the arch ring and can be more accurately found than 
with filled spandrels. 

With spandrels filled with earth the dead load carried by the arch ring 
is that due to the weight of the roadway, of the filling, and of the arch ring 
itself. The earth filling is usually assumed to act vertically, in which case 
the forces acting on the arch are easily computed. For arches in which 
the ratio of rise to span is small, such an assumption is sufficiently correct. 
A common assumption for weight of earth fill where the actual value is 
unknown is 100 pounds per cubic foot. 

Since the pressure produced by the earth filling against the extradosal 
surface of the ring is really inclined, being nearly vertical near the crown 
and considerably inclined near the springings, it is sometimes advisable in 
an arch of large rise to take account of the horizontal component of the 
pressure near the springings. The earth pressure acting against an inclined 
plane may be found either algebraically or graphically. The algebraic 
solution is given under the subject of retaining walls, page 665, and in the 
example of arch design the inclined pressure is taken into account for 
illustration, although it is really unnecessary in the case selected. (See p.576.) 

OUTLINE OF DISCUSSION ON ARCH DESIGN 

The method of designing an arch by the elastic theory is illustrated by the 
example on pages 574 to 582. The steps to be taken are there stated in 
full. 

In the following pages the reactions at the supports, which in an arch 
are not simple vertical forces, and the relations between the outer loads and 
the internal stresses, are first treated briefly so as to understand the theory 
in a general way. Next (p. 553), the working formulas are given for find¬ 
ing the thrust, shear and bending moment at the crown, and at intermediate 
points in the arch ring. From these, the force polygon and the line of 
pressure, which is an equilibrium polygon drawn for a pole distance equal 
to the horizontal thrust, may be drawn (p. 555). The method of determin¬ 
ing the stresses due to temperature and rib shortening is given (p. 556). 
Since the lines of pressure do not ordinarily pass through the center line of 
the arch ring, the pressures on the various sections are eccentric, and the 
distribution of stress in an arch under different conditions is discussed at 
length, the same analyses applying also to any other member like a column, 
subjected to eccentric pressure (p. 558 to 574). Diagrams are presented 




I 


ARCHES 545 

to aid in the determinations. Following the example, the design of arch 
abutments is given (p. 583), and beyond this are general directions with 
reference to construction details. Several typical arches are illustrated 

(P- 589)- 

RELATION BETWEEN OUTER LOADS AND REACTIONS AT 

SUPPORTS 

An arch differs from a beam in that under vertical loads the reactions 
at the supports of the arch are inclined, while for a beam the reactions are 
vertical. The loads acting on the arch, together with the reactions caused 
by the loads, constitute the entire system of forces acting, and for a com¬ 
plete analysis of the arch the relation between these forces should be deter¬ 
mined. This relation is more simply deduced if for each reaction there are 
substituted its horizontal and vertical components. 

For arches symmetrical about the center line of span the following analy¬ 
sis is applicable. For unsymmetrical arches, methods similar to those pre¬ 
sented in the following pages are to be employed although the necessary 
formulas are too long to be given here. 

NOTATION 

H r and V x = horizontal and vertical components of the left reaction. 

H 2 and V 2 = horizontal and vertical components of the right reaction. 

M 1 and M 2 = moments at left and right supports respectively. 

M = moment at any point on arch axis having coordinates x and y. 

M c , H c , V c = moment, thrust and shear at the crown. 

M l — moment at any point on left half of arch axis of all loads between the 
point and the crown. 

M r = moment at any point on right half of arch axis of all outer loads 
between the point and crown. 

m = number of divisions into which the half length of arch axis is divided, 
x = short length of arch axis. 

/ = moment of inertia of cross section about the gravity axis. 

L = horizontal span of arch axis. 
r = rise of arch. 

E c = modulus of elasticity of concrete. 
n = ratio of moduli of elasticity of steel to concrete. 

R = resultant force acting on any section of the arch ring. 

N = thrust = normal component of resultant R. 

V = shear = radial component of resultant R. 


546 


A TREATISE ON CONCRETE 


H = horizontal component of resultant R. 

P = any concentrated load. 

J L = change in span length due to any cause, + for an increase, — for a 
decrease. 

t “ rise or fall in temperature of the arch ring from the mean in degrees 
Fahrenheit. 

c = coefficient of linear expansion or contraction. 

/ = average unit compression in concrete of arch ring due to thrust. 

<p = central angle subtended by the axis of the arch. 
x,y = coordinates of any point on the axis of the arch ring. 

Three-Hinged Arch. The use of the three-hinged arch is discussed 
on page 539. Since its analysis is simplest and at the same time illustrates 
important principles of arch design, it is considered first. 

Referring to Fig. 157, it is seen that there are two unknown components 



of each reaction, making four unknown quantities, H „ F,, H«, V 2 , which 
require four equations to solve them. From statics we have the three 
equations of equilibrium: 

Algebraic sum of vertical components = zero. 

Algebraic sum of horizontal components = zero. 

Algebraic sum of moments of all forces about any point = zero. 

We have here an additional equation from the fact that the bending 
moment at the crown hinge = o. Therefore the four components of the 
reactions can easily be found. Suppose there is only one load, P, on the 
span. Then 




and F, 


P (L-z) 
L 



Since, for equilibrium, the moment at the crown hinge must be o, the 
resultant reaction on the left must pass through the left hinge, or 

, (L \ . Fj L 

M - ) — II x r = o. Ilcncc IL = - (4) 

\ 2 / 2 r 

V v H j = components of left reaction. V v H 2 = components of right reaction. L = span. 
r = rise. 














A RCHES 


547 

When all loads are vertical, or in any case when the loads are symmetrical 
about the center, = H 2 . 

When the loads are not symmetrical and also not vertical, H 2 can be easily 
found, after H x has been determined as above, from the relation that the 
algebraic sum of all the outer horizontal forces = o. In a three-hinged 
arch, then, the reactions having been found by means of simple statics 
as above described, the thrust, shear and bending moment on any section 
of the arch can be computed and sections designed.* 

Two-Hinged Arch. Under the action of the loads on this arch there 
are produced two components of the reaction at each support, making in 
all four unknowns, H lt V u H 2 , V 2 . From statics we have the three funda¬ 
mental equations of equilibrium, as given above. We must find an addi¬ 
tional equation from the theory of elasticity. This additional equation is 
obtained from the fact that the span does not change its length under the 



action of the loads. From mechanicsf we know that if the arch were 
fixed at B and free at A, the horizontal motion of A (the origin of coordi- 

s 

nates) is given by I My —, where 2 denotes the summation of the products 


of My —for each section of the arch. Now, since the arch is really pre- 
El 


vented by the support from moving horizontally at point A, the above 
deformation can be placed equal to o, and we have then the fourth equation 
s 

I My -—- = o, which, in addition to the three from statics, enables us to 
El 


find the reactions H u H 2 , V 2 . As soon as the reactions are known, the 
thrust, shear and bending moment at any section of the arch can be found. 


*Three Hinged Masonry Arches; Long Spans Especially Considered, by David A. Molitor, 
Transactions American Society of Civil Engineers, Vol. XL, p. 31. 

•{•“Mechanics of Engineering,” by Irving P. Church, 1908, p. 449. 












548 


A TREATISE ON CONCRETE 


In a similar manner the conditions of equilibrium can be obtained for an 
arch with only one hinge (at the crown). 

“Fixed” or “Continuous” Arches. A method frequently followed 
with the hingeless arch is to consider the reactions at the ends in the same 
way as in hinged arches, but the simpler method is to take the forces at a 
section through the crown. However, in order to better understand the 
theory and the relation of Ihe external to the internal forces, the arch reac¬ 
tions at the supports will be discussed first and afterward the analysis will 
consider the forces at the crown. 

Let Fig. 159 represent a hingeless arch. The loads having been deter¬ 
mined, there are at each support three unknown quantities, namely, the 
vertical and the horizontal components and the point of application of the 
reaction. Or, instead of saying that the point of application of the reaction 



is unknown, we can say that there is a bending moment at each support, and 
that this moment, together with the horizontal and vertical components of 
the reaction, makes three unknown quantities at each support to be found. 
There are then six unknown quantities to be determined, namely, H u V l} 
M u H 2 , V 2 , M 2 . 

Statics provides the three fundamental equations of equilibrium (see 
page 546), hence three additional equations must be determined from the 
theory of elasticity. These three additional equations are given from the 
three following conditions: 

The change in span of the arch = Ax — O 

The vertical deflection at A (the origin of coordinates) = Jy = O 

The change in direction of the tangent at the arch axis at A = A<f> = O 

These three conditions must be true since the arch is fixed at A and at B, 
the abutments being assumed immovable 













From mechanics,* 


ARCHES 

549 

From mechanics,* 


Jx =Z B A My~ =0 

(5) 

O 

II 

, y — 1 

^ tq 

II 

(6) 


( 7 ) 

These three equations are general formulas. They are not used directly 
in arch computations but are necessary in the theoretical derivation of the 
working formulas given in paragraphs which follow. 

These three equations express the conditions that the horizontal, vertical 
and rotary movements of the left end of the arch ring each equal zero, 


so far as these motions are caused by the bending moments only , acting on 
the different sections from B to A. The movements due to the thrust and 
shear within the ring are not here considered. By means of equations (5), 
(6), (7) and the three from statics (see p. 546) we can solve for the six 
unknown quantities at the supports, namely, the horizontal and vertical 
components of each reaction and the moment at each support, and having 
thus found the reactions, the stresses within the arch ring can then be com¬ 
puted. 

RELATION BETWEEN OUTER FORCES AND THE THRUST, SHEAR 
AND BENDING MOMENT FOR THE FIXED ARCH 

In Fig. 160 let the arch A B be fixed at the two supports. If the loads are 
fcncwn, the horizontal and vertical components of the reactions and also the 
moment at each support of the arch may be found, as has been shown 
above. Having these three quantities for each support, the point of appli¬ 
cation of each reaction may then be determined. 

Thus in Fig. 160 the point of application at the left support is at a , dis- 

M x M 2 

tant y x vertically from A, where y x = — . Similarly at B, y 2 = —. Having 

computed y x and y 2 , thus locating the points of application of the reactions, 
the force polygon and its equilibrium polygon, abed, can be drawn, as 
described more fully on page 577, and the latter will be the true line of pres¬ 
sure for the loading shown. The stresses on any section such as D may 

M = moment. s = short length of arch axis. E = modulus of elasticity. I = moment 
.nertia. d x = change of span length, xy = coordinates of a point. 

*See “Mechanics of Engineering,”by Irving P. Church, 1908^.449, or any general treatise 

on mechanics. 



55° 


A TREATISE ON CONCRETE 


be then studied. The resultant of all outer forces on the left of D is a force 
acting along the line a b of the equilibrium polygon and having a magnitude 
eauai to the force O 0 of the force polygon. This resultant outer force O 0 



u' 


Fig. 161.—Forces Acting upon an Arch Section. (See p. 550.) 

acting along ab is resisted by inner forces, i. e., stresses, on the section D 
which is redrawn in Fig. 161. 

Th.- force R is the force opposing the resultant O 0 . This force is equiva- 

















ARCHES 


55 T 


lent to a force R acting at the arch axis and a bending moment = Rid = 
Hu, where H is the horizontal component of R and u is the vertical distance 
from point D on the arch axis to the equilibrium polygon; u' is the perpen¬ 
dicular distance from point D to the force R = O 0 . For vertical loads II 
is constant throughout the length of the arch ring. 

1 he resultant force R acting at D can be resolved into two components 
one of which, N, is tangential to the axis at D and therefore normal to the 
section of the arch ring; the other component, F,is perpendicular to the axis 
and parallel to the section. 

A 7 is the thrust, that is, the tangential component of the resultant force 
on the section. 

V is the shear] that is, the radial component of the resultant force on the 
section. 

Hu or Ru' is the bending moment about the gravity axis of the section. 

Evidently there are sections of the arch where the equilibrium polygon 
intersects the arch axis. At these sections the bending moment is zero. 
Furthermore, if the equilibrium polygon is normal to any section there will 
be no shear on that section. It is possible then to find sections where there 
is no moment, or no shear, or possibly where there is neither moment nor 
shear. There is always a thrust on every section. 


THRUST, SHEAR AND MOMENT AT THE CROWN 

Instead of actually finding the components of the reactions and the 
moments at the supports by the plan indicated on page 549, it is simpler to 
find the thrust, shear and moment at the crown. Having these, the equilib¬ 
rium polygon may be drawn and the thrust, shear and moment at any point 
may be found. The thrust, shear and moment at the crown can be found 
by use of equations (5), (6), (7), page 549, in which M is the moment of 
any point D of Fig. 160, page 550, expressed in terms of the values at the 
crown. Instead, however, of determining these quantities by means of 
these equations, shorter expressions for the thrust, shear and moment at 
the crown maybe obtained by taking the origin of coordinates at the crown 
and studying the motion at that point. 

In Fig. 162, CD represents the vertical section at crown, upon which acts 
the resultant pressure along the line A B. In the lower part of the figure, for 
this resultant force is substituted the horizontal thrust, H c , the shear, V c , 
acting at the center of the section CD , and the moment M c . 

Referring to Fig. 163, page 552, and accepting C as origin of coordinates, 


552 


A TREATISE ON CONCRETE 


Let 

x,y, — coordinates of any point D, 

M l =■ moment at any point D on left half of arch axis of all loads between 
the point and the crown. 

M r — moment at any point D on right half of arch of all loads between 
the point and the crown. 
m =* number of divisions of half of the arch axis. 



Fig. 162. —Moment and Thrust at the Crown. (See p. 551.) 



Fig. 163.—Coordinates of Any Point in Arch Axis. (See p. 551.) 

The formulas given below require that the arch be divided so that 
the ratio of length of any division to its average moment of inertia is 
constant. Because of this requirement the end divisions with large 
moments of inertia may be long, even with comparatively short divisions 
at the crown. This may cause an inaccuracy which can be largely elimi¬ 
nated by subdividing the load on the end divisions. 

The greater the number of divisions the more accurate the results. 

For an arch divided in such a way that the ratio of the length of any 
division to its average moment of inertia is constant (see page 554) 




























A RCHES 


553 


the three unknown quantities, V c , H c , and M c may be found from form¬ 
ulas* 




mZM R y + mZM L y - Z M R Z y — ZM L Z y 
2 [: mZy 2 — (Zy) 2 ] 

ZM L x-ZMrfc 
2 Zx 2 

ZM r + ZM l - 2H c Zy 


V c = 


M c = 


2 VI 


(16) 


(17) 


(18) 


*The horizontal motion of C, Fig. 163, as in preceding analysis, due to bending moments on sec- 

B s 

tions between B and C, is-Z ^ My-yy? The horizontal motion of C due to the bending moments 
on sections fc 

tion, hence, 


on sections between A and C ,is 2 My —* These two motions are equal but opposite in direc 

C El 


I* My 


s 

El 


-2 


Similarly the vertical motions at C are equal, 


C 

y B . - J_ y A 

2 C Mx El ~ ^ C 


My Tl 

(8) 

Mx E j 

(9) 


Also the changes in direction of the tangent to the axis at C are equal, but opposite in 
direction, hence, 


V B a, -L 

~ C M El 


2 C M El 


(10) 


If each half of the arch axis be divided into m divisions in such a way as to make y constant for 

.5 

all the divisions (See p. 554) the factor ~y and also E may be cancelled. In the equations (8), (9) 

(10), M, I, x , y, denote respectively the bending moment, moment of inertia of the cross-section, 
and coordinates at the center point of each division of the arch axis. 

At center of any division between A and C the bending moment is 

M = Me — Vex + Hey — Mr (ii ) 

At center of any division between B and C the bending moment is 

M = M c + Vex + H c y - M L (12) 

Placing these values of M in equations (8), (9) and (10) and collecting terms, we have 

2 Mc 2. y + 2 Hc 2 y 1 — 2 Mr y — 2 Ml y =0 ( 13 ) 

2 V c 2 x 2 — 2 Ml x -f 2 Mr x — o ( 14 ) 

2 mM c + 2 H c 2 y — 2 Mr — 2 Ml = o (15) 

Combining (13) and (15), 

i2 Mr y + m2 Ml y — 2 Mr 2y — 2 Ml 2 y 

2 [ m 2 y 1 — (2 y) 2 j 


Hr, = 


m. 


From (14) 
From (15) 


V c = 


2 Ml x -2 Mr x 


2 x 2 


Me = 


2 Mr + 2 Ml - 2 H c 2 y 


2 m 


(, 6 ) 

(17) 

(18) 


M — moment. H c — crown thrust. V c = crown shear, m = number divisions of half 
axis, x, y — coordinates of a point. 















554 


A TREATISE ON CONCRETE 


These are fundamental equations in arch analysis. The method of 
application is illustrated in the example, page 574. 

All 1 signs denote summations for one-lialf of the arch axis. 

All numerical values of M } , M R , x, y, are positive. 

A positive value of V c indicates that the line of pressure at the crown 
slopes upward toward the left; a negative value, upward towards the right. 

A positive value of M c indicates a positive moment at the crown; a nega¬ 
tive value, a negative moment. 

The moment at any point between B and C is 

M - M c - V c x + H c y - M R (19) 

while at any point between A and C 

M = M c +V c x+ II c y -M l (20) 




Fig. 165.—Diagram for finding Length of Arc of a Circle. 


(See p. 554.) 


GRAPHICAL METHOD FOR FINDING CONSTANT - 

I 

Fig. 164 and Fig. 165 give a graphical method of determining the length 

M — moment. He — crown thrust. ? c = crown shear, x, y = coordinates of a point, 
j = length of division of axis. I = moment of inertia r 



























A RCHES 


555 


of divisions for a constant . If the arch axis is made up of arcs of circles, 

the length of any arc ACB is equal to three halves of the straight line AC.* 
The point C is found in Fig. 165 by dividing the chord AB into thirds and 
drawing a radius through the one-third point. If the arc is an ellipse, a 
simple method of drawing which is given on page 202, the length may be 
measured from the drawing. Having found the length of the half axis and 

drawn it as a horizontal line, the constant — is found as shown in Fig. 164 by 

computing four or more values of I, the moment of inertia, at different 
points and plotting these to locate the curves as shown. Beginning at the 
lower left corner of the diagram, trial diagonals (parallel to each other) atid 
vertical lines are drawn, so that the number of spaces between the verticals 
will represent the number of divisions into which the half arch must be 
divided. If at the first trial the final diagonal does not come out exactly at 
the upper right corner which represents the crown of the arch, a new slope is 
tried for the parallel diagonals. 

LINE OF PRESSURE 

Having determined the thrust and moment at the crown, the line of pres¬ 
sure may be drawn as shown in folding Fig. 181, opposite page 580, from 
which the compression and tension at different sections may be found after 
determining the thrust and eccentricity from the formulas which follow. 

It is well to draw the line of pressure before considering the temperature 
and the effect of the rib shortening, and then afterwards study these, adding 
or deducting the stresses for the most unfavorable conditions. 

EFFECT OF TEMPERATURE AND THRUST 

The thrust acting throughout the ring tends to shorten the span. A 
change of temperature of the ring tends to shorten the span when the tem¬ 
perature falls or to lengthen the span when the temperature rises. The 
tendency for the span to change its length by a distance J L due to any cause 
is resisted by a horizontal component II and a moment M x acting at each 
support, and by a thrust and moment in the arch ring. d L is positive for 
an increase and negative for a decrease in span length. 


*Method given in Nouvelles Annales de Mathematiques, Jan. 1907. The error for 40 degrees 
is less than jq^oo> * or 7° degrees is less than jqV o> for 9° degrees is less than o* 


556 


A TREATISE ON CONCRETE 


The thrust and moment at the crown may be found from formulas* 



I mE A L 
s 2 \mly 2 — (2 y) 2 ] 


(23) 


and 



H c Iy 

m 


(24) 


Rise in Temperature. Under a rise of temperature of the arch ring of 
t degrees Fahr. the span L would tend to increase in length an amount 
of dL , c being the coefficient of linear expansion. Substituting for J L in 
(23) the value of ctL, the thrust at crown is 

I ctLmE 

Hc= 1 y) 2 ] (2S) 

The value of the temperature coefficient, c, in equation (25) may be taken 
for concrete as 0.0000055. Dimensions must all be in same units; if in 
feet, E must be in pounds per square foot. Using a value of E c of 2,000,000, 
E is therefore 2,000,000 X 144= 288,000,000 pounds per square foot. 

Moment at crown is 

H c Iy 

M c - - ' (26) 

m 


*The change in total span length, the two halves of the arch being equal, is 


C My El = AL ( 2I ) 

The change in inclination of tangent to axis at crown is 

2i C M Jl~° (») 

Replacing the M of equations (21) and (22) by M c + H c y, which is the moment at any point D, 

j 

Fig. 166, in terms of moment and thrust at the crown, and making j constant, there results 

-McZy + i^Hdf-tL 
mM c + H c 2 y — o 


From which 


and 


H c = 


m E A jj 


s 2 [m 1 ' y 2 — (2’ y) 2 ] 

H c ly 


M c = - 


m 


U3) 


(24) 


M = moment. He = crown thrust, m = number divisions of half axis. s = length of 
division of axis. I = moment inertia. L = span. E — modulus of elasticity. Jl=- change of 
span length, t = rise or fall of temperature, c = coefficient of expansion, at, y = coordinates of 
a point. 








ARCHES 


557 


The moment at any point D may be found as soon as the values of H c 
and M c have been determined by means of the relation 

M = M c -t- Hj (27) 

or we can say that the moment at any point equals the thrust H* multi¬ 
plied by the distance from the point in question to the line 00 , Fig. 166. 


x c 



Above the line OO, Fig. 166, the moments are all negative, being a maxi¬ 
mum at the crown, and below OO they are all positive, being maximum at 

ly. 

A and B. The line OO is below the crown a distance d = —- At the two 

m 

points where OO intersect the arch axis the moments are zero, as is evident 
from equations (24) and (26). 

Fall in Temperature. Here the thrust at crown is 


I c tLmE 

Hc= ~ 7 7 \mJf - ( Yfr ] 

where c is 0.0000055, an d moment at crown is 

H c Zy 


M c = - 


m 


(28) 


(29) 


and, as above, 

M = M c + H c y (30) 

In placing a numerical value for H c in the last two equations, it should 
be observed that it is a negative quantity. If in the equations the values 
of L and y are in feet, E is in pounds per square foot. Above 00 the 
moments are all positive, below they are all negative. The thrust at the 
crown is really a tension in this case. 


M = moment. He = crown thrust, nt = number divisions of half axis, s = length of 
division of axis. I = moment inertia. L = span. E == modulus of elasticity, t =rise or fall of 
temperature from mean, c = coefficient of expansion, x, y = coordinates of a point. 

♦The horizontal thrust is constant throughout the arch, hence H c at the crown equals H at 

the support. 
















5S» 


A TREATISE ON CONCRETE 


An increase and a decrease of 20 degrees Fahr. is probably a sufficient 
allowance for concrete arches with filled spandrels. For arches with open 
spandrels the range in temperature of the concrete is somewhat less than 
that of the surrounding air. For example, in the latter case with a range 
of temperature of the air from —20 degrees to +100 degrees Fahr., the 
range for arch computation should be taken at least 40 degrees on each 
side of the mean temperature. 

The methods of combining the temperature moments and thrusts with 
those due to loads is illustrated in the example, page 579. 


EFFECT OF RIB SHORTENING DUE TO THRUST 


The thrust acting throughout the arch ring tends to cause a shortening 
of the span, which, if / is average compression (obtained by averaging 

fL 

values in computation of ring) for unit area, = = J L 

JOj 

Hence 


I f Lm 

^ c s 2 [m 2 ' y 2 — (2'y) 2 ] 


(3 x ) 


and 



H c 2y 

m 


(32) 


and, as in temperature stresses, 

M - M c + H c y (33) 

The effect of the rib shortening is similar to a fall in temperature. 

All the summations above are for one-half the span only, m = number 
of divisions in one-half of the arch axis. 

The effect of rib shortening is slight in many cases but in a flat arch it 
may be considerable. 


DISTRIBUTION OF STRESS OVER CROSS SECTION 

The analyses of stress distribution which follow apply not only to an arch 
but also to any section where there is combined compression and bending. 

In an arch, having determined the thrust, shear and bending moment 
at any given section of the arch ring, the distribution of stress upon the 
section must be next investigated in order to compute the maximum stresses 

M — moment. He — crown thrust. m = number divisions of half axis, s = short length 
of arch axis. I moment inertia. L — span, y = coordinate of a point, f — compression 
in concrete. 




ARCHES 


559 

in the concrete and the steel to see on the one hand that they do not exceed 
safe working loads, and on the other hand that the design is as economical 
as possible. 

Concrete is strong in resistance to direct shear (See p. 382), and hence 
the shear is generally negligible in concrete and reinforced concrete arches, 
although it should be considered in stone masonry arches. Since, also, as 
will be shown, the bending moment is the thrust times its eccentricity, it 
follows that the determination of the thrust, which is the normal compo¬ 
nent of all the forces acting, together with the location of its center of pres¬ 
sure, permit the determination of the stresses required in designing any 
section of an arch or of any section of any member subjected to eccentric 
stress. Every section of the arch or of a beam or of a column must be of 
such dimensions or with such reinforcement that the safe working stresses 
in the concrete shall not be exceeded. 

Plain concrete sections and reinforced concrete sections are considered 
separately, the same notation being used for both. 


Notation 

Let 

R = resultant of all forces acting on any section. 
f c = maximum unit compression in concrete. 

f' c = maximum unit tension in concrete or minimum compression. 

N = thrust, a component of the forces normal to the section. 

y = shear, the component of the force R parallel to the section. 

b — breadth of rectangular cross section. 
h — height of rectangular cross section. 

e = eccentricity, that is, the distance from gravity axis to the point of 
application of the thrust which is the intersection of the line of 
pressure with the plane of the section. 

M = bending moment on the section. 

y = perpendicular distance from gravity axis to any point in the section. 

I = moment of inertia of entire cross section of concrete about the hori¬ 

zontal gravity axis. 

/ = moment of inertia of cross-section of steel about the horizontal grav- 

5 

ity axis. 

A = total area of section of concrete. 

C 

A 8 = total area of section of steel. 

y 1 = perpendicular distance from gravity axis of unsymmetrical section 
to outside fiber having maximum compression. 



A TREATISE ON CONCRETE 


560 

y, ■=■ perpendicular distance from gravity axis of unsymmetrical section 
to outside fiber having maximum tension or minimum compression. 
/' = maximum unit compression in the steel. 

f s = maximum unit tension or minimum unit compression in the steel. 
p = ratio of steel to total area of section; for rectangular sections p = 

ratio of steel area to bh. 

'E 8 

n =— = ratio of moduli of elasticity of steel and concrete. 

k — ratio of depth of neutral axis to depth of beam h. 
kh = distance from outside compressive surface to neutral axis. 
d f = depth of steel in compression. 
d = depth of steel in tension. 

a = distance from center of gravity of symmetrical section to steel. 
e 0 = value of eccentricity which produces zero stress in concrete at outer 
edge of rectangular section opposite to that on which thrust acts. 
C a , C e = constants. 

DISTRIBUTION OF STRESSES IN PLAIN CONCRETE OR 

MASONRY ARCH SECTIONS 

In designing plain concrete or stone masonry arches, the maximum com¬ 
pressive stresses must be kept within the safe working compressive strength 
of the material, and the point of application of the thrust must not lie out¬ 
side of the middle third of the section. When investigating an existing struc¬ 
ture, however, it may be found that the thrust acts outside of the middle third, 
so that a determination of the stresses in such cases must also be considered. 

Plain Arches with Rectangular Cross Section. In plain concrete or stone 
masonry arches of rectangular cross-section there are five special cases 
depending upon the point of application of the thrust, as follows: 

(a) Thrust acting at gravity axis of cross-section. 

( b ) Thrust not acting at gravity axis of cross-section, but within the mid¬ 

dle third of the section. 

(< c ) Thrust acting at edge of middle third of the section. 

(1 d) Thrust acting outside of the middle third of the section and material 
able to carry tension. 

(e) Thrust acting outside of the middle third of the section and material 
not able to carry tension. 

Each of these ca^es will be considered. 

(a) When the thrust acts at the gravity axis of the cross-section the stress 
is compression over the entire section and is uniformly distributed 
as in Fig. 167. 



ARCHES 


561 


Maximum compression in concrete is 

' N 

/c = hh ( 34 ) 

( b ) The thrust acts within the middle third but not at the gravity axis, 
as shown in Fig. 168. When the thrust acts at any other point than the 
gravity axis there is combined bending moment and direct stress to be con¬ 
sidered. If the bending moment is positive, the thrust acts above the 
gravity axis; if negative, the thrust acts below. In either case the thrust 

N 

produces a unit compression of — over the entire section. The moment 
causes compression on the side of the axis where N acts and tension on the 


K 




ARCH AXIS > - 


04 


04 


Fig. 167.—Stresses Caused by a Force 
Acting in the Middle of Plain Con¬ 
crete Section. (See p. 560.) 



Within the Middle Third of Plain 
Concrete Section. {See p. 561.) 


opposite side. By mechanics, the intensity of stress due to the moment, M % 

Mv 


at a distance y from the gravity axis is 


The actual combined stress 


N My. 

at any distance y is then the sum of these two stresses, namely, — ± —j- 

The positive sign applies to stresses on the side of the axis where N is 
applied and the negative sign to stresses on the opposite side. 

bJf 

Since for a rectangular section, I = — and M = Ne, thrust multi¬ 


12 


plied by eccentricity, we have: 


N 


Stress at any point y distance from gravity axis - — ( 1 ± 


12 ey 


( 35 ) 


bh \ h 3 

The stress at all points of the section is compression and the maximum 

M = moment, fc = compression in concrete. N — thrust, b = breadth. h = height. 
y = distance from gravity axis, e = eccentricity. I = moment of inertia. 
























































562 


REINFORCED CONCRETE DESIGN 


and minimum values are at the top and bottom of the section, respectively, 

h, 

that is, when y «= —- 


Maximum compression = f c — 
Minimum compression = f' c — 


N 

bh 

N 

bh 


1 + 


1 — 


6 e 

h 

6 e 


(36) 


(37) 


(c) When the thrust acts at the edge of the middle third the eccentricity 
h 

e = —and the maximum and minimum values of the stresses are found by 
0 

h 

placing— for e in the last two 

formulas of case (b). Fig. 169 
shows the distribution in this case. 
Maximum compression in con- 
2 N 

crete - jh (38) 

Minimum compression in con¬ 
crete = o. 

(d) If the thrust acts outside 
of the middle third and the ma- 



Fig. i 69.—Stresses Caused by a Force Act¬ 
ing at the Edge of the Middle Third of 
Plain Concrete Section. (See p. 562.) 


terial is capable of carrying some tension, the distribution of stress is as 
shown in Fig. 170. There will be compression over a large part and tension 
over the remainder of the section. 


Maximum compression = f c = 


N 

bh 


6 e 

1 + h 


, N ( 6e\ 

Maximum tension = /"„=— 1 — — I 

c bh \ h/ 


( 39 ) 

(40) 


Evidently in each of the above cases (a), (b ), (c), ( d) the maximum com¬ 
pressive and minimum compressive (or maximum tensile) unit stresses are 

N ( 6 e\ 

given by the one general formula — ^ 1 ± — ). This applies for rectangular 

sections and will hold so long as the safe tensile strength of the concrete is 
not exceeded. 

In arches of plain concrete or of stone, tension should not be allowed to 
exist. 

(<?) When the thrust acts outside of the middle third and the material 


































ARCHES 


563 



Fig. 170.—Stresses Caused by a Force 
Acting Outside of the Middle Third of 
Plain Section. (Seep. 562.) 


is not able to carry tension, the stress is distributed as compression over 
a depth less than the entire depth of the section, and cracks may be expected 
on the “tension” side. The distribution of stress is shown in Fig. 171 below, 

where (in addition to notation 
already presented on page 559). 

g = distance from point of 
application of thrust to most com¬ 
pressed surface. 

Maximum compression = 

2 N 

3 H ^ 

Plain Arches with Irregular 

Cross Section. If the section is 
not rectangular, the maximum 

N Ney. x 

unit compression = — + j ’ 

and the minimum unit compression (or maximum unit tension) = 
N Ney 2 

-j- — ' jT . When the second term of this equation is greater than the 
first, the concrete is in tension. 

DISTRIBUTION OF STRESSES IN REINFORCED CONCRETE 

SECTIONS 

Reinforced Concrete Sections of any Shape. The distribution of 
stress caused by combined thrust and bending moment over a section 
containing steel reinforcement is 
shown by the following formulas. 

As in column design (page 490) 
the area of the steel in compression 
may be replaced by an equal area 
of concrete by multiplying the steel 
area by n, the ratio of the modulus 
of elasticity of steel to the modulus 



of concrete. Similarly, their mo- Fig. 171.— Stresses Caused by a Force 
ments of inertia may also be com- Acting Outside the Middle Third of 

pared, and the section treated as if plain Concrete Section - <?*» 5 6 3 -> 

it were of concrete without steel. 

The unit stress then in the concrete at any distance, y, from the gravity 

y x y 2 = distances respectively from gravity axis to maximum compression of tension. 
b — breadth of cross section. 































































5 6 4 


A TREATISE ON CONCRETE 


N Ney 

axis is —j-— ± -—. The stress may be compression over the 

entire section or may be compression over a portion of it and tension over 
the remainder. The formulas apply in either case so long as the safe tensile 
stress in the concrete is not exceeded. 


Maximum compression in concrete = f c = 


N 


+ 


Ney { 


, where 


A c + nA 8 I + nl s 
y x is the distance from the gravity axis to outermost fiber of concrete on the 
side of the gravity axis on which the thrust acts. 

N Ney 3 


Maximum compression in steel = f s 


n 


A c + nA , 


+ 


I + nl 


s 


, where 


y 3 is the distance from gravity axis to center of gravity of steel on side of 
gravity axis on which the thrust acts. 

N Ney 2 


Minimum compression in concrete = f = 


A„ + nA 0 I + nl, 


, where 


y 2 is the distance from the gravity axis to the outermost fiber of concrete on 



-- b -► 




^ • 


» - < 


LINE OF THRUST 









< 

> 



4s 



' 

1 ? 




? 

k 

J 


• • 

5 

' ' 


Fig. 172. —Cross Section of an Arch Rib. ( See p. 564.) 


the side of the gravity axis opposite to that on which the thrust acts. This 
minimum compression is of course tension when the second term in the 
last equation is greater than the first. 


Minimum compression in steel = / = n 

S 

y 4 is the distance from the gravity axis to center of gravity of steel on the 
side of gravity axis opposite to that on which the thrust acts. 

Reinforced Concrete Rectangular Sections. For rectangular sections 
the above general formulas for sections ux any shape may be 
put into slightly simpler forms by substituting the proper terms and 
assuming equal amounts of steel above and below the center. Special 


N 


Ney A 


A r 4* nA, I + nl a 


, where 
































ARCHES 


565 


cases for convenient use in design are also treated below. Since total 

bh 3 

moment of inertia of combined section, /+/,=—+ npbha 2 ; area of 

section, A, = bh and area of steel in the section, A s , = pbh , we have: 

Unit stress in concrete at any point at a distance, y, from gravity axis 

N 


is 


± 


12 ye 


bh L 1 + np h 2 + 12 npa 2 _ 

Maximum unit compression in concrete 


Sc = 


N 

bh 




6 he 


1 + np h 2 + 12 npa 2 _ 


(42) 


Maximum unit compression in steel 


/; = 


nN 

Jh 


+ 


12 ae 


1 E np h 2 + 12 npa 2 _ 


(43) 


Minimum unit compression (or maximum unit tension) in concrete 


fc = 


N 


6 he 


bh L 1 + np h 2 + 12 npa 2 _ 

M nimum unit compression (or maximum unit tension) in steel 


(44) 


/. = 


nN 

bh 


12 ae 


(45) 


f’lhliC- 



3 


GRAVITY AXIS 


_ i + np h 2 + 12 npa 2 _ 

There are four cases which may occur depending upon value of e. 

(1) Thrust applied at grav¬ 
ity axis, as in Fig. j 73, where 
there is no moment on the sec¬ 
tion and the stress is uniformly 
distributed. In this case the 
second term in the brackets of 
the above formulas becomes 
zero. 

(2) Thrust applied at such 
distance from the gravity axis 
as to cause compression on 
whole section of the concrete, 

as in Fig. 174. Here the above formulas are used directly. 

n = ratio elasticity. N = thrust. y = distance from gravity axis, fc = compression in concrete 
fs = tension or minimum compression in steel, b = breadth, h — height, e =■ eccentricity 
p = ratio of steel, a = distance from center of gravity of section to steel. 


Fig. 173. Stresses Caused by Force Acting 
at Gravity Axis. (See p. 565.) 
























































566 


A TREATISE ON CONCRETE 


(3) Thrust applied at such distance from gravity axis that the compres¬ 
sion at one surface becomes zero, as in Fig. 175. In this case the formulas 
may be simplified as follows: 


Maximum unit compression in concrete, 

2 N 

c bh( 1 + np) 

Maximum unit compression in steel, 

, nN 

f _= 

8 bh {1 + np) 


2 a 



Minimum compression in concrete = o. 

Minimum compression in steel, which is very small, 

nN 

^® bh( 1 -f 2 p) 



(46) 



(48) 


(4) Thrust applied at such distance from the gravity axis that there is 
tension at one surface, as in Fig. 176. 

The most important question for decision is the compression in the con¬ 
crete, which must not exceed a safe working stress and is readily found 
from formula (42), page 565, and the determination of whether the 
opposite surface is in tension or 
compression. A simple method 
for determining this is given in the 
following paragraphs together 
with a diagram, further simpli¬ 
fying the process. 

If the eccentricity is so great 
that tensile stress is found in the 
concrete as determined by methods 
described in the following para¬ 
graphs, a special treatment must 
be given to determine the stresses, 
as discussed on page 570. 

In case the result from formula (44) is negative, the stress on this surface 
of the concrete is tension. 

Eccentricity. As in plain concrete arches, the location of the center 
of thrust determines the distribution of the stress. The stress on one side of 


If'nhh I 1 ^ 

- 





— — — - — — 



c 

w 

< 

AftCH 

STEEL* 

<N 

AXIS 

L; 

ts 

< 

STEE S 






Fig. 174.—Stresses Caused by a Force 
Producing Compression upon the 
Whole Reinforced Section. {See p. 

565-) 


n = ratio elasticity. N = thrust. f c = compression in concrete, fs = tension or minimum 
compression in steel, b = breadth, h = height, p = ratio of steel. R = resultant of forces. 













































ARCHES 



Fig. 175.—Stresses Caused by a Force Acting at 
a Distance e 0 from Center of Gravity of Rein¬ 
forced Section. {See p. 566.) 


567 

the gravity axis is always compression and if the thrust acts at the gravity 
axis there is uniform compression over the section. As the center of 
thrust lies farther and farther from the gravity axis, the compression at the 
opposite surface decreases until finally it becomes zero and then tension. 

Equation (44), page 
565, gives a means of 
determining the eccen¬ 
tricity for which there 
can be neither tension nor 
compression at the sur¬ 
face opposite to that on 
which the thrust acts. 
For a reinforced arch this 
eccentricity is usually 
h 

more than - that is, the 
6 

line of pressure must not necessarily lie within the middle third. 

When the first term in the brackets of this equation is greater than the 
second, the minimum stress in the concrete will be in compression; when 
the two terms are equal, the stress is zero in the outer edge of the concrete 
on the side opposite to 
that on which the thrust 
acts; when the second 
term is greater than the 
first, this stress will be 
tension. By equating 
the two terms the value 
of the eccentricity, e , 
may be found for which 
the stress at the edge 
is zero. 

Using previous nota¬ 
tion and also letting e 0 = value of e which makes the stress zero 

h 2 + 12 npa 2 1 

6 h 



Fig. 176.—Stresses Caused by a Force Acting at a 
Distance Larger than e 0 from the Axis of Gravity 
of Reinforced Section. {See p. 566) 


= 


(49) 


1 + np 

If the computed eccentricity, e, is greater than e 0 the concrete is in tension. 
Diagram for Determining Compression and Eccentricity. By intro¬ 
ducing selected values for some of the letters in formula (49) its solution 
is simplified. If the ratio of moduli of elasticity of steel to concrete is 

e = eccentricity, h =■ height, n = ratio elasticity, p - ratio of steel. 

































































5 68 


A TREATISE ON CONCRETE 


assumed to be 15, and if the steel is assumed to be imbedded in the con- 

4/^ • 

crete y 1 ^ of the total depth from each surface so that 2 a = —, which is a close 

5 

approximation in ordinary design, formula (49) becomes 

__ 1 + 2S. 8 p ^ j 

h 6+90 p 

where — is the eccentricity producing zero stress at one surface divided 
h 

by the'total thickness of the arch or beam. The curve in the lower right hand 

£ 

portion of the diagram, Fig. 177, page 569, is plotted and the values of — 

/ 1 / 

can be read for any percentage of reinforcement. For example, if h at any 
section is 30 inches and the percentage of steel 0.8% (i. e., if p = 0.008) 

e 0 

— = 0.183 from the diagram, and hence e 0 = 5.49. That is, the center of 

fl' 

thrust cannot be more than 5.49 inches from the gravity axis without 
producing tension in the concrete. 

If, then, the eccentricity of the thrust on the section in question as previ¬ 
ously determined from the line of pressure, or from computation, is greater 
than the e 0 derived from the curve, there is tension in the concrete, and the 
percentage of steel may have to be increased or else the depth of section, h, 
increased. In the latter case it must be remembered that an increase in h" 
with the same area of steel results in a reduction in the percentage of steel. 

For determining the maximum compression in the concrete, the curves 
in the left-hand portion of the diagram, Fig. 177, have been drawn for 
certain values of wand p. If the same values are selected as are given above, 
n = 15 and 2 a = f/q the formula (42) on page 565 becomes 


h — 


N 

bh 


e 

+ T 


i + 1$ p h 1. + 2 8.8 p _ 


(5i) 


or for definite values of e , h and p 


fc = 


NC ( 

~bh 


( 5 2 ) 


In the diagram mentioned, the values of C e are plotted for values of - 
and different percentages of steel. 

To illustrate the use of the diagram, after having found that the eccentric¬ 
ity does not produce tension in the concrete, if the eccentricity is 3 inches 

» 

N = thrust. f c = compression in concrete. b = breadth. h = height. e = eccentricity. 
p = ratio of steel. Ce — constant. 








VALUES OF | 
























































































































































































































































































































































































































57 ° 


A TREATISE ON CONCRETE 


and the thickness of the arch, h, is 30 inches, the value of C e for 0.8% steel 

1.38 iV. 

(that is, for p = 0.008) is 1.38 and f c = — 

Distribution of Stress When One Surface is in Tension. When 

the thrust is applied at a distance from the gravity axis with eccentrictiy, e , 
greater than that given for e 0 by formula (49), page 567, and the concrete 
is assumed unable to carry any tension , the above general formulas are 
not easily applied and the following method may be used. Here the steel 
on the side opposite to that on which the thrust acts is designed to carry all 
the tensile stresses. In this case having a section with a bending moment 
and thrust, there are three unit stresses to be determined, namely, maxi- 



Fig. 178.—Stresses Caused by a Force Producing Compression and Tension 
upon a Reinforced Section, Tensile Strength of Concrete Neglected. (See 
P- 57 °-) 

mum unit compression in concrete, maximum unit compression in steel, 
and maximum unit tension in steel. The method of procedure is similar 
to that used for beams in Appendix II, page 757. Referring to Fig. 178, 
the unit stress in the upper steel, as shown by inspection, is 

f ‘ = nf '( l ~kh) (53) 

The unit tension in the lower steel is 

d — kh 

f* = n ^ c kh 54 

Hence, when the compression in concrete, f c , is known, the stresses in the 
steel are determined by the above formulas. Since the sum of the stresses 


« = ratio elasticity. N = thrust. fc = compression in concrete. /« = tension in steel 
f's = compression in steel, b = breadth, h = height, p = ratio of steel. k = ratio depth 
neutral axis, d = depth tension steel, d' — depth compression steel. R = resultant of forces. 
















































ARCHES 


57i 


acting on the section must be equal to the thrust, we have, since each steel 

. P bh 

area is- 

2 


N = 


/. pbh 

2 


T 


f c bkh 
2 


J.pbh 

2 


Placing values of f a and f 8 from (53) and (54) in (55), 


( 55 ) 


N = 


f c bli k 2 + 2 npk — np 


( 56 ) 


The moment of the stresses about the gravity axis, which is obtained by 
taking the sum of the moments of all the stresses about the gravity axis 
and eliminating f s and f s by use of equations (53) and (54), is 


\M — f c bh 2 


npa 2 k k 2 
h 2 k 4 6 


( 57 ) 


Designating by C a the quantity 
we may write 


npa 2 k 
h 2 k ^"4 


M = CJ c bh 2 


k 2 ' 

6 


from equation (57) 


( 58 ) 


Hence in investigating a given section of an arch,if M, b y h, C a are known, 
the unit compression in the concrete is 



M 

Cjh 2 


( 59 ) 


To solve this equation easily, values of C a should be taken from curves. 
Fig. 180, page 573, gives values of C a for n — 15, 2 a = \h and various 
values of k. 

Evidently before using equations (57) or (59) to find the unit compres¬ 
sion in the concrete, the position of the neutral axis must first be determined. 
To do this we must find the value of k. Since the moment M = Ne, that is, 
the thrust multiplied by the eccentricity, equation (56) may be multiplied 
by e and equated to (57). From this process, the following equation con¬ 
taining k is obtained 

k * + 3 +6npk k = * np k + ~hr (6o) 


M — moment, ti = ratio elasticity. N = thrust. fc= compression in concrete. fs = tension 
in steel, j's = compression in steel, b = breadth. h = height, e — eccentricity, p = ratio 
of steel. k — ratio depth neutral axis. Ca = constant. 




















Fig. 179. —Diagram for Determining Depths of Neutral Axis for Different Eccen- 

4 

tricities. Based on n = 15 and 2a = — h. (See p. 574.) 


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 

VALUES OF k, RATIO OF DEPTH OF NEUTRAL AXIS TO DEPTH OF STEEL BELOW COMPRESSED SURFACE OF BEAM. 




















































































































































































































































































































































































































































573 



Fig. 180. —Diagram for Determining Constants Ca to be used in Formula (59). 


Based on n = 15 and 2 a = - h. (See p. 571.) 


















































































































































































































































































































































































































































































































































































































































574 


A TREATISE ON CONCRETE 


and k may be obtained from this equation if the size of section, percentage 
of steel and eccentricity are known. 


e . 4 

By solving this formula for - , using n — 15 and 2a = ~h, we have 

' l 5 


e — k 3 + f k 2 + 14.4 p 
h 3 k 2 + 90 pk - 45 p 


(61) 


from which equation, curves for—are readily drawn for different percen¬ 
tages of steel. In Fig. 179, page 572, curves are plotted by this formula, 
using n — 15 and 2a = |A, and from these the depth of the neutral axis 
k, may be found.* This is illustrated in the example, page 580. 

In finding the unit compressive stress in the concrete for a given section 
having an eccentricity greater than e 0 (see page 567) and containing a known 
quant ty of steel, ihe following quantities would be known: breadth, b; 
depth, h\ ratio of steel, p\ ratio of elasticity, n; eccentricity, e; and moment, 
M. The method of procedure of finding f c , the maximum compression in 
the concrete, may then be as follows. 
e 

Determine t. Enter the bottom of Fig. 179, page 572, with this value 

ri/ 


, e 

ot 7 and find the k corresponding for (he given percentage of steel. Then with 

rl 

this value of k enter Fig. 180, page 573, and find C a . Apply formula (59), 


M 

page 571, where/„ = 

Having found the unit stress in the concrete, the unit stresses in the steel 
may be determined from formulas (53) and (54), page 570. 


METHOD OF PROCEDURE FOR THE DESIGN OF AN ARCH. 

The design of an arch is a trial process; the design being selected and 
then investigated to see if the sections are of sufficient strength. If the arch 


*If the value of k must be determined directly, substitute k = z — ^ — — J when 

equation (60) takes the form z 3 + pz + q = o, and since by Cardan’s formula, 

z = \ ~ + (7 *) + ^ - to - + ( ~ p ) 

the value of k may be computed. This follows the method suggested by Professor Morsh in a Der 
Eisenbetonbau,” 1906, p. hi. 

h = height, e = eccentricity, p = ratio of steel, k = ratio depth neutral axis. 













ARCHES 


575 


first chosen is too large or too small it must be revised and the process 
repeated. 

Since the location of the line of pressure and also the stresses are affected 
by the loading, it is customary either to compute the arch for the dead load 
plus concentrated loads located at the most unfavorable positions, or else 
to compute it for the dead load plus a uniform live load covering one-half 
the arch and also covering the entire arch, to see that the working stresses 
are not exceeded. 

The following steps indicate the method of procedure for the design of a 
highway bridge shown in folding Fig. 181, opposite page 580. The com-' 
putations are for the live load over one-half the span. The procedure is 
similar when the entire span is loaded. 

1. Lay out on a drawing the preliminary curve assumed for the in- 
trados. (See p. 540). 

2. Assume a crown thickness in accordance with the formula on page 541. 

3. Lay out the curve of the extrados and the surface of the roadway. 
The extrados may be a 3-centered curve, but it is better to use an arc of 
a circle if possible. It should be so placed as to give a ring thickness at 
the quarter points of the span of ij to ij times the crown thickness, and 
a ring thickness at the springings of 2 or 3 times the crown thickness in 
this first trial. 

4 Draw the arch axis midway between the extrados and the intrados. 

5. Divide the arch axis into distances such that the ratio of each distance 
to the moment of inertia of the cross-section of the ring at the center of the 

s ,. 

distance is a constant; that is, - is a constant. This can be done by trial 

by beginning at the crown and working towards the springings or by the 
method described on page 554. The moment of inertia is of the combined 
section of concrete and steel about the gravity axis , hence the size and posi¬ 
tion of the steel rods must be first assumed, when I may be computed by 
the formula on page 565. The ratio of area of steel to total area of section 
at crown may be arbitrarily taken in the first place from 0.007 to 0-0125, 
that is from 0.7% to 1}%. The divisions are separated by vertical sections. 

In the problem here solved the distance, s, next to the crown is 1.14 ft., 

and that next to the springing is 7.82 ft. The constant ratio, y for this arch 

is 11.4* On folding Fig. 181 the centers of the divisions are shown by circles 
and are numbered 1, 2, 3, etc. All distances are in feet and all quantities 

♦Greater accuracy may be obtained by using a larger number of divisions than here chosen, 
and also by subdividing loads P x and P. M . 


576 


A TREATISE ON CONCRETE 


involving distance are in foot units. A section of the arch i foot wide 
transversely is considered. 

6. Compute the dead and live loads and enter these loads as indicated 
by P x P 2 , etc., at the center of gravity of each division. In the accompany¬ 
ing design, a live load of ioo pounds per square foot covers the right half 
span, while on the left is the dead load alone of the masonry taken at 150 
pounds per cubic foot plus the earth fill taken at 100 pounds per cubic foot. 


Table I. Ordinates and Moments in Computation of Example 


Points 

X 

y 

X 2 

y 2 

^ ; 

m r 

m l* 

MrX 

M Ly 

M Ry 

10 and 11 

0.56 

O.OI 

°-3 

0.0c 

00 

00 

00 

00 

00 

00 

9 and 12 

1 • 7 1 

0.04 

2.9 

0.00 

39 i 

5 21 

668 

891 

16 

21 

8 and 13 

2.88 

0. II 

8.3 

0.01 

1 205 

I 603 

3 47 ° 

4 616 

13 2 

176 

7 and 14 

4.11 

0.23 

16.9 

0.05 

2 520 

3 346 

10 357 

13 75 2 

580 

770 

6 and 15 

5-43 

°-39 

2 9-5 

0.15 

4 47 i 

5 9 2 3 

2 4 2 77 

32 162 

1743 

2 3 10 

5 and 16 

6.89 

0.63 

47-5 

0.40 

7 3 2 7 

9 672 

5 ° 4 8 3 

66 640 

4 616 

6093 

4 and 17 

8.57 

0.97 

73-5 

0.94 

11 584 

15 216 

99 2 75 

13° 401 

n 237 

14759 

3 and 18 

i °-59 

1.50 

112.2 

2.25 

18 242 

2 3 79 1 

193 183 

25 1 947 

2 7 3 6 3 

35 686 

2 and 19 

I 3 -I 7 

2 -39 

173-5 

5-71 

29 480 

3 8 ° 45 

388 252 

5 QI °53 

70 457 

90 928 

1 and 20 

17-94 

5 -H 

321.8 

26.41 

5 8 553 

74 i 9 2 

1 052 235 

1 331 004 

301 476 

3 81 347 

y 

1-0 

OO 

11.41 

786.4 

35 9 2 

co 

00 

CO 

CO 

»-* 

172 309 

1 822 200 

2 332 466 

417 620 

53 2 ° 9 ° 


All distances in foot-units; all moments in foot-pounds 


Values of H c , V c and M c at crown for Live and Dead Loads. 


H c - 


10 (417620 4- 532090) — 11.41 (133873 + 172309) 


v c = 


2 l 10 X 35.92 — (11.41) 2 ] 
1822200 — 2332466 


+ 13 107 lb. 


1 573 


324 lb. 


M c = 


172 309 + 133 873 — 2 X 13(107 X n.41 


20 


= + 354 ft- lb. 


Values of H c and M c at crown for Rise in Temperature. 


1 .0000055 X 20 X 41.88 X 10 X 2000000 X 144 

H c 11.4 2(10 X 35.92 — (11.41) 2 ] ~ lb* 

~ 2-545 X 1 Mi . .. 

M c = ~ = — 2900 ft. lb. 

Values of H c and M c at crown for Rib Shortening. 

1 66 X 41.88 X 10 X 144 

Hc ~ 11.4 2 [10 x 35.92 - (n.41) 2 ] ~ ~ 760 lb * 

— 760 X 11.41 

M c — — = + 870 ft. lb 

c 10 ' 


The horizontal components of the earth pressure are so small that they 
are neglected, except that, for purposes of illustration, they are shown in 
the case of the load adjoining each springing, where the horizontal compo¬ 
nents are computed by formulas for earth pressure on page 666. The 
point of application of the horizontal and vertical components, as shown 
for P u is taken at the arch axis. In practice, earth pressure is negligible 









































ARCHES 


577 


in the design of flat arch rings of the type here selected, and all loads may 
be taken as vertical. Only where the ratio of rise to span is large need the 
horizontal components of the earth pressure be considered. 

7. Make a table similar to Table 1, page 576. The values of x and y 
are scaled from the drawing, and are the coordinates of the center points of 
the divisions of the arch axis. The crown point of arch axis is here taken 
as the origin of coordinates. The values of M L and M R are computed. M L 
represents the moment at each of the center points 1 to 10 inclusive of all 
loads lying between the point in question and the crown. Thus M L for 
point 10 is o; for point 9, M L = 340 X 1.15=391 ft. lb.; for point 8, M L = 
391 + 696 X 1*17 = I2 °5 ft.lb.,and soon. The moment at each “center” 
point being obtained from that at each preceding “center” point. M R of 
course represents the moment at each of the center points n to 20 inclusive 
of all loads lying between the point in question and the crown. For a 
symmetrical loading M L would equal M R for each pair of center points, 
such as 1 and 20. 

8. Compute H c V c M c , that is, the thrust, shear and moment at the 
crown, as on page 576, by using equations (16), (17), and (18),page 553. 
If the sign of V c is plus the line of pressure (equilibrium polygon) at the 
crown slopes upward towards the left; if minus, as in the present case, 
upwards toward the right. A p us sign for M c indicates a positive moment; 
a minus sign, a negative moment at the crown. For the arch in folding 
Fig. 181, the crown thrust H c = 13107 pounds, V c = — 324 pounds and 
M c = + 354 ft. pounds. 

9. Draw a force polygon as shown in folding Fig. 181 by laying off to 
scale the loads P,, P 2 , etc., as o — 1, 1 — 2, etc. Find the pole by laying 
off V c downward (because negative) from the crown point, 10, and then 
laying off H c horizontal. The hypothenuse of the triangle having H c 
and V c for sides thus slopes upward to left or upward to right, according 
as V c is + or —. 

10. Draw the equilibrium polygon as shown on the arch of folding Fig. 
181. The resultant pressure acts above the axis at the crown a distance, 
M c 

-==r = e if M c is plus, and below by the same amount if M c is minus. 

Since here, as is shown later, e = +0.028 feet, this distance is laid off verti¬ 
cally above the axis at the crown and through this point the resultant pres¬ 
sure is drawn parallel to the ray O 10 of the force polygon and so on. It is 
not really necessary to draw the equilibrium polygon if the moments and 
eccentricities are computed for the various sections as outlined under item 
11, but the polygon, which is the line of pressure, affords a good check on 
the algebraic work. 


578 


A TREATISE ON CONCRETE 


11. Determine the moment,thrust,and eccentricity, and if desired the 
shear at the center points, i, 2, 3, etc., of the divisions, and enter in a table 
as shown below. The moment is computed from formulas (19) and (20) 
on page 554, the values of whose terms have already been found by items 
7 and 8. The thrust and shear may be scaled from the force polygon. For 
example, at section 1 on folding Fig. 181 the thrust line is drawn parallel 
to the tangent to the axis at 1, and the shear line at right angles to the thrust 
line. The eccentricities, e, of the sections 1, 2, 3, etc., are computed by 
dividing the moment on the section (see page 561) by the thrust for that 
section just scaled. For positive moments and therefore positive values of 
e , the line of thrust lies above the arch axis. 

12. Compute the thrust and moment at the crown due to variation in 
temperature by formulas (25) and (26), page 556, the moments on the 


Table 2. Final Moments and Thrusts 




LIVE 

AND 

DEAD 





TEMPERATURE 

RIB SHORTENING 

Point 

H c y 

V c x 

Mom. 

Thrust 

Ecc. 

Mom. 

Thrust 

Mom. 

Thrust 

1 

67370 

~5 812 

+ 

3 2 59 

4- 

! 436 o 

+ 0 

2 3 

± 

10180 

± 1970 

— 

3 ° 3 ° 

— 610 

2 

31325 

-4267 

~ 

2068 

+ 

14000 

— 0 

■ l 5 

± 

1 —i 

OO 

O 

±2310 

— 

' 95 ° 

— 700 

3 

19660 

343 1 


i6 59 

+ 

13920 

— 0 

12 

± 

910 

±2430 

— 

270 

-73° 

4 

12713 

-2777 

— 

1:193 

+ 

13600 

— 0 

10 

rb 

44c 

± 2500 

4- 

130 

-740 

7 

3 OI 4 

~ I 33 I 

— 

4 8 3 

+ 

13240 

— 0 

°4 

=F 

2 3 2 ° 

± 2 53 ° 

4- 

690 

— 760 

9 

524 

~ 554 

— 

67 

4- 

13160 

— 0 

005 

=F 

2800 

± 2 545 

4- 

840 

— 760 

12 

5 2 4 

“ 554 

+ 

9 u 

+ 

13120 

+ 0 

07 

=F 

2800 

± 2 545 

4 - 

840 

— 760 

H 

3 OI 4 

-! 33 * 

4- 

1 353 

4 - 

13200 

4-o 

10 

=F 

2 3 2 ° 

± 2 53 ° 

4 - 

690 

— 760 

17 

12713 

-2777 

4 - 

627 

4- 

i 3 6 4 ° 

4-0 

°5 

± 

440 

±2500 

4 - 

130 

-740 

18 

19660 

343 

— 

346 

4 - 

14040 

— 0 

°3 

± 

910 

±243° 

— 

270 

-730 

19 

3 r 3 2 5 

-4267 

— 

20^9 

4 - 

14200 

— 0 

>5 

± 

3180 

± 2310 

— 

950 

— 700 

20 

67370 

— 5812 

” 

656 

+ 

14840 

— 0 

°4 

±iqiSo 

± 1970 

— 

3030 

— 610 


Thrusts in lb. Moments in ft. lb. Shear in arch design is small and need not be computed. 


various sections by formula (27), page 557, and the thrusts and shears by 
resolving the crown thrust into tangential and radial components, as shown 
in the small force polygon in the diagram. 

A rise in temperature of 20 degrees Fahr., and a fall of the same amount, 
is sufficient even in the northern part of the United States for arches with 
filled spandrels. 

For the arch shown on folding Fig. 181 the crown thrust H c , due to 
temperature, is a tension of 2545 lbs., and & compression of equal amount. 
The crown moment M c is + 2900 ft. lb. and - 2900 ft. lb. 

13. The effect of rib shortening due to the thrust is comparatively slight. 
Where necessary to compute it, use formula (31) and (32), page 558. (See 
P- 576 .) 

For the problem here shown the thrust at crown due to this cause is 
— 760 lb , and the moment is +870 ft. lb. 

14. Having prepared a table similar to Table 2, page 578, showing 






























ARCHES 


579 


thrusts and moments on the various sections i, 2, 3, etc., due to dead and 
live loads, temperature, and rib shortening, compute the maximum unit 
compression in the concrete and maximum unit tension, if any, in the steel 
by use of formulas on pages 565 to 574. 

Table 2 shows thrusts and moments for only a few of the sections of this 
arch, since it is unnecessary to compute all of them. A selection of the 
more critical sections may be made by inspection of the equilibrium poly¬ 
gon. The following shows the computation of the maximum unit stresses 
at the crown for the arch infolding Fig. 181, as outlined in items 11 to 13. 


Live and Dead Loads and Rib 
Shortening. 


Moment 

+ 354 
4 - 870 


Thrust 

+ 13107 Live and dead 
760 Rib shortening 


= 0.1 ft. 


-{-1224ft.lb. +12347 lb. 

M 1224 

N 12347 
p = ratio of steel at crown =0.0092 
Consulting lower right hand part 
of Fig. 177, page 569, it is seen that 

the value of - for 0.92% is greater 

(> 

than - =0.1. Hence there is com- 
li 

;pression over the entire section. 

From formula (42), page 565, max. 
compression in concrete, 


/e" 


12347 

I X I 


+ 


_ 1 + 15 (.0092) 
6 (1) 0.1 


i) 2 ] 


(i) 2 + 12 (l5) .OO 92 (J) 2 
= 17100 lb. per sq. ft. 

= 119 lb. per sq. in. 

Stresses in steel need not be com¬ 
puted. 

The above may be more quickly 
solved by the use of the curves on 
the left part of Fig. 177, page 569. 


Live and Dead Loads and Rib 
Shortening Plus Temper¬ 
ature. 

Moment Thrust 

+ 1224 + 12347 

+ 2900 — 2545 Temp. 


+ 4124 ft. lb. 

M 
e = 


+ 9802 lb. 

4124 


.42 ft. 


f c = compression in concrete, e =* eccentricity. M = moment. N 
k = ratio depth neutral axis, a = distance centre of gravity to steel 


N 9802 
Consulting lower right hand part 
of Fig. 177, page 569, it is seen that 

^0 

the value of — for 0.92% of steel 

e 0.42 

is much smaller than — = *- = 

h 1 

0.42. Hence there is tension over a 
part of the section. 

From formula (60), page 571, the 
value of & is found to be 0.6. From 
formula (59), page 571, the value of 
the maximum compression = 35 700 
pounds per square foot = 248 pounds 
per square inch. From formula (54), 
page 570, maximum tension in steel 
= 1440 pounds per square inch. 

The approximate value of the 
above compression in concrete may 
be more quickly found by the use 
of curves, Fig 179 and 180, and 
pages 572 and 573 as shown below. 

thrust, h = height. 












58° 


A TREATISE ON CONCRETE 


The method of computation for other points in the arch is similar, and 
stresses should be determined at sections where they appear to be the max¬ 
imum. 

From table 2 it is evident that although at point 20 the moment due to 
dead and live load is very small, its combination with moments due to tem¬ 
perature and rib shortening makes it one of the critical points. The moment 
and thrust due to live and dead load and rib shortening is 
M = — 656 —3030 = — 3636 ft. lb. and N = 14840 —.610 = 142301b. 
3686 e Q 

Hence, e n =-~= 0.26 ft., for h = 1.97, — = 0.13, p = 0.0037. 

14230 h 

Inspecting the lower part of Fig. 177, page 569, it is seen that the whole 

e 

section is in compression. From the same diagram for — = 0.13 and p = 


14230 x 1.65 

°- 00 37 > C e = 1.65. Using formula (52), page 568,/,. = ■ x ~ - - = 
83 lb. per. sq. in. 

Combine now the moment and thrust due to live and dead load with 
those due to temperature and obtain M = — (10180 + 3686) = — 13866 

' e 

ft. lb., N = — 1970 + 14230 = 12260 lb., e = 1.13 ft. — = 0.57. 

e 

In Fig. 179, page 572, k — 0.37 corresponds to - = 0.57. By locating 

this value of k in Fig. 180, the constant C a = 0.094 is obtained, which sub- 

. . . . , * , 13866 X 12 

stituted m formula (59), page 571, gives f c = -—- ■ -- - —r- 2 

0.094 X 12 X (1.97 X 12 y 

= 264 lb. per sq. in. The stress in steel from formula (54) is f s — 15 X 264 

1.80 — 0.37 X 1.97 0 „ 

- ——-— = 5800 lb. per sq. in. 

0.37 X 1.97 

Similar computations should be made for all critical points and when the 
stresses are either too small or too large, the dimensions or even the shape 
of the arch must be changed. Small changes may be made without refigur¬ 
ing the whole arch. For larger changes, all computations should be re¬ 
peated and a new line of pressure determined. 


LOADINGS TO USE IN COMPUTATIONS 

The usual practice is to make two sets of computations; in the first place, 
proportion the arch ring for a live load covering the entire span and then 
for one covering only one-half the span. These two loadings are approxi¬ 
mations, more or less exact, to the true loadings which produce the maxi- 





58i 


FIG. 181. EXAMPLE OF ARCH DESIGN 

(See pp. 574 to 580) 


\ 













7124 



LIVE LOAD ON HALF.SPAN=IOO POUNDS PER SQUARE FOOT 

x-..,...... .. M 


SURFACE OF ROADWAY 


SECTION AT CROWN 


SPAN OF AXIS 4I.88f t. 


CLEAR SPAN 40ft. 0 


." 

/ Q^C0 MPJ T £D THRUST H CR OWN', U c 2£ LBS. 
THRUSTS DUE TO CHANGE iN TEMPERATURE 


P—4 

1 1 / 

1 

\ 3 - T 

^ 4 DIAM. RODS 

j I . 


/ 


A 


-t 

£ 

■ 



14 


Fig. 181 .—Example of Arch Design. 






































































































ARCHES 


583 


mum effects. By computing a table for the thrusts and moments due to a 
load of unity at different points, or by the use of influence lines, the exact 
loading to cause maximum stresses may be found. 

ALLOWABLE UNIT STRESSES 

For highway bridges the maximum compression in the concrete of the 
ring should not exceed 500 pounds per square inch due to live and dead 
loads, nor more than 600 pounds per square inch due to live and dead 
loads, temperature and rib shortening combined. For railroad bridges 
three-fourths of the above values may be used. 

DESIGN OF ABUTMENT 

The design of the foundation of an arch bridge is as important as that 
of the arch itself. The arch is designed on the assumption that the founda¬ 
tion is unyielding, and this condition must be approached as nearly as pos¬ 
sible in order to insure the stability of the whole structure. 

The depth of the foundation as well as the shape is dependent upon the 
local conditions, and in the more difficult cases these have to be chosen after 
exhaustive studies. A certain shape of abutment is first assumed, and this 
is then reviewed to see that the load upon the ground does not exceed the 
allowable load and that it is well distributed. Allowable loads are discussed 
on page 541. 

The forces acting on the foundation are: 

(1) the thrust of the arch; (2) the weight of the foundation; (3) the 
weight of the earth above it; and (4) the lateral earth pressure. The thrust 
of the arch is the largest when the live loading extends over the whole span 
of the arch, and for this the line of pressure should be drawn first. A line 
of pressure for the thrust on account of the total dead load and of the live 
load extending only over one-half the span opposite to the abutment also 
should be drawn to see whether, because of intersecting the abutment higher 
up, it does not produce larger pressure on the foundation. A good 
scheme is to design the abutment in such a way that the line of pressure 
on account of one thrust intersects the base a little way to the left of 
the center while the other intersects to the right of the center. In some 
cases a third line for the total dead load, plus live load on the half span 
nearest the abutment should also be drawn. 

The line of pressure of the forces should be as near to the center of the 
base as possible, since the maximum unit pressure is the smallest when the 
load is distributed uniformly over the entire section. This also prevents 
uneven settling of the foundation, and thus adds considerably to the stability 
of the whole structure. 


584 A TREATISE ON CONCRETE 


CD 













































ARCHES 


585 


Fig. 182, page 584, clearly illustrates the design of an abutment. The 
outline is assumed, then the location and magnitude of the forces acting 
upon the abutment are found and the line of pressure determined. If the 
assumed outline is not satisfactory it should be revised. 

For the benefit of those who are not familiar wath the common principles 
of such design, the steps will be considered in detail. The magnitude, 20,500 
pounds, and position of the arch thrust is given in the arch example. Since 
the weight of the masonry acts through its center of gravity, this point must 
next be found and this is most readily done by dividing the outline of the 
abutment into triangles and rectangles. The weights of each of these prisms 
one foot thick are readily computed, and the center of gravity found through 
which the weight force acts. A force polygon for any pole distance, as 
shown in the upper left corner of the diagram, is drawn and the equilibrium 
polygon, by the intersection of the closing lines, locates the resultant of the 
weight which, by computation, is found to be 5850 pounds. 

The pressure on AB consists of the horizontal pressure on BE , and the 
weight of the prism of earth w r hose cross-section is ABFG* and thickness 
one foot. Taking the weight of one cubic foot of filling at 100 pounds, the 

10 + 15 


weight of the prism w T ould be 


X 6.3 X 100 = 7880 pounds. 


The horizontal pressure on BE is equal to the difference between the pres¬ 
sures on BF and EF. 

Let 


w == weight of one cubic foot of earth, 
then, if the weight of earth is assumed at 100 pounds, from formula (2), 
page 664, pressure on the plane 


w 100 

BF = — X BF xi BF = — X15 X -i 15 = 1870 pounds, 
0 0 

and on the plane 

w 100 

FF = — X FF X I FF = — X 10 X J 10 = 830 pounds. 
6 "6 

Hence horizontal pressure on plane BE = 1040 pounds. 

The point of application is found from the formula (7), page 666. 

In the case under consideration II — 15 feet, h — 10 feet, where II is the 
depth of point B and h the depth of A or E below the line of surcharge. 

The horizontal pressure on BC is by formula (6), page 666, 180 pounds, 
and the point of application may be assumed in the middle of BC without 
appreciable error. 


* The live load being ioo pounds per foot is equivalent to a surcharge one foot in height. 







586 


A TREATISE ON CONCRETE 


Having thus located all forces and found their magnitude, the line of 
pressure is drawn. This procedure consists simply in finding the resultant 
of two forces intersecting in one point. The line representing the thrust is 
prolonged until it intersects the line representing the weight of masonry, 
5850 pounds. Beginning at this, the magnitude of the thrust, 20,500 pounds, 
is laid off to any desired scale and the resultant of this with the weight of the 
masonry, 5850 pounds, is found to be 25,200 pounds. Combining this new 
force in turn with the earth pressures of 8100 pounds and 180 pounds com¬ 
pletes the line of pressure with a final resultant thrust of 31,500 pounds. 

Having found the line of pressure, the thrust is divided by the projection 
of the base on a line at right angles to the thrust and the maximum pressure 
on the ground is found by formula (36), page 562, to be 5000 pounds per square 
foot. 

The same result is obtainable by the following simple graphical method: 

Find the average unit pressure by dividing the thrust by the area of the 
. projection of the base, drawn perpendicular to the thrust. In this case we 

have —-— = 4500 pounds per square fooc. Plot this, to any convenient 

7 

scale, perpendicular to the projection to the base at its center; connect the 
J points of the base with the top of this perpendicular, as shown by the dash 
lines in Fig. 182, and produce one of these lines till it intersects the line rep¬ 
resenting the direction of the thrust. The perpendicular distance of this 
point from the projection of the base is the maximum thrust and the dis¬ 
tance of the other intersection of a slanting line with the thrust line is the 
minimum thrust. To draw the trapezoid of pressure, draw, through these 
two intersections, lines parallel to the projection of the base, as shown, and 
the extremities of these parallel lines will fix the two corners of the trap¬ 
ezoid. The maximum pressure is always at the end of the base nearest the 
thrust. 


ERECTION 

As in other reinforced structures, the erection is as important as the design. 
Perhaps the first essential is the centering which should be planned out in 
advance almost as carefully as the arch itself. 

Methods of Arch Construction. There are two general methods of 
laying the concrete in an arch, each of which has strong advocates. By 
the first, the arch is laid in separate blocks across the bridge, and by the 
second, in narrow ribs from abutment to abutment. If the block method 
is followed, the lowest stones at the springing line are laid first, then stones 



ARCHES 


5 8 7 


I 


intermediate between the spring and the key, next the two stones each side 
of the key, and finally, after filling in the intermediate blocks, the key is 
placed. This distributes the weight of the concrete uniformly over the 
arch center, and prevents unequal settlement, which tends to crack the 
arch near the springing lines. On the other hand, the entire weight falls 
upon the center, and the latter must be very strongly built. The arch 
thrust acts at right angles to the joints, and as the blocks extend clear 
across the bridge, there is no danger of longitudinal splitting, but the radial 
joints offer planes of weakness in bending. 

By the other method the work can be readily arranged so that a day’s 
labor consists of the laying of a single rib, thus forming a complete arch of 
itself, which as soon as it sets bears its own weight. This arch section has 
no joints, so that when subsequently loaded the bending moment is best 
resisted. 

A small arch, where the center can be solidly built, may be laid at one 
operation, commencing at both abutments and working toward the key 
so that it is in fact a monolith. 

The spandrel or face walls may be carried up at the same time the arch 
ring is laid, or may be connected with it later by leaving short lengths of 
steel projecting radially from the concrete of the arch. 

If steel is introduced, the consistency of the concrete must be wet enough 
to thoroughly coat it. This may be accomplished by a quaking or jelly- 
like mixture, which requires but slight ramming. 

From an architectural point of view, the treatment of the face is of much 
importance. For a discussion of the different methods reference should 
be made to page 288. 

Railings and ornamental w’ork may be cast in molds if preferred and 
put in place after hardening. 

Centering. The falsework for concrete arches is practically the same 
as for stone arches except that close lagging is necessary. It must be rigid 
during the construction of the arch and stiff enough to prevent its distor¬ 
tion from the unsupported weight of the concrete before the keying of the 
arch. 

The design of the centering is frequently governed by the character of 
the ground underneath. In general the framed wood centering made into 
a truss rests upon pile or trestle bents. The spacing of these bents is deter¬ 
mined by the foundation and the difficulty of placing them, and by the 
height and span of the arch. In certain cases it is possible to support the 
centering in whole or in part by the reinforcement, although this is not 
usually economical because more carefully framed steel is required than is 



5 88 


A TREATISE ON CONCRETE 


necessary for reinforcing the arch. In at least one case* reinforced con 
crete forms were used. 

In connection with the description of arch centers which he has built, Mr. 
James W. Rollinsf, Jr., gives the following notes: 

For small arches the simplest center is a circular rib made of three pieces 
of 2-inch plank, laid with broken joints, all being spiked solidly together, 
with a tie of plank at the springing. On this, i-inch lagging is laid close. 
For a larger arch, the circular rib, as above described, with generally three 
braces, one at center and one on the quarter at each side, is used, the 
center of the whole rib having a post under it. We have used such a center 
up to 30-foot span for both brick and granite arches, carrying a 30-inch arch 
sheeting. 

The design of a center for larger arches depends upon local conditions, 
also upon the relation of rise to span. In flat arches, with low side walls, 
it is well to use posts with intermediate bracing, on numerous supports. 
In a high arch we may use long braces extending directly from a center 
support to the rib, at intervals of 6 feet to 8 feet. 

Mr. Rollins advocated for wedges, seasoned oak, 8 inches wide, 4 inches 
thick at the thick end, 2 inches at the thin end, and 18 inches long, planed 
on sliding faces, and thoroughly greased. When setting the center, these 
wedges, placed between the caps on the bents and the corbels under the 
lower chord of rib, are tacked together to prevent slipping. 

Boxes filled with sand are frequently used between the caps of the bents 
and the lower chords of the trusses in place of wood wedges. The sand 
in these must be thoroughly packed to prevent settlement of the concrete 
before setting. The sand is readily removed by letting it out through a hole 
in the box. Jack-screws also may answer the same purpose as wedges or 
sand boxes. By any of these means the centering is easily lowered. 

The ribs of the centering are usually made of several pieces of plank 
spiked or bolted together. Upon the ribs rests the lagging, which usually 
consists of one or two layers of planking having the top surface smoothed 
to give a good surface to the soffit of the arch, and laid with tight joints. 
With thin lagging care must be taken to prevent deflection. 

Instead of the ribs forming a part of the truss, they are frequently sup¬ 
ported directly upon the wedges resting upon the caps of the bents, the 
posts of which run up to the soffit of the arch for that purpose. 

The centering should be cambered, that is, should be made higher than 
called for in the arch plans at the center, so that when it is removed, the arch 
will be in the position assumed for it in the design. Some engineers make 

* Engineering News, Aug. 30, 1906, p. 215. 

■{■Journal Association of Engineering Societies, July 1901, p. 10. For examples of centers 
built in various places, see References, Chapter XXXI. 




























































































































































































































590 


A TREATISE ON CONCRETE 


the camber equal to the deflection of the arch which would be caused by 
the live and dead loads. 

In striking the centers sudden settlement must be avoided and the cen¬ 
ters must not be removed until the concrete has attained good strength. 
The time of removal must be determined by the design of the bridge and 
the weather. For light highway bridges four weeks is usually suffi¬ 
cient, while for a heavy arch of long span eight weeks may be' required. 

EXAMPLES OF ARCH BRIDGES 

Mystic River Bridge, Medford, Mass. This arch, illustrated in 
Fig. 183, page 589, is of the Monier type and carries a parkway over the 
river. It was built in 1906 by the Metropolitan Park Commission, Mr. 
John R. Rablin, Chief Engineer. 

The arch has a span of 60 feet, a rise of 8 feet, and a crown thickness 
of 18 inches. Both the intrados and the extrados are segmental. The side 
walls are of concrete with a vertical expansion joint at each abutment. 
The retaining wall for the earth fill over the abutments is of reinforced 
design and curved as shown in the details in the drawing. 

Granite Branch Railroad Bridge. A railroad bridge of similar de¬ 
sign to the Mystic River Bridge was built by the Metropolitan Park 
Commission of only 4 feet longer span than the highway bridge described. 
The heavier loading necessitated a thickness of crown of 24 inches instead 
of 18 inches with a thickness at springing still greater in proportion. 

3-Hinged Ribbed Arch on Ross Drive, District of Columbia. A 
different type of structure and one which illustrates the combination of 
arch ribs with a reinforced concrete floor system is illustrated in Fig. 184, 
page 591. This was built in 1907 by the Engineering Commissioner, 
Washington, D. C., Mr. W. J. Douglas, Engineer of Bridges. 

The central arch is 100 feet clear span and 15 feet rise, and the roadway, 
which is 16 feet wide and macadamized, is laid upon a 6-inch reinforced 
concrete floor slab supported by longitudinal concrete girders which in turn 
rest upon columns supported directly by the concrete ribs. The three arch 
ribs, which are reinforced as shown, are 2 feet wide throughout their length 
with a thickness of 2 feet 6 inches at the crown. 

Each hinge consists of two steel castings, shown in detail, with a pin 4 
inches in diameter, and these hinges are imbedded in the concrete. An 
expansion joint is provided in the roadway deck over each springing. The 
floor of the arch was computed for a 6-ton wagon, and the ribs for a live 
load of 100 pounds per square foot of roadway. The maximum compression 
on the concrete of the ribs under live and dead loads is 500 pounds per 
















































































































































































































































































































59 2 


A TREATISE ON CONCRETE 


square inch, and there is no tension. The cost of the structure was $8ooo, 
which is equivalent to about $3.00 per square foot of the roadway. 

Walnut Lane Bridge, Philadelphia. A notable structure in concrete 
is the Walnut Lane Bridge built as it is with a clear span of 233 feet. 
The arch was completed in 1908 under the direction of the Bureau of Sur¬ 
veys, Mr. George S. Webster, Chief Engineer and Mr. Henry H. Quimby, 
Assistant Engineer. The principal arch consists of two ribs, upon which 
rest cross walls connected by small longitudinal arches of 20 feet span 
carrying the spandrel wall supporting the I-beams of the floor. 

A fine photograph of the arch is shown in Fig. 156, page 532, and cross 
sections illustrating the design in Fig. 185, page 592. The balustrade is 
entirely of concrete, the posts being molded on the ground and the sur¬ 
face washed off with water to reveal the aggregate. 

Other Notable Bridges. For references to other bridges built in recent 
years, see Chapter XXXI. 




































































































































































































SIDEWALKS AND BASEMENT FLOORS 


593 


CHAPTER XXIII 

SIDEWALKS, BASEMENT FLOORS AND PAVEMENTS 

The introduction of reliable American Portland cements has rendered 
concrete available for sidewalks and other similar purposes at a price not 
more than two-thirds of that previous to 1890, when German and English 
cements were used. Portland cement being thus commercially within 
reach of builders, masons have become familiar with its use, and concrete 
sidewalks, because of their economy and durability, are supplanting those 
of other materials. 

Street pavements are also being made of concrete, and with apparent 
success * by methods similar to those which obtain in sidewalk construction. 

The essentials for a good concrete sidewalk are an artificial foundation 
of firm but porous material, through which the rain water may percolate, 
a base of good strong concrete, and a wearing surface of rich mortar, 
troweled to a smooth, dense surface. The walk must be divided into 
blocks, with the joints between them forming lines of weakness, so that if 
any cracks occur through shrinkage, settlement, or frost, they will occur 
at the joints and thus not be noticeable. 

Vault light construction in concrete requires even greater skill than 
ordinary walks, and should never be attempted by inexperienced con¬ 
structors. 

The construction of basement floors is similar to sidewalk work except 
that in dry ground an artificial foundation is not always necessary, and, 
there being less danger of settlement and frost, the blocks of such a floor 
may be of larger size, having occasional joints to provide for contraction 
from changes in temperature. 

Floors above the ground level in buildings whose design is considered 
m Chapter XXIV, page 609, may be surfaced with mortar in a manner 
similar to the wearing surface of walks, or the concrete may be floated 
without the extra coating of mortar. 

• 

MATERIALS FOR CONCRETE SIDEWALKS 

The selection of a first-class Portland cement is an absolute necessity.f 
Natural cements will not stand the wear, and Puzzolan cements are liable 

^Engineering News, Jan. 28,1904, p._ 84. 

fSee Cement Specifications, p. 29. - • 


594 


A TREATISE ON CONCRETE 


to surface deterioration from the action of the weather. Walks have been 
built with a Natural cement concrete base, and a wearing surface of Port¬ 
land cement mortar, but the results have been unsatisfactory, for even 
if the surface coat is laid before the Natural cement concrete base has set, 
the Portland cement does not adhere strongly and is likely to scale off. 

Mr. Harry T. Buttolph* suggests that the breaking up of the surface 
appears to be due to the difference in expansion of Natural and Portland 
cement. He has noticed that the surface of such slabs sometimes curls up 
like a sheet of paper. 

For the foundation, by which is meant the prepared surface underneath 
the concrete, any porous material such as broken stone, gravel (preferably 
with sand screened out), or cinders may be employed. 

For the base, which consists of a layer of concrete from 3 to 5 inches 
thick, ordinary materials, such as broken stone and sand, screened gravel 
and sand, or gravel as it comes from the bank without screening, may be 
used for the aggregate. Unscreened gravel is not generally advisable, 
however, because a more uniform mixture can be obtained by screening 
the gravel and remixing the sand with it in definite proportions. (See 
p. 112.) The proportions frequently used in our large cities for the concrete 
base are 1 part Portland cement to 2 parts sand to 5 parts stone, based in 
some localities upon the volume of cement as packed in the barrel, and in 
others upon the volume loose, although the resulting proportions obtained 
in the two cases are very different. (See p. 218.) In many cases these 
proportions are richer than is necessary. In Germany,f proportions 1:3:6 
are recommended for heavy duty, and 1: 5: 10 for light work, while for 
ordinary requirements 1:4:8 are specified. The last two proportions 
appear rather lean for ordinary conditions, but 1:3:6, if the relative 
volumes are based on a unit of 3.8 cu. ft. to the barrel, should be satis¬ 
factory for ordinary conditions, with 1: 2^: 5 for more important construc¬ 
tion, or for pavements to be subjected to severe usage, such as teaming. 
If the proportions are based upon the volume of cement measured loose, 
the required parts of sand and stone must be-decreased by about 10%; 
thus 1:3:6 would become about 1: 2J: 5^. 

The wearing surface, whose thickness varies in different specifications 
from J to 1 inch, should be laid with the same first-class Portland cement 
as is the base. Customary proportions are equal parts of cement and 
aggregate. Either sand, or fine crushed rock, or a mixture of the two, 

♦Personal correspondence. 

f“How to Use Portland Cement,” translated from the German of L. Golinelli by Spencer 
B. Newberry, p. 26. 


SIDEWALKS AND BASEMENT FLOORS 


595 


may be used to form the mortar. If crushed rock is used, — and good 
crushed rock is usually preferable to sand, — it should be of a texture such 
as granite or trap, which will break into cubical, rather than flat or lami¬ 
nated fragments. The size of crushed stone specified by the majority of 
engineers is that which will pass a J-inch sieve, although a few cities require 
finer material, Chicago, for example, specifying* torpedo sand ranging 
from J-inch down. Such sand is too fine to give a strong mortar. On the 
other hand, some cities, including Omaha, Neb.,f require crushed stone 
which will pass a ^-inch mesh sieve. 

The requirements in various cities throughout the United States in 1900 
are shown in the following table: 


Requirements in Various Cities.% (See p. 595.) 


City. 

F oundation. 

Base. 

Wearing 

Surface. 

Dry 

Coating. 

Size of Blocks. 

Guarantee. 

Thickness. 

Material. 

* 

Thickness. 

Proportions. 

Thickness. 

Propor¬ 

tions. 

Propor¬ 

tions. 

Cement. 

Sand. 

Cement. 

Sand. 


aa 




aa 






(J 

a 

►—t 


U 

a 

HH 


U 

a 

HH 





Boston .... 

12 

Broken stone, gravel or 










cinders. 

3 

1:2:5 

1 

I : I 

... 

.3^ to 6 ft. sq. 

IO 

Rochester.. 

6 

Sand, gravel, broken 










stone or cinders. 

|| 

i : s 

1 

2 : 3 



3 

Philadelphia 

3 

Sand, gravel, broken 

1 1 



O 



O 



brick, stone or cinders 

2 


2 

1 : 2 

t : t 



Washington 

0 

4 

1:2:5 

1 

2:3 

1 : 1 


r* 

0 

Chicago_ 

1 2 § 

Cinders. 

4l 

1:2:5 

a 

4 

1 : 1 

... 

5 ft. x 6 ft. 

IO 

Milwaukee . 

4 

Cinders or broken stone 

2 i 

1:3:5 

1 

1 : 1 

... 

24 to36sq.ft. 

... 

St. T.nuis 

8 

Cinders 

3 ! 

1 : 2 

A 

1 : 1 



I 

Omaha .... 

4 

Gravel, slag or stone... 

0 2 

3 

i:2:4 

Z 

I 

1:2 

3:1 


5 


Coloring Matter. The appearance of a walk is improved by being 
slightly colored. The following formulas aie recommended by Mr. I,. C 
Sabin :^| 

*1899 Specifications. 

-}-i898 Specifications. 

jFrom Typical Concrete Sidewalk Specifications, by Sanford E. Thompson, in Cement , July 
1900, p. 85. 

§No foundation required where the soil is clean sand. 

|(Specified for each contract. 

^[Sabin’s “Cement and Concrete”, 2nd Edition, p. 382. 







































50 


A TREATISE ON CONCRETE 


Colors for i : 2 Mortar. By Louis C. Sabin (see p. 595) 


MATERIAL. 

§ LB. PER 100 LB.CEMENT. 

4 LB. PER 100 LB. CEMENT. 

COST PER 
LB. 

Lamp Black 

Light slate 

Dark blue slate 

15 cents 

Prussian Blue 

Light green slate 

Bright blue slate 

50 “ 

Ultra Marine Blue 


Bright blue slate 

„ _ U 

2 0 

Yellow Ochre 

Light green 

Light buff 

3 “ 

Burnt Umber 

Light pinkish slate 

Chocolate 

TO “ 

Venetian Red 

Slate, pink tinge 

Dull pink 

2 % “ 

Red Iron Ore 

Pinkish slate 

Light brick red 

aj * 


Note: Colors vary with quantity of material added. Cost is per lb. of coloring matter. 
Colors are apt to fade unless formed by color of crushed rock. 


Quantity of Materials Required. The volumes of materials required 
to cover a certain area of surface are determined by the thickness of the 
walk or floor, the proportions in which the materials are mixed, and the 
character of the materials. 

The following table gives the approximate quantity of materials necessary 
for 100 square feet of surface for walks of various thicknesses of base and 
wearing surface. It is assumed in compiling the table that the coarse 
aggregate of the base contains about 45% voids, and that the stone and 


Materials for 100 Square Feet of Concrete Sidewalks. (See p. 596.) 
Proportions based on a barrel unit of 3.8 cubic feet. 


Base. 

Wearing Surface. 


Proportions. 

1: 2p 5 

Proportions. 

1:3:6 


Proportions. 

1: x 

Proportions. 

1: ii 

Proportions. 

1:2 

C /5 

ch 

<L> 

0 

-4—> 

0 



•*-> 

0 


Stone. 

C /5 

C /5 

<L> 

0 

-4—> 

0 


c 


0 


O 

-E 

s 

0) 

O 

T 3 

0 

d 

C/) 

Stone 

E 

<D 

u 

"O 

O 

rt 

C/2 

u 

0 

H 

s 

<D 

u 

4 

c 

c 3 

c n 

E 

4 J 

u 

0 

d 

an 

<u 

E 

(U 

CJ 

4 

a 

rt 

CO 

in. 

bbl. 

cu. yd. 

cu. yd, 

bbl. 

cu. yd. 

cu. yd 

in. 

bbl. 

cu. yd. 

bbl. 

cu.yd. 

bbl. 

cu.yd. 

A 

I.IO 

°-39 

00 

6 

0.94 

0.40 

O.80 

1 

5 

>o 

00 

6 

O.I 2 

0.68 

O.14 

0.56 

O.16 

3 

1-33 

0.47 

0.94 

I * I 3 

0.48 

0.96 

1 

4 

1.28 

0.18 

1.02 

0.21 

0.85 

O.24 

3 \ 

i-55 

°-55 

1.10 

1.32 

0.56 

1.12 

1 

1.70 

0.24 

1.36 

0.29 

i-i3 

O.32 

4 

1.77 

0.63 

1.25 


0.64 

I.28 


2.13 

0.30 

1.70 

0.36 

1.41 

0.40 

4 i 

1.99 

0.70 

1.41 

1.70 

0.72 

I.44 


2.56 

0.36 

2.04 

043 

1.69 

O.47 

5 

2.21 

0.78 

1.56 

1.89 

0.80 

I.60 

2 

3-41 

0.48 

2.72 

o -57 

2.26 

0.63 


Note. —Select and add together the quantities of each material corresponding to the required thickness 
and proportions of base and wearing surface. 





















































SIDEWALKS AND BASEMENT FLOORS 


597 


sand are measured loose by shoveling into boxes or barrels, on the basis of 
the volume of a cement barrel of 3.8 cubic feet. For example, proportions 
1:3:6 are equivalent to 1 barrel Portland cement, 11.4 cu. ft. of sand and 
22.8 cu. ft. of broken stone or gravel, while proportions 1: 2 are equivalent 
to 1 barrel of Portland cement to 7.6 cu. ft., or one bag of Portland cement 
to 1. 9 cu. ft. of sand or crushed stone. The variation in volume of mortar 
produced with sand and crushed stone of different fineness may affect the 
quantities for wearing surface by at least 10%, but to provide for such 
variation, and to allow for waste, 10% has been added, in computing the 
values, to the quantities in the table on page 231. 

Since the volumes are given separately for the base and wearing surface, 
the quantities required for walks of other thicknesses may be readily esti¬ 
mated, as illustrated in the following example: 

Example : — What materials will be required for a walk 8 ft. in width 
and 150 ft. long, the base to be 3 in. thick, of concrete in proportions 
1:3:6, and the wearing surface one inch thick, in proportions 1 part cement 
to 1 part sand? 

Solution: — Referring to the table we find directly that for 100 sq. ft. 
of base 3 in. thick, 1.13 bbl. Portland cement, 0.48 cu. yd. sand, and 0.96 
cu. yd. broken stone or gravel are required. Similarly, for 100 sq. ft. of 
the wearing surface one inch thick we should require 1.70 bbl. cement and 
0.24 cu. yd. sand. For each 100 sq. ft. of completed walk there would 
therefore be needed 2.83 bbl. cement, 0.72 cu. yd. sand, and 0.96 cu. yd. 
broken stone or gravel; and since there are 1 200 sq. ft. in an area of 150 
by 8 ft., for both base and wearing surface we should require 34 bbl. 
Portland cement, 9 cu. yd. sand, and 12 cu. yd. broken stone or gravel. 

TOOLS 

The following implements are required in ordinary concrete walk 
construction: 

Mortar box for mixing the materials for wearing surface. 

Platform about 12 ft. square for mixing concrete* (see Fig. 7, p. 22). 

One or more iron wheelbarrows for handling the materials and the 
concrete (see Fig. 4, p. 18). 

Square-pointed shovels (see Fig. 3, p. 18). 

Hoe. 

2-inch scantling of a width corresponding to the thickness of the walk. 

|-inch stuff of same width as scantling, for curved forms. 

Steel square. 


♦Sometimes unnecessary. 


A TREATISE ON CONCRETE 


598 

Spirit level. 

Straight-edge long enough to extend across die walk. 

Two rammers about 5 inches square, with handles about 4 feet long 
(see Fig. 99, p. 281). 

Wooden stakes. 

Iron pins and twine for stretching line. 

Mason’s trowel. 

Pointing trowel. 

Plasterer’s steel trowel (see Fig. 186, p. 601). 

Plasterer’s wood float. 

Groover (see Fig. 187, p. 601). 

Edging trowel (see Fig. 188, p. 602). 

Dot roller (see Fig. 189, p. 602.) 

METHOD OF LAYING SIDEWALKS 

Successful sidewalk construction is as dependent upon careful attention 
to small details which have been proved essential to good workmanship, as 
upon adherence to the more general directions given in any set of specifica¬ 
tions. The full description of methods to be employed in laying a walk 
are given for the benefit of those who are unable to take advantage of the 
experience of specialists in this line. Experienced contractors often can 
perform such work better and cheaper than it can be done by day labor. 

Thickness of Walk. A total thickness of 4 inches of concrete and 
mortar laid upon a 10-inch foundation of porous material gives excellent 
results for ordinary sidewalks, although 5 inches is often required for 
public works. In locations subject to wide changes in temperature, as 
Boston and vicinity, a thickness of 4 inches has proved satisfactory, while 
in some cities 3^ inches only is required. For a 4-inch walk it is advisable 
to make the base 3 or 3^ inches and the wearing surface 1 or J inch thick. 
The slope of surface often adopted is J or f inches to the foot. 

Driveways or walks which are subjected to excessive wear may be 
5 or 6 inches thick, the upper 1 or ij inches constituting the wearing 
surface. 

Foundation. The construction of the foundation is as important as 
the laying of the concrete. For out-of-door construction the foundation 
should generally be from 6 to 12 inches thick, depending upon the character 
of the soil. In localities unaffected by frost and having soil sufficiently 
porous to carry off surface water, the foundation may be omitted entirely, 
and the concrete laid upon natural ground excavated to the required depth. 


SIDEWALKS AND BASEMENT FLOORS 


599 


In Washington, D. C.,* no foundation is specified, and even in Chicago* 
it is not required where the soil is clean, porous sand. For basement oi 
cellar floors which are not to be subjected to frost, the concrete may usually 
be placed directly upon the soil; but in compact ground, or where surface 
water is troublesome, blind drains of pipe or of cobble stones, carefully 
rammed, should be laid at various points. 

The materials for a foundation, where such is required, may be broken 
stone, gravel, cinders, or coarse sand. In order to make it more porous, 
broken stone or gravel should be screened. Whatever material is em¬ 
ployed it must be thoroughly rammed so as to present a firm and unyielding 
surface. Cinders or sand should be thoroughly wet when being rammed. 

Concrete Base of Walk. The coarse concrete constituting the main 
body of the walk is generally called the base. Before this coarse concrete 
of the base is placed, the surface must be carefully laid off into squares or 
blocks. Such divisions are absolutely essential, since the joints furnish 
lines of weakness along which cracks will occur if the concrete is affected 
by the freezing of the soil beneath tree-roots, unequal settlement, or tem¬ 
perature changes, and also facilitates the replacing of a block if one is 
injured from any cause. 

There are three distinct methods of forming separate blocks: (a) laying 
the blocks alternately, and then filling in between them; ( b ) allowing the 
scantling of the forms o remain in place until after the concrete is laid, 
and then filling the spaces they occupied with lean mortar or sand; (c) 
placing tarred paper between the blocks. The first method is usually 
preferable. 

The size of the blocks depends upon the width and shape of the walk or 
floor. Blocks nearly but not quite square have a better appearance than 
those which are distinctly oblong. The limit of size for a 4-inch walk is 
generally placed at 6 feet square. In 5-inch work this may be safely 
increased to 8 feet square. Joints should be placed around trees and about 
6 inches from buildings, manholes, or other adjacent structures. 

After ramming and leveling the foundation, if there is no curb to be 
formed, strips of scantling 2 inches thick, and of a width corresponding to 
the thickness of the walk, are placed on edge along the back and front lines 
of the walk, and held in place by stakes driven behind them. These strips 
should have notches cut in them to designate the location of the dividing 
line between the blocks. Other strips, located by these notches, are placed 
across the walk, which is now ready for the concrete. 

The concrete materials in the specified proportions are mixed as de- 

♦Specifications for 1899. 


6oo 


A TREATISE ON CONCRETE 


scribed on page 20. If the surface of the road is hard and smooth, the 
mixing may be done upon it without any platform. In any case, it must 
be very thorough, some contractors employing a man to rake each shovelful 
as it is turned by the two shovelers. Enough water should be added to 
produce a jelly-like consistency, the mortar rising to the surface when 
lightly rammed. The surface of the coarse concrete must be below the 
level of the top of the forms so as to give room for the finishing coat, or 
wearing surface. 

If the walk or floor is laid in alternate blocks by the first method (a), 
described above, the forms around each block are left in until after the 
top coat or wearing surface has been placed, and has slightly stiffened, 
when they may be removed and the alternate blocks laid. The latter 
must be placed on the same day, however, to avoid difficulty in forming 
the surface joints between the stones. If a filler is placed between the 
blocks, the forms are lifted soon after the concrete of the base is laid, and 
before the wearing surface is spread, and the joints filled with sand or, in 
some cases, by a “separator” of lean mortar mixed, say, 1 part cement to 
4 or 5 parts sand. Whatever the material used, it must be weaker than 
the concrete. 

Wearing Surface. As soon as a few of the blocks of concrete base have 
been laid, and before they have set, the mortar for the wearing surface must 
be placed. This surface, as described on page 594, consists of a mixture 
of cement and sand, cement and fine crushed stone, or cement and a 
mixture of sand and stone. The materials should be very exactly propor¬ 
tioned, so as to give a uniform color. The cement must not be mixed with 
the sand long in advance of its use because the natural moisture in the sand 
will cake the cement. If the work is progressing so slowly that the cement 
must be measured by pailfuls, a determination must first be made of the 
number of pails of loose cement in a bag or barrel of packed cement, and 
the number of pails of sand in a barrel of loose sand, then the relative 
volumes calculated ,to allow for the increase in bulk of the loose over the 
packed cement. Each pail must be filled in exactly the same way, so that 
one measure will not be more densely packed than the next. The sand 
and cement must be mixed dry until the color is absolutely uniform, when, 
if coloring matter is used, it is added to this dry material. Water is added 
to give about the consistency employed by a mason in laying brick, so that 
it can be readily leveled off with a straight-edge. This mortar is carried 
from the mortar box to the walk in pails, and smoothed off with a straight¬ 
edge guided by the tops of the forms. 

The surface is roughly floated with a plasterer’s trowel, shown in Fig. 186, 


SIDEWALKS AND BASEMENT FLOORS 


601 



Fig. i 86 . —Plasterer’s Trowel, or Metal Float. 
(See p. 600.) 


soon after leveling with the straight-edge, but the final floating is not 
oerformed until the mortar has been in place from two to five hours and 
has partially set. The final floating is done first with a wooden float and 
afterwards with a metal float or plasterer’s trowel. Just before the float¬ 
ing, a very thin layer of “dryer,” cQnsisting of dry cement and sand, mixed 
in proportions 1: 1 or even richer, is frequently spread over the surface, 
but this is generally undesirable as it tends to make a glassy walk. 

The surface is now 
ready to groove, for by 
this time the intermediate 
stones should be in place. 
As has been stated, the 
cross joints are in line 
with notches in the out¬ 
side forms. The mason 
can thus locate the joints 
between the blocks of base concrete. To find the line exactly, he runs his 
small pointing-trowel down through the upper layer, and feels for the 
joint below. With the ends of the joints thus marked, he lays a straight¬ 
edge flat across the walk against these marks, and, walking across on the 
straight-edge, marks the line and also cuts through the partially set mortar 
and concrete by running his small pointing-trowel to the full length of the 
blade. Moving the straight-edge back a fraction of an inch, he runs his 
groover (see Fig. 187) along the line cut by the trowel, using the straight¬ 
edge for a rule. Both edges of the walk are rounded off by the edging 
trowel (see Fig. 188), which is a small float with one of its edges curved. 
The entire surface is finally gone 
over once more with the metal 
float to erase any marks or 
scratches which may have been 
made. A dot roller (see Fig. 

189) or grooved roller may be em¬ 
ployed to relieve the smoothness. 

The exact time at which the surface should be floated depends upon the 
setting of the cement, and must be determined by the mason. Considerable 
skill is required in this troweling to prevent the formation of hair cracks by 
over-troweling, and to insure a surface which will not wear rough as a result 
of insufficient troweling. 

If the walk is exposed to the hot sun it may be necessary to cover 
it with a wood or canvas frame, or with moist sand, for several days 



Fig. 187.—Groover. (Seep. 601.) 




























602 a TREATISE ON CONCRETE 

after its completion, as it is absolutely necessary that it shall not dry 
out too quickly 

Effect of Frost upon New Concrete Sidewalks. If concrete sidewalks 
are exposed to frost before thoroughly hard and dry, the surface is likely to 
blister and scale off in patches about ^ inch thick. It is best, therefore, 
to avoid sidewalk construction in freezing weather. 

Concrete Curbing. Concrete curbing for artificial sidewalks is largely 

displacing stone curbing. The curb 
is built just in advance of the walk. 
It is divided into blocks and is sep¬ 
arated from the walk by joints similar 
to the joints between the blocks. The 
soil is excavated, and a foundation 
Fig.i 88 .- Edging Trowel. (See p. 6 oi.) porous materials of the same thick¬ 

ness as that employed under the walk 
proper is placed and rammed. In Boston* a layer of ordinary concrete 
12 inches wide and 8 inches deep is placed upon this foundation to underlie 
the curb. The curb proper is 12 inches deep and 8 inches wide at the 
bottom, tapering on the outside to a width of 7 inches at the top, with its 
inside face vertical. At least one inch of the face and of the surface con¬ 
sists of mortar or granolithic, like the 
wearing surface of the walk. A typical 
sidewalk and curb is shown in Fig. 190. 

The back of the curb is formed against a 
temporary plank. For the face mold, a 
12-inch planed plank is set on edge to 
the proper batter and may be held in 
place by driving stakes about 4 inches 
out from it, and nailing strips from the 

top of these stakes to the top edge of the 
plank, so that they can be knocked up 

and the plank loosened without disturb¬ 
ing the face of the curb. When ready 
to place the concrete for the curb, which 
should be laid before the layer of con¬ 
crete underlying it has set, a i-inch board is placed on edge just inside 
of the 12-inch plank, with occasional thin strips or wedges between 
it and the plank. The coarse concrete of the curb is then placed back 
of this board, and thoroughly rammed so that its surface is one inch 

♦Specifications for 1899. 



Fig. 189. —Dot Roller. 
(See p. 601.) 

















SIDEWALKS AND BASEMENT FLOORS 603 

below the top of the forms, and when sufficiently hard, the i-inch board 
is drawn up from the face, and with the aid of a trowel its place is filled 
with wearing surface material. The outside form is generally allowed to 
remain over night, and in the morning the outside surface is floated. A 
ruled joint like that between the blocks is formed between the curb and 
the remainder of the walk. 

A metal corner is sometimes laid in the exposed edge of the curb to 
protect it from wear. 

Combined Curb and Gutter. One of the advantages of a concrete walk 
lies m the ease with which it is adapted to special construction. A gutter 
5 or 6 inches thick, with a pitch corresponding to the crown of the street, 
is often laid in combination with the curb. It is underlaid with a porous 



Fig. 190. —Typical Concrete Sidewalk and Curb. (See p. 602.) 


foundation, and in some cases by a sub-soil tile drain. The blocks forming 
the combined gutter and curb are made about 6 feet in length, and are in 
alternate sections so as to form definite cross joints, but each section of 
the curb and gutter must be built together, with no longitudinal joint 
between them. 

Vault Light Construction. Sidewalk lights over basement areas or 
subways are formed of circular lights of plate glass, set in reinforced con¬ 
crete slabs, supported by steel or reinforced concrete beams. Steel rods 
about inch diameter are interlaced in both directions between all of 
the rows of glass discs. The width of the slab between beams is governed 
by the thickness of the slab, a customary width being 3 to 4 feet. The 
dimensions of the beams and girders, whether of steel or reinforced concrete, 
depend upon their loading and span. (See table, p. 508.) A typical vault 
































604 


A TREATISE ON CONCRETE 


light construction supported by steel girders and stiffened by concrete ribs 
as designed by Mr. Ross F. Tucker, is illustrated in Fig. 191. 

If concrete beams or stiffeners are used, they must be laid at the same 

time as the slabs are placed, so as to be in the same piece with them, but 

♦ 

contraction joints must be provided as shown. In laying the slabs, the 
position of the glass discs may be located by an iron plate with holes of the 
size of the glass discs. On top of this iron form, a layer of oiled paper is 



*76* STEEL ROD 

SECTION THROUGH LIGHTS 



spread to prevent the cement sticking to it, the lenses are set upon the 
paper over the boles, the reinforcing rods placed, and the mortar poured 
around the glass, and its surface troweled after partially setting, same as 
the surface of a granolithic walk. After the mortar has become thoroughly 
nard, the metal plate and the paper may be removed. 

COST AND TIME OF SIDEWALK CONSTRUCTION 

The cost of concrete sidewalk or basement floor construction is extremely 
variable. The job at any one location is likely to be small, not occupying 














































































SIDEWALKS AND BASEMENT FLOORS 


6° 5 

more than a few days, so that the time and expense of transporting men 
and materials, and the time getting started upon the work, constitute an 
important item. The skill of the men employed in placing and finishing 
the concrete affects the cost still more, since an experienced gang may 
easily lay three times as much surface of walk in a day as inexperienced 
men, even if the latter are accustomed to ordinary concrete work. Exca¬ 
vation is another variable item, depending upon the quantity of earth to be 
removed and the character of the material. 

A gang of convenient size consists of — 

One mason. 

One man to assist the mason in placing forms, and to level and ram the 

concrete. 

Three men mixing and placing coarse concrete for base. 

One man mixing top dressing for wearing surface. 

If excavation is included in the work, more laborers may be needed. 
The amount of walk covered by a gang is limited by the surface which can 
be floated and troweled by the mason. Unless he works overtime, the 
laying of concrete must stop about the middle of the afternoon in order 
that the wearing surface may have opportunity to set. Meanwhile, the 
concrete gang may prepare and ram the foundation and get everything in 
readiness to begin concreting promptly the next morning. With a gang of 
the size suggested a foreman adds considerable to the expense, and it is 
often advantageous to so arrange the work as to make the mason responsible 
for its quantity and quality. A bonus paid for an excess over a certain 
area of surface covered is an effective incentive for a good day’s work. In 
order to properly fix such a bonus the employer must know the relative 
times required for plain sidewalk and curb. The size of the blocks must 
also be considered, since the labor upon the joints forms a prominent 
division of the work. 

Under average conditions a mason skilled in this class of work should 
float and trowel a surface of 600 to 700 square feet in eight hours, if no 
allowance is made for time which is necessarily lost between jobs and in 
commencing work. This lost time will lower the average by an amount 
varying with the size of the job. If the excavation is ready, five men work¬ 
ing with the mason should prepare the foundation and place the base 
concrete and the mortar for the wearing surface for a walk 4 to 4^ inches 
thick. For a thicker walk, one more man may be required in the gang to 
keep up with the mason, since a thick walk requires more concrete or 
mortar. 

The contract price for a granolithic or artificial walk from 4 to 5 inches 


6o6 


A TREATISE ON CONCRETE 


in thickness, with Portland cement at about $2.00 per barrel, varies from 
$0.22 to $0.30 per square foot. The cost of curbing runs about $0.75 to 
$1.00 per linear foot without a metal strip, and 25 to 50 cents higher 
with it. 

DRIVEWAYS 

For driveways the concrete is laid similarly to that in sidewalk construe- 
tion. The total thickness may be 5 inches for light travel, or 6 io 7 inches 
for heavy teaming. Grooving the surface in 6-inch squares affords foothold 
for the horses. 


CONCRETE STREET PAVEMENTS 

Concrete pavements in alley ways, constructed like sidewalks except 
marked off into small blocks, have been in successful use in Boston and else¬ 
where, since 1894. In 1896 a street pavement built in Richmond, Ind., by 
Mr. H. L. Weber, proved so successful that many other concrete pavements 
have been laid there, and the use has been extended to other cities. Re¬ 
sults have been satisfactory where traffic is not too heavy, and where the 
very best of materials and workmanship have been employed. 

The construction of concrete street pavements is similar to sidewalk 
construction but even greater care must be used to be sure that it is mono¬ 
lithic from top to bottom so that there can be no separation of layers. Un¬ 
less the soil is very porous so as to drain off the water and at the same time 
form a non-compressible foundation, a porous material like broken stone 
or screened gravel thoroughly compacted and rolled should be laid for a 
depth of about 5 to 6 inches. Sometimes a 6-inch concrete foundation is also 
advisable. After laying the foundation a concrete base 4 inches to 6 inches 
thick is laid in proportions of about 1 : 2\ : 5 and the wearing surface must 
be placed at the same time or immediately following it so as to make one 
solid layer. The construction of the wearing surface is the most critical 
part of the work, for upon it depends the durability of the pavement. The 
best aggregate is crushed granite or trap or a mixture of this and sand. It 
must be free from dust and a considerable proportion of it should be as large 
as J in. in size. Instead of using 1 : i| or 1 f 2 mortar, it is still better to 
form a true concrete, using proportions of about one part cement to one and 
one-half parts sand to two parts of crushed screenings. This is laid wet 
and may be troweled and divided into small blocks, or may be given a rough 
finish to afford a good foothold for horses. Expansion joints should be 
made along the curbs and across the street about every 30 feet apart. 


CONCRETE BUILDING CONSTRUCTION 


607 


CHAPTER XXIV 

CONCRETE BUILDING CONSTRUCTION 

The rapid development of the use of concrete both in the United States 
and Europe is the best evidence of its adaptability for a building material. 
This is exemplified in numerous structures which, not only from an en¬ 
gineering standpoint but architecturally as well, are models of the builder’s 
art. 

In work above ground, concrete is most extensively employed in the 
building of floors and roofs. Its especial availability for this class of con¬ 
struction has been made possible by the introduction of numerous systems 
of metal reinforcement, the application of which has resulted in the reduc¬ 
tion of the thickness and brittleness of the slabs. 

The fire-resisting qualities of Portland cement concrete when composed 
of first-class materials, such as sand, and gravel, hard broken stone, or 
cinders, appear both from experimental and actual fire tests to be equal or 
superior to those by any other material. (See Chapter XVIII, p. 327.) 
Moreover, its strength and permanence, when it is carefully laid and prop¬ 
erly reinforced, are unquestioned, and by employing a wet mixture the 
mortar in the concrete surrounds and effectually prevents the corrosion of 
the metal with which it is reinforced. 

Its fire-resisting quality has led to the adoption of reinforced concrete 
for stairways, for columns and girders, and finally for entire buildings. 
The growing confidence in its utility for office buildings seems to promise 
for it successful competition with steel fireproof construction and a wide use 
in this class of structures. The cost of the reinforced concrete for an 
office building built of this material in 1904, based on actual construction 
records, with cement at $2.00 per barrel delivered on the work, was about 
20% less than the estimated cost of the steel and tile of ordinary fireproof 
construction. As the concrete portion constituted about one-fifth of the 
total cost of the building, the net saving is reduced to about 4%, a very 
considerable sum, however, when figured on a fifteen-story office building. 
There is also an additional saving in other materials due to the reduction 
in height of the building because of the thin concrete floors, and to the 
fewer coats of plaster, with omission of furring, on walls and ceilings. 

The Ingalls Building, designed by the Ferro-Concrete Construction 
Company and erected in Cincinnati, O., in 1903, was the first notable 


6o8 


A TREATISE ON CONCRETE 


example of a concrete office building in the United States. Sixteen stories 
high, it is entirely of concrete, with the exception of the facing of the exte¬ 
rior walls. 

For factory building reinforced concrete is gradually superseding “slow- 
burning” mill construction with its brick walls and timber beams and col¬ 
umns. In certain cases the concrete has been found actually cheaper than 
the wood, three 6 story factory buildings in Cambridge, Mass., for example, 
being erected in 1908 at a lower cost than competitive estimates for wood 
and brick construction. Even if the cost for reinforced concrete runs from 
8% to 10% higher than the estimate for brick walls, timber columns and 
girders, and plank floors since the concrete portion is only about one-half 
the total contract, the increased cost of the entire building is only 4% to 
5%. The concrete building has greater durability and is fireproof, thus 
reducing running expenses and affording lower insurance rates. 

For dwellings and other small buildings the cost of the forms alone may 
exceed that of the materials and labor on the concrete. In estimating the 
labor, allowance must be made for the time which is often necessarily lost 
in waiting for the cement to harden or the forms to be removed. For these 
reasons it may be more economical to work with a small gang, taking an 
entire day to lay the concrete to the height of one section of forms. 

For the cellar and foundation walls of frame or brick houses (see p. 619), 
concrete is usually cheaper than rubble masonry. 

A method of construction of light curtain or division walls consists in 
plastering Portland cement mortar upon metal lathing. A 2-inch wall thus 
made forms a permanent and fire-resisting partition. (See p. 627.) 

Molded blocks of mortar or concrete (see p. 629), or concrete tile (see 
p. 629), are adapted to certain classes of structures. Under favorable con¬ 
ditions the cost may be less than that of a brick wall of equivalent thickness. 

CONCRETE FLOORS 

Concrete floor slabs are supported by steel or sometimes by timber gir¬ 
ders, or are formed in combination with reinforced concrete girders. The 
metal reinforcement which is universally adopted for the slab not only 
reduces the thickness and weight of the floor, but prevents sudden failure, 
an extremely important consideration in this class of structures. 

Concrete floor panels between steel girders must compete chiefly with 
porous tiling and brick arches. The relative cost of these three materials, 
while dependent upon the location of the work and market prices, is usually, 
all things considered, in favor of concrete. The encasing of the steel 
I-beams with fine concrete or mortar affords fire protection to the girders 
and, if desired, a continuous surface for plastering. 


CONCRETE BUILDING CONSTRUCTION 609 

Design of Concrete Floors. The design of a complete floor system with 
reinforced concrete beams, girders and slabs is illustrated in the example, 
pages 468 to 474. The details of the design are also treated in Chapter 
XXI and the tables in the same chapter, pages 507 to 526, give means to 
determine very quickly the dimensions and reinforcement for different spans 
and loadings. Reinforced floors are strongest when made continuous over 
several bays provided they are properly reinforced at the top over the sup¬ 
ports as well as in the bottom at the center. It is essential that the beam 
and slab shall be laid at the same operation. Slabs laid between steel I- 
beams, as in Fig. 193, page 616, are not so strong as when built in with 
reinforced concrete beams. 

The arrangement of the floor beams and girders in a building of rein¬ 
forced concrete depends upon so many considerations that special study 
is required in each case. 

The smallest quantity of material is required with floor panels of short 
span and frequent floor beams to support them. However, very thin slabs 
and beams of concrete are not easy to construct properly, and there is 
difficulty in imbedding the metal, so that we may, in general, limit the 
thickness of both to not less than 3 inches. For the slabs this minimum 
should be raised where a floor is liable to sudden strains, such as the falling 
of a load, which tend to punch a hole through the floor. For beams a 
more practical minimum width is usually 5 or 6 inches, since the cost of 
the form, which is but slightly more for a large than for a small beam, is 
a considerable item, and a deep, thin beam is in danger of buckling and 
requires frequent cross beams or stiffeners. 

The spacing of the beams may, therefore, be governed in some cases by 
the required thickness of the floor slabs and in others by their own eco¬ 
nomical construction. Similar considerations, applied to column and foun¬ 
dation construction, govern the design of the principal girders. 

The Ingalls Building* presents an example of slabs of long span sup¬ 
ported by heavy girders, and the factory of the Pacific Coast Borax Com¬ 
pany)* an example of thin floor slabs with frequent deep but narrow concrete 
beams. 

In simple cases the dimensions and reinforcements of concrete floor gir¬ 
ders may be obtained directly from the tables, pp. 509-511. More difficult 
problems require mathematical calculation as treated in Chapter XXI. 
Not only must the size of the tension rods in the bottom of the beam be 
considered, but also the size and location of the U-bars, the reinforcement 

*See page 611. 

•j-See page 621, also Engineering Record, July 30, 1898. 


6io 


A TREATISE ON CONCRETE 


in the top of the beam, if required, and the proper connection with the col¬ 
umns. The girder illustrated in Fig. 192, page 613, is a typical design 
for a concrete beam supporting a heavy load, although the dimensions and 
reinforcement apply, of course, to a particular piece of construction.* 

There are several methods of laying floors supported by steel girders, 
one of the most common of which is illustrated in Fig. 193, page 616. The 
haunches of the slab are carried down to the lower flange of the I-beam, 
the under surface of which may be covered with metal lathing for fire 
protection and plastering. The I-beam may be entirely enclosed in the 
concrete, but it is difficult to place the material under the lower flange. 
Where head room is very valuable, the top of the slab is laid flush with the 
top of the beams and the metal is placed between the beams instead of 
running over them. In either case the outline of the concrete may form 
the ceiling, the plastering being placed directly upon it so as to form panels, 
or the ceiling may be suspended from the I-beams on metal lathing. 

Floors are sometimes laid as continuous slabs, imbedding simply the 
upper flange of the I-beams in the concrete. The forms are cheaper to 
construct, but the strength is less than with the haunches, and the web of 
the I-beam is not protected from fire. For ceilings, separate slabs may be 
formed resting upon the lower flanges of the I-beams. Still another type 
of floor consists of concrete arches sprung between the lower flanges of the 
I-beams, just as brick arches are formed, and filled to the floor level with 
cinders. They do not necessarily require reinforcement. 

The metal reinforcement in a floor slab should be as near to the under 
surface as is consistent with durability and fire resistance. For a strictly 
fireproof building it is safest to allow at least an inch of concrete below the 
metal, but under ordinary conditions this may be reduced to f inch or 
2 inch, provided the concrete is mixed wet and carefully placed around 
and under it. If'plain rods are used, they must be prevented from slipping 
by selecting very long lengths or by anchoring the ends, or both. If the 
ends are bent for this purpose, there must be a considerable thickness of 
concrete beyond the bend to prevent the tendency under load to straighten 
out and thrust through the concrete. 

Safe Floor Loads. The following loading for floors, suggested for the 
Boston building laws by a committee of the Boston Society of Civil Engi¬ 
neers in 1904, represents first-class modern practice: 

All new or renewed floors shall be so constructed as to carry safely the 
weight to which the proposed use of the building will subject them, and 
every permit granted shall state for what purpose the building is designed 

*See also designs suggested, page 45',. 


CONCRETE BUILDING CONSTRUCTION 


6n 


to be used; but the least capacity per superficial square foot, exclusive of 
materials, shall be: 

For floors of dwellings and for apartment floors of apartment and public 
hotels, fifty pounds. 

For office floors and for public rooms of apartment and public hotels, 
one hundred pounds. 

For floors of retail stores and public buildings, except schoolhouses, 
one hundred and twenty-five pounds. 

For floors of schoolhouses, other than floors of assembly rooms, eighty 
pounds, and for floors of assembly rooms, one hundred and twenty-five 
pounds. 

For floors of drill rooms, dance halls and riding schools, two hundred 
pounds. 

For floors of warehouses and mercantile buildings, at least two hundred 
and fifty pounds. 

The loads for floors not included in this classification shall be deter¬ 
mined by the Commissioner, subject to appeal, as provided by law. 

The full floor load specified in this section shall be included in propor¬ 
tioning all parts of buildings designed for dwellings, hotels, schoolhouses, 
warehouses, or for heavy mercantile and manufacturing purposes. In 
other buildings, however, certain reductions may be allowed, as follows: 
In girders carrying more than ioo square feet of floor, the live load may be 
reduced by io per cent. In columns, piers, walls, and other parts carrying 
two floors, a reduction of 15 per cent of the total live load may be made; 
where three floors are carried, the total live load may be reduced by 20 
per cent; four floors, 25 per cent; five floors, 30 per cent; six floors, 35 per 
cent; seven floors, 40 per cent; eight floors, 45 per cent; nine or more 
floors, 50 per cent. 

Weight of Concrete in Floors and Girders. The following table is 
based on an average weight of broken stone or gravel concrete of 150 lb. 
per cubic foot, and of cinder concrete of 112 lb. per cubic foot, to each of 
which has been added the weight of 4 lb. per cubic foot to provide for 
maximum weight of about 1% of reinforcing steel. 

The weight of stone concrete varies not only with the proportions of the 
mixture (see p. 361) but also with the specific gravity of the aggregate, and 
for particular cases, the weights on page 3, which are based on tests made 
at the Watertown Arsenal and Washington University and checked by 
calculation from the specific gravity of different materials, may be used 
instead of the table. The table, however, is sufficiently exact for ordinary 
practical purposes. 

Floors in the Ingalls Building. In the Ingalls Building at Cincinnati, 
Ohio, whose floors above the second floor were designed for a live loading 
of 60 pounds per square foot, the principal panels, which are about 16 feet 
square, are 5 inches in thickness, and reinforced with f-inch rods. Smaller 


6l2 


A TREATISE ON CONCRETE 


panels of 3 to 6 feet in length are about 3 inches thick with J-inch bars. 
The spacing of the rods varies with the length of the span. Where the 
panels are approximately square, the tension rods run in two directions, 
and where the panels are long and narrow, the tension rods run across the 
panel, with J-inch rods about 3 feet apart running lengthwise of the panel, 
to prevent contraction cracks. The principal girders are 32 feet long 
between centers of columns, and 27 inches in depth (measured to surface 
of concrete floor), and of width varying from 20 inches at the lower floors 
to 16 inches at the upper floors. Cross girders about 16 feet in length and 
18 inches deep, of widths varying from 12 to 9 inches, are placed in the 
center of the span of the main girder, thus dividing the floor into slabs 


Weight 0 } Reinforced Concrete in Slabs and Beams. (Seep. 6 11 .) 


Weight of Reinforced Slabs per Square Foot. 

Weight of Reinforced Beam one inch 
wide per foot of length. 

Thickness 

Stone Concrete 

Cinder Concrete 

Depth of Beam 

Stone Concrete* 

in. 

lb. 

lb. 

in. 

lb. 

2 

26 

19 

6 

6.4 

2 i 

32 

24 

7 

7-5 

3 

38 

29 

8 

8.6 

3i 

45 

34 

9 

9.6 

4 

51 

39 

xo 

10.7 

4 i 

58 

43 

12 

12.8 

5 

64 

48 

14 

15.0 

5i 

70 

53 

16 

17.1 

6 

77 

58 

18 

19.2 

7 

90 

68 

20 

21.4 

8 

103 

77 

2 5 

26.8 

9 

115 

87 

3 ° 

3 2 - 1 

10 

128 

97 

35 

37-4 


* Multiply by the length of beam in feet times its width in inches. 


about 16 feet square. Fig. 192, page 613, is an isometric view showing the 
dimensions and reinforcement of the floor, main girder, cross girder, wall 
column, and wall in the fourth and fifth floors. The total distributed 
loading on the main girder is about 15 tons live load in addition to the 
weight of the reinforced concrete. 

Materials for Floors. A first-class Portland cement which will meet 
the standard specifications given on page 29 must be selected. The 
rules for the selection of the aggregate are the same as for other classes of 
concrete' The size of the coarsest aggregate is often limited to one inch, 
but if well graded, so that the larger particles will not'collect and prevent 
the flow of the mortar around the steel, the limit of size for beams, say, 

















613 


FIG. 192 TYPICAL REINFORCING IN BUILDING 

CONSTRUCTION 

(See p. 612) 



CONCRETE BUILDING 


CONSTRUCTION 


fir-? 



/ j | Wl NDOW OPENING ^ ^ 

[j ]j 5 IN.FLOOR^ 

l^-VERTICAL TWISTED STEEL 
11 RODS.EXTENOINQ from MIDDLE^'' \ 
| I OF STORY TO MIDDLE OF STORY, N s 
|| &. DIMINISHING IN NUMBER AND ''-v 

,| SIZE, FROM THE BASEMENT TO 
|| IOTH STORY.- WHERE BUT FOUR 
I, • "BARS ARE CONTINUED TO THE 
V TOP ST^Y. 

J^WALL COLUMN 

^^COMPRESSION RODS WITH* MILLED BUTT 
' JOINTS. ENCLOSED IN PIPE SLEEVE, AND 
I GROUTED WITH CEMENT. (SEE DETAIL.) 

| JOINTS OCCUR AT A POINT JUST ABOVE 
ALTERNATE FLOORS. 

- J these RODS DIMINISH IN i*0ZE AND 
** NUMBER UP TO THE 5TH A*ND 9TH 

STORIES,(ACCORDING TO THE COLUMN,) 
WHERE THEY ARE DISCONTINUED. 


I IN. RODS' 


NOTE;- DOTTED LINES, SHOW OUTLINES OF CONCRETE CONSTRUCTION 
FULL LINES SHOW STEEL.BARS LAID IN CONCRETE 


DETAIL OF 
PIPE SLEEVE JOINT 
FOR COMPRESSION RODS 


VERTICAL TWISTED STEEL 

^JP'NO FROM MIDDLE 
OF STORY TO MIDDLE OF STORY, 
& DIMINISHING IN NUMBER AND 
. S '^S THE BASEMENT TO 
°I«r^. TORY '* WHERE BUT four 
I BARS ARE CONTINUED TO THE 
TOP STORY. 


BARS 


JLalternate 

|FLOOR LEVEL 


NOTE:- Whoops in cols. 12 ins. o. o. where compression bars are used. 

AND 20 INS. O. C. FOR STORIES ABOVE, WHERE COMPRESSION BARS ARE 
DISCONTINUED. 


FIG. 192. Typical Reinforcing in Building Construction, showing one-half of a main Girder, Floor and Wall Column. (See p. 612.) 



























































































































CONCRETE BUILDING CONSTRUCTION 615 

5 inches in width and floors not less than 4 inches thick may be as high 
as 1 j inches. 

Cinders for concrete should contain but little unburned coal and be free 
from soot. A clean cinder will not discolor the palm when held in it and 
rubbed with the fingers. Usually a better mixture can be obtained by 
screening the fine stuff from the cinders, and then, if gritty, mixing it with 
sand, than by using unscreened material, although if the fine stuff is found 
by tests to be uniformly distributed through the mass, it may be used with¬ 
out screening and a smaller proportion of sand added. 

Usual proportions for floor concrete are 1:2^15, that is, one barrel 
packed Portland cement, 9.5 cu. ft. sand, and 19.0 cu. ft. of screened stone 
or screened cinders. If the thickness of the floor is such as to provide a 
wide margin of safety, the proportions may be 1:3:6 (based on a barrel of 
3.8 cu. ft.), while for extra strong work 1:2:4 may be specified. For 
beams and girders 1:2:4 and 1: 2J: 5 are common proportions. Cinder 
concrete should not be used for girders, but under certain conditions may 
be employed for floor slabs. While it is lighter in weight, generally cheaper, 
and equal in fireproof qualities to first-class stone concrete (see p. 329), it 
is not so strong. Hence, for the same loading a greater thickness is re¬ 
quired, and it is not usually economical even for floor slabs except the span 
and the loading are so small that the thickness of the floor is governed, not 
by required strength, but simply by the practical conditions of laying which 
limit it to a thickness of not less than 3 inches. In carefully designed 
reinforced buildings stone concrete is generally preferred. 

The quantity of cement, sand, and stone or cinders required for any 
structure may be calculated from the table on page 231, or, for slabs, taken 
directly from the table on page 596. 

Laying Floors. The general directions for mixing and placing concrete, 
given in Chapter II, p. 20, and Chapters XIV, and XV, are applicable 
to building construction. 

The concrete must be mixed wetter than in sidewalk or basement floor 
construction, as described in the preceding chapter, so that the mortar 
may flow around the metal and thoroughly coat and protect it from rust 
and fire. The criterion of wetness may be that unless handled quickly it 
will flow off the shovel. 

If the concrete floor is to provide a wearing surface, a granolithic finish 
may be given to it by laying a mortar wearing surface before the lower 
portion has set, as described for sidewalks in the preceding chapter, or the 
concrete may be troweled without the coating of mortar. The latter plan 
is amplv sufficient for floors which are not subjected to excessive wear. 





6 i6 


A TREATISE ON CONCRETE 


For a board floor, nailing strips are laid upon the concrete, or imbedded 
in it at right angles to the supporting beams. With cinder concrete the 
plan is sometimes followed of nailing the floor boards directly into the con¬ 
crete. The objection to this is that the surface of the concrete must be 
leveled with great care, and it is difficult to relay the boards if a new floor is 
required because the concrete becomes so hard with age. 

The cost of the labor of laying a concrete floor is dependent upon the 
character of the building. In a case under the observation of the authors 
where the floors consisted of cinder concrete resting upon steel I-beams, 
a gang of nine laborers, with a foreman (in addition to the engineman, who 
ran the elevator,) mixed concrete in the basement to supply a gang of 
eleven men, with foreman, who, on one of the upper floors, were placing 



Fig. 193. — P'orm for Concrete Floor between Steel I-Beams. (See p, 616.) 


metal, wheeling concrete, leveling it, and cleaning forms. Six carpenters, 
with foremen, were employed building the forms, which were supported 
from the girders, in advance of the concreters. This gang averaged 22 to 
25 batches (corresponding to 17 to 19 cu. yd.) of 1 : 2 : 5^ cinder concrete in 
nine hours. 

Floor Forms. In a large building the floor panels should if possible be 
so designed that the same forms may be used more than once, although 
they must not be removed until the concrete has attained sufficient strength 
to sustain its own weight and any loading which will come upon it. 

If the floor slabs are supported by steel I-beams, the forms may be 
attached to the lower flanges, as shown in Fig. 193 a design of Mr. Wil¬ 
liam F. Kearns. The steel, however, must be bent up further from the 
support than is shown in the drawing and carried nearer to the top of the 
s ] ab to prevent cracking near the I-beam. 





























































CONCRETE BUILDING CONSTRUCTION 


617 

If the girders are also of concrete, the supports for the form must be heavy 
enough to carry the weight of the beam of concrete, as well as the floor slab 
and the men and materials upon it. The forms must be so tight as to 
prevent the water and thin mortar running away from the concrete and 
carrying off the cement. This may best be accomplished by tongued- 
and-grooved or bevel-edged boards, but it is often possible to use square- 
edged lumber if it is thoroughly wet to swell it before placing the concrete. 

Joints in the beam forms may be 
covered with cleats. 

A simple form of clamp for 
beam or small column forms, 
used originally in Europe, is shown 
in Fig. 194. The hook, A, is a 
plain piece of flat iron J inch by 
1J inches, with one end bent and 
curved as shown. The dog, B, 
is a square piece of iron, with the 
end slightly turned and a hole 
slightly larger than the flat iron, 
A, punched through it. This is tightened by hammering on its lower end. 
The outward pressure of the form boards upon its upper end causes it to 
bind, and prevents it from slipping back. If it fails to hold, in any case, 
a wooden wedge is readily driven in to assist in tightening. 

CONCRETE STAIRS 

The design of concrete stairs is a simple problem in reinforced concrete 
construction. A stairway may consist (1) of an inclined slab of reinforced 
concrete with the steps molded upon its upper surface, or (2) of two or, for 
a wide stairway, three inclined girders to form the stringers, with the stairs 
between them. The first method is suitable for short flights not over 8 
or 10 feet in length measured on the slope, and the thickness and reinforce¬ 
ment are calculated as for a slab supported at the ends. (See pp. 512 to 
515.) The principal reinforcement is of course in the direction of the 
length with occasional cross metal for stiffening. A slab 5 inches thick 
measured at the foot of the risers is suitable for a stairway half a story high. 

When built with side girders, the dimensions of each of the latter may 
be calculated as a concrete beam with a longitudinal rod near the lower 
surface. A small rod also runs across from girder to girder at the foot of 
each riser so that the risers are practically reinforced beams. It is usually 
cheaper to construct the under side of the stairs as a slab than to build 



HOLE . 

r x T 




*■ \i* 


I k 
« 


Fig. 194. — Clamp for Beam or Small 
Column Form. ( See p. 617.) 
























6 i8 


A TREATISE ON CONCRETE 


forms for each stair. The forms for the stringers may consist of planks 
notched for treads and risers, with boards nailed across as molds for the 
faces. If a fine finish is desired, the method of surfacing described for 
curbing may be followed. (See p. 602.) 

CONCRETE ROOFS 

Concrete roofs are designed and laid in much the same manner as are 
floors. The forms also are similarly constructed. As the weight of the 
roof itself forms a large proportion of the total load upon the girders, cinder 
concrete, because of its light weight, is especially adapted to this class of 
construction. The strength of the concrete may also play a smaller part in 
roofs than in floors, because the length of span may be governed by other 
conditions, and the concrete may often be laid as thin as is practicable to 
lay it and properly imbed the metal. 

The wetness of the concrete is limited by the slope of the roof, although 
for a steep slope it may be necessary to confine the surface of the concrete 
by forms. 

The proper thicknesses and reinforcement for different spans may be 
obtained from tables on page 512 or 515, selecting the weights from the data 
in the paragraphs which follow. 

Roof Loads. A roof load is made up of the weights of the roof itself, 
the roof covering, the snow load, and the wind load. 

The weight of the concrete may be obtained from the tables mentioned. 

Prof. Mansfield Merriman* gives the following estimates for the weight 
of roof covering: 

Tin, 1 lb. per square foot of roof surface. 

Iron, 1 to 3 lb. per square foot of roof surface. 

Slate, 10 lb. per square foot of roof surface. 

Tiles, 12 to 25 lb. per square foot of roof surface. 

Average may be taken at 12 lb. per square foot. 

The snow load varies with the slope of the roof and the locality. Prof. 
Merriman allows for an approximate average 15 lb. per square foot of 
horizontal area. 

The wind load, which acts horizontally, varies with the velocity of the 
wind, a usual pressure being assumed as 40 lb. per square foot of vertical 
surface. This pressure multiplied by the sine of the angle of slope of the 
roof gives the pressure normal to the surface. 

In practice it is common to specify a minimum value for the roof load to 

* Merriman’s “Roofs and Bridges,” p. 4. 


CONCRETE BUILDING CONSTRUCTION 


619 

include the weight of the roof covering, snow, wind and any moving loads 
which may come upon it. A usual value for this total is 30 pounds per 
square foot. 

It is seldom advisable to build concrete roofs without an external cover- 
ing, such as tar and gravel. However, small surfaces laid by expert work¬ 
men at one operation to avoid joints and designed with special reinforce¬ 
ment have given satisfaction. 

Concrete is adapted to roofs of special design. One form is the dome, 
which is discussed and illustrated on page 626. 

CONCRETE WALLS 

If Portland cement concrete could be laid in thin walls as cheaply as in 
mass work it would be one of the most inexpensive materials for permanent 
construction. As a matter of fact, an experienced contractor can build a 
6-inch wall of concrete which will be stronger, more durable, and no more 
expensive than a 12-inch wall of brick. 

The chief cost in concrete wall construction is in the labor of building 
and raising the forms and of hoisting the concrete. The former varies 
with the method of construction and the number of angles in the wall. In 
the case of a large structure the concrete may be hoisted in elevator buckets* 
by power. If the building is small and the concrete is hauled up by hand 
in buckets to a height of, say, 15 feet, at least twice as many men will be 
required to fill pails, haul up, and carry to place as are needed for measur¬ 
ing and mixing the concrete on the platform below. 

Methods of surfacing concrete walls are described on page 288. Plaster¬ 
ing is unsatisfactory. 

Cellar Walls. Cellar or basement walls adapted to withstand earth pres¬ 
sure may be thinner when of concrete than when built of stone, because 
laid as a continuous vertical slab supported at top and bottom. 

For a wall of 1 : 2\ : 5 Portland cement concrete with a spreading base 
imbedded in the earth, a thickness of 10 inches will withstand without 
reinforcing metal a pressure of 6 feet of earth. If the top of the wall is 
strengthened by a wooden sill imbedded in or dogged to the concrete, and 
the sill is stiffened by floor joists, the wall becomes a slab supported at its 
bottom by the earth and at its top by the sill. A 6-inch wall 8 feet high 
will thus withstand the pressure against it of 6 feet of earth. However, 
}-inch rods, spaced about 2 feet apart in both directions, will greatly 
stiffen so thin a wall, and prevent cracks before the concrete is thoroughly 
hard. If desired, a coping of concrete wider than the wall itself may be 
formed at the top and a J-inch rod placed horizontally in its inner face. 

♦Method used at the Ingalls Building is illustrated in Engineering News , July 30, 1903, p. 95 


/ 


620 


A TREATISE ON CONCRETE 


The earth must not be filled in against the back of the wall until three oi 
four weeks after placing, unless portions of the interior forms are left in 
place and carefully braced. 

Designs for reinforced concrete retaining walls are illustrated on page 666. 

A simple form for a cellar or foundation wall is illustrated in Fig. 195 
A ranger, A A, is lined, and lightly spiked to occasional studs whose pointed 
ends are driven into the ground, and kept in line by strips of wood running 
from it to stakes in the bank. In some cases it may be advisable also to 
set a lower ranger between the studs and the bank. Occasional stakes, 
BB, are driven in the ground, and a ranger, CC, for the inside row of studs, 



is laid on top of them, lined, and lightly spiked to them, while the upper 
ends of these studs are held by cleats, DD, run across to the inner row of 
stud?. Vertical strips, EE, about J inch square, are placed inside of each 
stud for the form planks to rest against, and after a section of concrete 
is laid are easily knocked out, and the form planks raised to another 
level. The first layer of concrete is allowed to flow out under the lower 
plank to form a footing, above which the cellar floor is laid. The number 
of the laborers and the height of the forms should be such that the planks 
may be raised each morning, provided the concrete is hard enough to 
withstand the pressure of the thumb without indenting. 







































































CONCRETE BUILDING CONSTRUCTION 


621 


Walls for Buildings. Concrete walls are either of single thickness, or 
double with an air space between. The double wall has greater stability, 
and the air space renders the interior of the building less subject to changes 
in temperature and more completely moisture-proof. Moisture is likely 
to collect on the inside of a single wall. 

A single concrete wall 4 inches thick with its base spread to provide 
a footing is at least equivalent to an 8-inch brick wall, and a 6-inch con¬ 
crete is at least equivalent to 12 inches of brick. It is advisable to place 
small reinforcing rods, about j inch in diameter, 12 inches to 2 feet apart 
in walls 6 inches thick or under, not only to increase their permanent 
strength, but to guard against accidents during or immediately after 
construction. Occasional projections or pilasters improve the appearance 
and add to the strength of a single wall. 

Each face of a hollow wall is usually 3 to 4 inches thick, 3 or 3^ inches 
being the minimum thickness at which concrete can conveniently be 
placed. 

The four-story factory building of the Pacific Coast Borax Company at 
Bayonne, N. J., designed by Mr. E. L. Ransome, is an excellent example 
of hollow wall construction. The thickness of both faces of the walls is 
3 1 inches. The walls of the first story are 16 inches from surface to sur¬ 
face, that is, the space between is 9 inches, while the walls of the upper 
stories are made thinner by reducing the width of the hollow space. The 
general construction of a hollow wall is illustrated in Fig. 197, page 623. 

The walls of the Ingalls Building consist of concrete 8 inches in thick¬ 
ness, faced with brick or marble. They are supported by reinforced 
columns spaced about 16 feet on centers, and the portions of the wall at 
the floor lines, that is, between the top of the window of one story and the 
window-sill of the story above, are, in reality, concrete beams reinforced 
by two ^-inch bars placed 2 inches above the top of each tier of windows, 
with J-inch horizontal bars 2 feet apart over the remainder of the wall. 
In addition to the column reinforcement vertical bars are placed 2 inches 
from each window opening. 

The marble facing is supported at each floor line by triangular projec¬ 
tions in the concrete, and the brickwork in the stories above by square 
projections 3J inches wide. The marble is also held at each horizontal 
joint by anchor bolts imbedded in the concrete, and the brickwork by ties 
of round, straight rods about 8 or 9 inches long and J inch in diameter, 
placed through small holes in the outer forms before concreting so as to 
extend 5 inches into the concrete. 

Wall Forms. A simple form for a cellar wall is illustrated and described 


622 


A TREATISE ON CONCRETE 


on page 620. A form for a wall of single thickness is illustrated in Fig. 196 
The concrete is first laid to the full height of the ribs, then the bolts are 
loosened, the ribs raised one-half their length, so that one-half of each still 
laps over the concrete to keep the wall true and straight, and the forms are 
again filled with concrete to the top. Two bolts to each pair of ribs are 
all that are required after the concreting is commenced. These are re¬ 
moved before the wall is hard, so that they need be simply greased and 
the holes filled solid full with mortar mixed in the same proportions as the 



mortar in the concrete. The collar and set screw shown in detail is con¬ 
venient where the walls or columns are of various dimensions, although 
usually an ordinary threaded bolt with nut and washer may be used. 

A design for a form for a hollow wall is shown in Fig. 197. The ribs 
and bolts are so arranged that the latter do not pass through the concrete, 
the form being raised when the concrete reaches their level. In the same 
figure is shown a style of tongued and grooved molding with edges slightly 
beveled, which may be used to form the horizontal joint instead of nailing 
























































































CONCRETE BUILDING CONSTRUCTION 


623 

a triangular strip upon the planks. If the surface is finished as a mono¬ 
lith of course no moldings are required. The forms must be nearly water¬ 
tight, to prevent the mortar running away from the stones. 

Placing Concrete in Walls. For thin walls it is necessary to use mushy 
concrete, so soft that it must be handled quickly or it will run off the 
shovel. It should not, however, be so wet that the mortar is watery, or it 
will run away from the stones and leave pockets in the finished work. 
The concrete should be joggled rather than rammed, the chief object 
being to prevent collections of stones in one place, which will cause notice¬ 



able voids on the surface. The ramming of concrete is discussed on page 
281, and methods of surfacing are described on page 288. 

The size of stone for walls is sometimes limited to f inch or one inch. 
However, a larger sized material, even up to 2 inches, has been used by 
Mr. Thompson in 4 and 6-inch walls with satisfactory results. 

CONCRETE COLUMNS 

Methods of design and allowable working stresses are recommended in 
Chapter XXI, page 488. Unless of very large diameter in proportion to 
























































































624 


A TREA TISE ON CONCRETE 

the length, columns should be always reinforced, not only to strengthen them 
but to guard against possible emergencies. If the steel is not actually 
figured to take stress, f or \ inch rods, one in each corner, are customary 
reinforcement. For wall columns or others where there is slight eccen¬ 
tricity, extra rods may be inserted on the side where there is the greatest 
stress. If the loading is appreciably eccentric, allowance must be made for 
it in the design, and the stresses and reinforcement may be computed from 
the analyses presented on pages 558 to 574. 

The columns of the Harvard Stadium,* illustrated in our frontispiece 
in process of construction, range in size from 14 inches square to 24 by 
33 inches, and contain | and ^-inch rods in the corners with square loops 
of J-inch rods placed around them horizontally at intervals of about fifty 
times the diameters of the loop rods. The allowable compressive stress 
for 1:3:6 concrete in columns was taken at 350 lb. per square inch. The 
outer wall is supported by hollow piers, 66 by 36 inches over all, 4 inches 
thick on the longer faces, and 6 to 8 inches thick on the ends. 

The 1904 specifications of the Prussian Public Works place the horizontal 
rods at distances apart of not more than thirty times their diameters. 

A typical section of column in the Ingalls Building is shown in Fig. 192, 
page 613. The rods designed to assist in bearing the compressive stress 
are 4 inches in diameter in the lower portion of the column, and are grad¬ 
ually reduced to one inch diameter at the upper stories. They are con¬ 
nected at the ends with pipe couplings and the joints grouted. The outer 
rods on each edge of the column are designed to resist the wind stresses. 
To avoid complication in the drawing, these are not shown at the floor 
level. 

The construction of the molds for a concrete column is illustrated in 
Fig. 198, which shows a column of the Harvard Stadium under construction. 

COST OF CONCRETE BUILDING CONSTRUCTION 

So many factors enter into the cost of concrete buildings that it is impos¬ 
sible to give data which will apply to all conditions without specifying the 
character of the design, the size, height and shape of the building and the 
unit cost of materials and labor. Anv structure must be accurately esti- 
mated, paying special attention to the cost of forms. A few general rules 
are given on page 26. 

Mr. Fmil Per rot f gives the following approximate average values per 

* Described by Lewis J. Johnson in Journal Association Engineering Societies, June, 1904, p. 293. 

J Proceedings National Cement Users’ Association, 1909. 



CONCRETE BUILDING CONSTRUCTION 


Fig. 198. — Molds for Columns at Harvard Stadium. (See p. 624.) 





626 


A TREATISE ON CONCRETE 


cubic foot for different types of buildings, which are useful for rough ap¬ 
proximate estimates by the prospective builder: 

1. Warehouses and manufactories. Cost, 8 to n cents per cubic foot. 

2. Stores and loft buildings. Cost, ii to 17 cents per cubic foot. 

3. Miscellaneous, such as schools and hospitals. Cost, 15 to 20 cents 
per cubic foot. 

These costs include the building complete, omitting power, heat, light, 
elevators and decorations or furnishings. 

DOMES 

Reinforced concrete is admirably adapted to the construction of domes, 
since the concrete can take all the compressive stresses, and the steel the 
tensile stresses developed in the lower curves of the dome and in the arch 
ring. 

While a number of domes have been constructed entirely of reinforced 
concrete, in Europe up to over 70 foot spans, the more common practice 
in America has been to carry a concrete shell on a framework of structural 
steel. 

Yale University Dome. An example of the latter type is the dome of 
one of the bi-centennial buildings at Yale University, New Haven, Conn., 
for example, 55 feet in diameter at the bottom and 34 feet high, consists 
of a skeleton of 24 8-inch I-beam ribs, supported at the top against a circular 
steel rim, with reinforcing metal imbedded in the 3Uinch thickness of con¬ 
crete between them. The surface of the concrete was formed by “screed- 
ing” it with a curved templet whose length was the entire height of the arch. 

Dome of Temple Adath Israel. A dome entirely of reinforced concrete 
is represented in cross section in Fig. 199, page 627. This is the main dome 
of the Temple Adath Israel at Boston, Mass., designed and built by Mr. O. 
W. Norcross, under the supervision of Mr. C. H. Blackall, Architect. 

The dome proper, which has a span of 52 feet 9 inches, is 5 inches thick 
at the haunch and 3 inches thick at the crown, and is composed of 1 : 2 : 4 
broken stone concrete. The reinforcement consists of expanded metal, 
3-inch mesh No. 10 gage, from the tension ring to the angle of rupture, and 
2-inch mesh No. 12 gage for the remainder of the section. The 5 by 4 by 
^-inch angle tension ring is supported by 4 by 3 by § inch angle struts, one 
on each side of all the haunch windows, which in turn carry the weight of 
the dome to the steel girders of the roof below. 

In designing the dome, the stresses were computed by Prof. William Cain’s 


CONCRETE BUILDING CONSTRUCTION 627 

analytical method,* the essential features being somewhat similar to the 
Habrich Construction as applied to domes in Europe. 



WALLS OF MORTAR PLASTERED UPON METAL LATH 

Partitions of plaster from metal lathing are used extensively for fire¬ 
proof office buildings and hotels, and are also adapted, when made with 
Portland cement mortar, to certain classes of outside walls. 

For a one-story building, timber or steel posts may be set upon concrete 
foundations, and the walls constructed by using j-inch or i-inch channel 
irons for studding, to which the metal lathing is attached, and then covered 
(on both sides) with Portland cement mortar about 2 inches thick, the stud¬ 
ding being generally set from 12 to 16 inches on centers, the spacing de¬ 
pending on the height of wall. Such walls are also adapted for high 
buildings where steel frames are used, as the studding can be securely 
bolted to the steel work, and the metal lathing and cement applied in the 
same manner as for one-story buildings. 

For curtain walls the first coat of mortar is usually mixed with one barrel 
of first-class Portland cement to three barrels of coarse sand, and one cask 
of lime putty, or paste, into which is mixed a small quantity of long cattle 
hair. The second coat, which is applied before the first coat is thoroughly 
dry, consists of one barrel of Portland cement to three barrels of sand with 
about a bucketful of lime putty, without hair. The finish coat is generally 
mixed in the proportions of one part Portland cement to two parts sand 

* Transactions American Society Civil Engineers, Vol. LV, p. 201. 








































628 


A TREATISE ON CONCRETE 


This finish coat may be troweled or floated to a smooth or rough surface, 
as may be desired, or it may be given what is known as a “slap-dash” 
finish by throwing the mortar on with a brush or twig broom. 

Ornamental Construction. Concrete or mortar may be cast by special 
molds into blocks of any desired size or shape, or molded for ornamental 
decoration in designs which vie both architecturally and in durability with 
finely carved sandstone, limestone, and granite. The color may be slightly 



Fig. 200.— Pouring Seat Slab of Harvard Stadium, (See p 62S.) 

varied by mixing different kinds of crushed stone. Artificial coloring 
matter is apt to fade. 

Ornaments are run whole in a mold which is made in halves, or are 
molded in two or three pieces and cemented together. Molds of plaster- 
of-Paris, shellacked within, are commonly employed. 

Another method of molding, similar to that employed for iron castings, 
is with fine, damp sand, which is sometimes treated by a patented process. 
A wooden core is made and sand packed around it, then the core is re¬ 
moved, and the mortar is poured in. The surfaces, after setting, may be 
rubbed down and floated. Fig. 200 illustrates the pouring of a seat slab 













CONCRETE BUILDING CONSTRUCTION 


629 


at the Harvard Stadium.* The wooden core, which was of the form of an 
L, for riser and tread, has been removed from the sand, reinforcing wire 
placed, and thick grout of the consistency of cream is being run in from 
a box car. The proportions of material were about one part Portland 
cement to 2j parts fine crushed trap rock under f-inch diameter. 

Surfacing is treated on page 288, 


CONCRETE BUILDING BLOCKS 

Numerous machines and patented methods are on the market for form¬ 
ing building blocks of Portland cement, mortar or concrete to compete with 
brick and stone for house fronts. Some of the machines form the blocks 
from concrete mixed rather dry and pressed into the mold, while other 
methods employ a semi-liquid consistency, and the material is merely 
poured into the molds. The blocks may be hollow so as to extend clear 
through the wall, or each face of the wall may be laid with separate blocks. 

If care is exercised in molding and the sizes and surface appearance of 
the blocks are varied, a wall of pleasing architectural effect is possible. 

The material for building blocks should be first-class Portland cement 
and fine crushed rock, or fine gravel and sand ranging in size from \ inch 
in diameter to dust. Fine sand or fine dust alone makes with Portland 
cement a very porous stone, and must therefore never be used. 


CONCRETE TILE 

Concrete hollow tile is being made for the same uses as terra cotta tiling 
for partitions and floors, and also for dwelling houses in the construction 
of outside walls as well as of interior partitions. The sizes and shapes of 
the blocks are varied for the different purposes. 

One of the best patented processes for making concrete tile consists in 
pouring wet concrete of the consistency of grout, into a mold and then, by 
application of a steam jacket, which forms a part of the mold, evaporating 
enough of the water from the concrete to permit the withdrawal of the tile 
from the mold within a few minutes. The product thus has the density 
and uniformity of wet mixed concrete, and is veiy.true and uniform in shape 
and size and in thickness of walls. Plastering appears to adhere to it bet¬ 
ter than to most other forms of concrete. 


♦Lewis J. Johnson in Journal Association Engineering Societies, June, 1904, p. 305. 


630 


A TREA TISE ON CONCRETE 


REINFORCED CONCRETE CHIMNEYS 

High factory chimneys of reinforced concrete are being built in this 
country and abroad. The cost, especially of those over 100 feet high, is 
usually much less than brick. If designed and built upon the same prin¬ 
ciples and by the same methods which have proved essential in other types 
of reinforced concrete construction, they can be depended upon to give 
permanent satisfaction. 

Reports* from a large number of chimneys have shown that concrete is 
unaffected by the heat from an ordinary steam boiler plant. The temper¬ 
ature in such chimneys seldom exceeds 700° Fahr. while 400° to 500° Fahr. 
is more usual. Experimental tests also indicate that concrete is not appre¬ 
ciably injured at temperatures of 6oo° to 700° Fahr.f 

To provide for extremes, it is advisable, however, to build an independ¬ 
ent inner shell of concrete or firebrick for at least a portion of the height. 
Concrete should not be used for a chimney in connection with special high 
temperature furnaces. 

Since concrete and steel have substantially the same coefficient of expan¬ 
sion J there is no danger of heat causing a separation of the reinforcement 
from the concrete. 

The expansive effect of heat is a more serious question. Stresses are set 
up in the shell of any masonry chimney because of the hot interior and cold 
exterior surfaces. A concrete chimney, however, has thinner walls so that 
the stress is less than in one of brick or tile and it is also better reinforced. 
Provision for temperature stresses are discussed in paragraphs on design 
which follow. 

Construction. A reinforced concrete chimney is more difficult to con¬ 
struct than many other kinds of concrete construction because of its height 
and shape, and it therefore should be handled by experienced builders. 

It is essential in chimney construction that the materials be very carefully 
selected. The sand as well as the cement should be tested by determining 
the actual tensile strength of mortar made from it. The stone preferably 
should be of the nature of a hard trap rock ^ inch maximum size. Propor¬ 
tions 1:2:3 have been found to give good results. A dry mix should not 
be used, since insufficient water will produce a porous concrete which does 
not adhere to the steel. The consistency must be wet enough to quake and 
form jelly-like mass when lightly rammed, so as to properly imbed and 

* A special investigation of reinforced concrete chimneys was made by Sanford E. Thompson in 
1907 for the Association of American Portland Cement Manufacturers. Many of the points here 
discussed are summarized from the report, which is printed as Bulletin No. 18 of the Association. 

I Tests of Metals, U. S. A. 

j See page 287. 


Fig. 201. 


to 


<N 




4 > 


7FTV*! 





^ AIR OUTLETS 
, 1 


CD 


B 


AIR INLETS 




fi 


111 


28 FT.O 





Design 


of Chimney of the Edison Electric Illuminating Co 
Brooklyn, N. Y. (See p. 632.) 















































































































A TREATISE ON CONCRETE 


632 

bond the reinforcement. No exterior plastering should be permitted because 
it is liable to check and scale. T he steel should be good quality round or 
deformed bars. Bars with flat surfaces like T-bars are inferior because 
the flat surfaces give a poor bond and the angles make the placing of the 
concrete difficult. Deformed bars of small size quite closely spaced are 
specially good for the horizontal steel to distribute the temperature stresses 
and high carbon steel of first-class quality also has advantages for the hor¬ 
izontal reinforcement. 

Design. The design of a chimney built in Brooklyn, N. Y., in 1907 is 
illustrated in Fig. 201. 

Design of Reinforced Concrete Chimneys. A reinforced concrete chim¬ 
ney consists primarily of a concrete shell with vertical steel bars imbedded 
in it all around the chimney. The shell must be of proper thickness and 
the steel bars sufficient in size and number to withstand the stresses due to 
the weight of the chimney and to the action of the wind. A chimney of this 
type differs essentially from one of brick in that the diameter at the base is 
so small as compared to the height that it would overturn under a heavy 
wind were it not for the vertical bars of steel which serve as anchors and 
hold it on the windward side. 

Wind, in blowing against a chimney, causes compression on the side oppo¬ 
site to the wind and tension on the side against which the wind is acting. 
This compression is resisted by the concrete and steel on the leeward side, 
while the tension or pull is taken by the steel on the windward side. 

In addition to the vertical reinforcement, a reinforced concrete chimney 
should be provided with horizontal hoops of steel, the object of which is to 
stiffen the vertical steel, to distribute cracks in the concrete due to a dif¬ 
ference in temperature between the interior and exterior and to resist the 
diagonal tension. 

In designing a reinforced concrete chimney the problem then is primar¬ 
ily to determine at various horizontal sections the necessary thickness of the 
concrete shell and the required amount of vertical reinforcement, so that 
the allowable working stresses in the concrete and in the steel shall not be 
exceeded under the action of the forces to which the structure may be sub¬ 
jected. The problem is one in mechanics, involving the equilibrium of a 
system of forces, and, with certain reasonable assumptions, the laws of me¬ 
chanics may therefore be applied to these forces, producing thereby certain 
rational formulas from which the necessary proportions of the chimney may 
be determined. The complete analysis and development of the most useful 
formulas are given in Appendix III, page 765, of this treatise, the formulas 
themselves being reproduced below. 


CONCRETE BUILDING CONSTRUCTION 


633 


The problem of the determination of stresses due to the difference in 
temperature between the interior and the exterior of the shell involves many 
uncertainties. The heat tends to expand the inner surfaces, producing 
tension in the outside surface of the shell and compression in the interior 
surface. Although the distribution of the stress is not clearly known, the 
variation of the heat through the shell not being uniform, tentative compu¬ 
tations indicate high stresses so that it is a question whether vertical tem¬ 
perature cracks can be entirely prevented any more than they can be pre¬ 
vented in brick or tile chimneys. The function of the horizontal steel may 
therefore be to distribute these cracks and to resist the vertical shear or 
diagonal tension. This horizontal steel should be distributed therefore by 
using small diameter bars closely spaced rather than large bars spaced fur¬ 
ther apart. Because of the possibility of vertical temperature cracks, the 
concrete should never be relied upon to carry tension or vertical shear, and 
the amount of horizontal reinforcement to resist this may be obtained in a 
similar fashion to the determination of vertical stirrups in a beam. In 
Appendix III, page 772, the analysis for the shearing stresses is indicated, 
and the final formula is presented below together with suggestions for adapt¬ 
ing the horizontal reinforcement to temperature stresses. 

The amount of vertical reinforcement, the thickness of the shell, and the 
percentage of horizontal reinforcement may be obtained from the following 
formulas, the derivation of which is given in Appendix III, page 765. 

Let 

W = weight in pounds of the chimney above the section under considera¬ 
tion. 

M = moment in inch-pounds of the wind about that section. 
f s = maximum tension in the steel in pounds per square inch. 
f c = maximum compression in the concrete in pounds per square inch 
(measured at the mean circumference). 


n 



= ratio of modulus of elasticity of steel to that of concrete. 


D = mean diameter of shell in inches (i. e., diameter of center of ring). 
r = mean radius of shell in inches. 
t = total thickness of shell in inches. 

A = total cross-sectional area, in square inches, of reinforcing bars in 
the section under consideration. 

k = ratio of distance of neutral axis, from mean circumference on compres¬ 
sion side, to the mean diameter 1). 

z, C P , C T = constants for any given value of k, Tables 1 and 2, pages 635, 
636. 


634 


A TREA TISE ON CONCRETE 


p 0 = ratio of area of steel hoop to area of concrete. 

h l = height in feet of chimney above section under consideration. 

F = effective wind pressure against chimney in pounds per square foot. 


Then 

A. 


8 (M — W z D ) 

CrfsD 


t = 


Po = 


2 W + (C T f s - Cp f c n) 

Cpfc D 

h x F 

+ 0.0025 


A 


+ 


7zD 


18.8/, t 



( 2 ) 

( 3 ) 


Formulas (i), (2), cmd (j) correspond to formulas (7), (£), awd (p) in 
Appendix 111. 

In the formula for p 0 , the first term gives the ratio of steel to resist verti¬ 
cal shear or diagonal tension, and the second term is an arbitrary ratio 
designed to distribute the temperature strains. To best distribute the tem¬ 
perature strains, a maximum spacing of the horizontal bars is recommended 
as 6 inches to 10 inches. 

In the formulas the terms z, C P and C T are constants, the values of which 
are fixed for any given position of the neutral axis. By means of tables 
1 and 2 (pp. 635-6) these constants may be easily and quickly determined 
so that the solution of formulas (1) and (2) is rendered quite simple after 
the selecting of the diameter and height of the chimney and computing the 
bending moments due to the wind at the various sections considered. The 
thickness of shell must be assumed in formula (1) in order to determine 
the average diameter D and to compute the weight W. A new computation 
may be made to correct this if necessary. For economical distribution of 
concrete and steel, computation must be made for several sections in the 
height. It is advisable to make the thickness of exterior shell never less 
than 5 inches but the number of steel rods may be gradually reduced toward 
the top. 

Summary of Essentials in Design and Construction. In the investiga¬ 
tion* referred to, the essential requirements are summarized as follows: 

(1) Design the foundations according to the best engineering practice. 

(2) Compute the dimensions and reinforcement in the chimney with 
conservative units of stress, providing a factor of safety in the concrete of 
not less than 4 or 5. 


* See footnote, p. 630. 







CONCRETE BUILDING CONSTRUCTION 635 

(3) Provide enough vertical steel to take all of the pull without exceed¬ 
ing 14,000 or at most 16,000 pounds per square inch. 

(4) Provide enough horizontal or circular steel to take all the vertical 
shear and to resist the tendency to expansion due to the interior heat. 

(5) Distribute the horizontal steel by numerous small rods in prefer¬ 
ence to larger rods spaced farther apart. 

(6) Specially reinforce sections where the thickness in the wall of the 
chimney is changed or which are liable to marked changes of temperature. 

(7) Select first-class materials and thoroughly test them before and dur¬ 
ing the progress of the work. 

(8) Mix the concrete thoroughly and provide enough water to produce a 
quaking concrete. 

(9) Bond the layers of concrete together. 

(10) Accurately place the steel. 

(11) Place the concrete around the steel carefully, ramming it so thor¬ 
oughly that it will slush against the steel and adhere at every point. 

(12) Keep the forms rigid. 

The fulfillment of these requirements will increase the cost of the struc¬ 
ture, but if the recommendations are followed, there should be no difficulty 
in erecting concrete chimneys which will give thorough satisfaction and will 
endure. 


Table 1. Values of Constants Cp , Cp, z and j for Different Positions of the 

Neutral Axis, (i. e., for various values of k) 

For use with equations (1), (2) and (3), page 634, and (7), (8) and (9), 
pages 771 to 773. k is ratio of distance of neutral axis from mean circum¬ 
ference on compression side to the mean diameter D. Value of k to suit the 
condition of the problem is obtained from Table 2, page 636. 


k 

C P 

Ct 

iy 

i 

0.050 

0.600 

3.008 

0.490 

0.760 

O.IOO 

0.852 

2.887 

0.480 

0.766 

0.150 

1.049 

2.772 

0.469 

°- 77 1 

0.200 

1.218 

2.661 

0.459 

0.776 

O.25O 

1 - 37 ° 

2 • 55 1 

0.448 

0.779 

0.30° 

1.510 

2.442 

0.438 

0.781 

o- 35 ° 

1.640 

2 -333 

0.427 

0.783 

0.400 

1 • 765 

2.224 

0.416 

0.784 

0.450 

1.884 

2-113 

0.404 

0.785 

0.500 

2.000 

2.000 

0-393 

0.786 

o- 55 ° 

2 .113 

1.884 

0.381 

0.785 

0.600 

2.224 

1 - 7 6 5 

0.369 

0.784 












636 


A TREA RISE ON CONCRETE 


Table 2. Location of Neutral Axis for various combinations of compressive stress, f c , tensile 

stress, f s and ratio of moduli, n, (see p. 633.) 


' ® 

% in v. 

w W 
H « J 

g H W 
^ (C M 

P H 

s « S 

* M Z 
5 CO M 

s 


RATIO OF DEPTH OF NEUTRAL AXIS TO DEPTH OF STEEL BELOW MOST COMPRESSED 

SURFACE OF BEAM 


n = 10 


Maximum compressive stress 
in concrete, f c 


n = 12 


Maximum compressive stress 
in concrete, f c 



300 

400 

Soo 

600 

700 

300 

400 

5 oo 

600 

700 

300 

400 

5 oo 

600 

700 

8000 

.272 

• 334 

. 384 

. 428 

. 466 

• 3 i° 

. 375 

.428 

• 474 

. 5 12 

• 360 

. 428 

.484 

• 530 

.568 

9000 

. 25 o 

. 308 

• 357 

. 400 

• 438 

.285 

• 348 

. 400 

•444 

• 483 

• 334 

. 400 

.454 

. 5 oo 

• 5 3 8 

IOOOO 

. 231 

. 286 

• 334 

• 375 

.412 

. 264 

. 324 

.375 

.418 

.456 

.310 

• 375 

. 428 

•474 

. 5 I 2 

IIOOO 

.214 

. 266 

.312 

• 353 

• 389 

. 246 

• 304 

• 353 

• 395 

• 433 

. 290 

• 353 

. 4 o 5 

. 45 o 

.488 

12000 

. 200 

. 25 o 

. 294 

• 334 

.368 

• 231 

.285 

• 334 

• 375 

.412 

.272 

• 334 

.384 

.428 

. 466 

13000 

. 188 

. 236 

. 278 

.316 

. 3S0 

.217 

. 270 

• 316 

• 356 

• 392 

.257 

• 316 

• 366 

.409 

• 447 

14000 

. 176 

.222 

. 263 

. 300 

• 334 

. 204 

.255 

. 300 

• 340 

• 375 

• 243 

. 300 

• 349 

• 391 

.428 

i 5 ooo 

. 166 

. 2 10 

. 25 o 

. 285 

.318 

. 198 

. 242 

.286 

• 324 

• 360 

• 231 

. 286 

• 334 

• 375 

.412 

16000 

. IS8 

. 200 

. 238 

.272 

• 304 

. 184 

. 231 

.272 

.310 

• 344 

. 220 

.272 

• 319 

. 360 

• 396 

17000 

. i 5 o 

. 190 

.228 

. 261 

. 291 

.175 

. 220 

. 261 

. 298 

• 330 

. 2 10 

. 261 

• 306 

.346 

• 382 

18000 

• 143 

. 182 

.218 

. 25 o 

. 280 

. 166 

.2 10 

. 25 o 

.285 

.318 

200 

. 25 o 

• 294 

• 334 

.368 

19000 

. 136 

. 174 

. 208 

. 240 

. 270 

. 160 

. 201 

. 240 

.275 

• 306 

. I92 

. 240 

• 283 

. 322 

• 356 

20000 

. 130 

. 166 

. 200 

. 231 

. 260 

. i 52 

. 194 

. 231 

. 264 

. 296 

. 184 

. 231 

. 272 

.310 

• 344 


n = 15 


Maximum compressive stress 
in concrete, f c 


In connection with reinforced concrete chimneys, the problems which 
arise are of two general kinds: 

(1) A problem in design, involving the determination of the necessary 
thickness of shell and required amount of reinforcement at the various 
sections of a chimney of given height and diameter. 

(2) A problem in the review or investigation of a chimney of given height 
and diameter having a certain thickness of shell and a given amount of 
reinforcement to determine the stresses in the concrete and the steel under 
the action of certain forces. 

The application of the foregoing formulas to such problems and the use 
of the accompanying tables may best be illustrated by the following numeri¬ 
cal examples, although the designer is advised also to refer to Appendix III, 
pp. 765-773 for a thorough understanding of the subject. * 

Design of a Chimney. Example 1. Given a chimney with height above 
section considered, no ft.; mean diameter at section considered, 10 ft.; allow¬ 
able pressure in concrete (f c ), 500 lb. per sq. in.; allowable tension in steel 
(f s ), 14 000 lb. persq. in.; ratio of moduli n, 15; wind pressure (on normal plane) 
50 lb., per sq. ft., weight of concrete taken as 150 lb. per cu. ft. What is the 
necessary thickness of shell and amount of reinforcement at the given section? 

Solution. As in all chimney designs, it is necessary here to make a trial 
assumption of the thickness of shell in order to estimate the weight. Suppose 


































CONCRETE BUILDING CONSTRUCTION 


637 


we assume a 6-inch shell for the entire height above the section. Assuming 
that a wind pressure of 50 lbs. per square foot on a normal plane corresponds 
to T 6 ff of 50 pounds or 30 pounds per square foot on the projected diameter 
of a cylindrical surface we have the bending moment due to the wind, 

M — [10.5 X no X 30] X Ap X 12 = 22 869 000 in. lb. 
and the total weight of the chimney above the section, 

W = 3.1416 X 10 X 0.5 X no X 150 = 259 180 lb. 

For f c = 500, f s — 14 000, and n = 15, table 1 gives k = .349 
For k — .349 table 2 gives Cp = 1.637, CT = 2 *335» z ~ -4 2 7 
Substituting in equation (1), 

8 (22 869 000 — 259 180 X .427 X 120) 

A s = -—--——• = 19.6 

2 *335 X 14 000 X 120 

Therefore 19.6 square inches of steel are required. 

If J inch round rods are selected, 45 of them would be required. 

Substituting in equation (2), we have 

19.6 

t = 2 x 259180 + [(2.335 x 14000) ~ (1*637 X 500 x is)] 3-1416 

1.637 X 500 X 120 

19.6 

4--= 6.6 inches 

3.1416 X 120 


Therefore a 6.6 inch shell would be used. 

In general the values of A s and t as thus obtained should be readjusted by 
computing W on the basis of the computed thickness of shell. In the case at 
hand, however, the original assumption of a 6-inch thickness corresponds, 
for all practical purposes, with the computed thickness of 6.6 inches, so that 
recomputation is, in this case, unnecessary. If the walls of the chimney taper 
in thickness the value of W must be altered accordingly.* 

Having determined the required thickness of shell and amount of vertical 
reinforcement there remains the question of the necessary horizontal or cir¬ 
cular reinforcement. Substituting in formula (3) for f s say 14000 lb., we 
have 


Po 


110 X 30 

--— X 0.002 s = 0.0044 

18.8 X 14000 X 6.6 


Area of steel, A s = 6.6 X 12 X 0.0044 = 0.35 sq. in. Thus J inch round rods 
should be spaced 6| inches on centers. 

In a similar manner any other section of the chimney may be proportioned. 

Review of a Chimney. Example 2. Given a chimney with height above 
section considered, 90 ft; mean diameter at section considered, 8 ft.; thickness 
of shell at section considered, 6 in.; vertical steel at section condsidered, 60 — f 
in. round rods; wind pressure (on normal plane, 50 lb. per sq. ft.); weight of 
concrete taken as 150 lb. per sq. ft.; ratio of moduli, n, 15. 

What are the maximum stresses in the concrete and in the vertical steel at 
the section under consideration? 


* In relatively high chimneys steel cannot be stressed to 14,000 lbs. per sq. in. (see p. 774 ). 







6 3 8 


A TREATISE ON CONCRETE 


Solution. A problem of this kind must necessarily be solved by a method 
of successive trials, since the position of the neutral axis is not known. 1 he 
location of the neutral axis is determined by the values of f c , f s and n, two of 
which, in this case, are unknown. The method of procedure, therefore, is to 
assume outright a trial position of the neutral axis, select the constants accord¬ 
ingly, substitute in equations (i) and (2) and solve them for f s and f c . 

Then see if the position of the neutral axis, as fixed by these values of 
f s and f c and the given n, is the same as the position assumed at the start. 
If the two positions agree, then f s and f c as found are the actual stresses, if 
not, a new position of the neutral axis must be assumed, new constants 
selected, and new' values of / s and f c computed from equations (1) and (2). 
Thus a series of trials must be made until the location of the neutral axis as 
assumed is consistent with the computed values of f c and f s together with 
the given n. 

In this problem, assuming 30 pounds pressure on the projected area, v r e have 
the bending moment due to the wind, 

9 ° • 11. 

M = [8.5 X 90 X 30] X — X 12 = 12 393 000 in. lb. 

2 

and the total weight of the chimney above the section, 

W = 3.1416 X 8 X 0.5 X 90 X 150 = 169 646 lb. 

A s = 60 X .3068 = 18.41 sq, in. 

Now suppose we assume the neutral axis at, say, k = .400 
For k = .400, table 1 gives Cp = 1765, Cj> — 2.224, z — -4!6 
Substituting in equation (1) we have 


18.41 


8 (12 393 000 — 169 646 X .416 X 96) 
2.224 X f s X 96 


whence / s = 11400 

Substituting in equation (2) we have 

18.41 

2 X 169646 + (2.224 X 11400 — 1.765 -fc l 5 ) - o 

3.1416 18.41 

1-765 X f c X 96 + 3.1416X96 

whence f c = 416 

Now f 8 = 11 400, f c = 416, and r = 15 gives k — .354 which does not cor¬ 
respond with our original assumption of z = .400. Evidently the true k must 
lie somewhere between the assumed and determined values, hence if we now 
assume, say, k = .375 and recompute, we obtain f s — 11 000 and f c =435, 
the values of which together with n — 15 gives k — .371 which checks fairly 
well with the assumption of k = .375. For all practical purposes we may 
therefore say that the maximum stress in the steel is 11 000 pounds per square 
inch, while the maximum stress in the concrete is 435 pounds per square inch. 
The results indicate that both the thickness of shell and the amount of steel 
are greater than are necessary for safe stresses. 






FOUNDATIONS AND TIERS 


639 


CHAPTER XXV 

FOUNDATIONS AND PIERS 

Concrete excels as a material for foundations, and here finds its widest 
and most important field of usefulness. It is pre-eminently adapted to 
such construction, because the stresses are chiefly compressive, the forms 
are easily built, and the surface appearance need not be considered. 

Concrete is peculiarly suited to under-water' foundations because, 
although it requires careful handling, it can be placed with great 
facility. It is now used even in piling. (See p. 650.) 

Within recent years concrete has been adopted for foundations above 
ground, such as bridge piers, and is standing the test of durability even 
when subjected to excessive wear and impact. (See p. 654.) 

Since the design of a foundation or sub-structure is governed almost as 
much by the character of the underlying rock or soil as by the super¬ 
structure, brief reference is made to the standard practice in estimating 
loads, although the treatment of engineering principles, as such, is not 
within the province of this treatise. 

Reinforced concrete footings are treated in detail (see p. 644). 

BEARING POWER OF SOILS AND ROCK 

Sound hard ledge will support the weight of any foundation and super¬ 
structure, but if the rock is seamy or rotten it may require thorough ex¬ 
amination and special treatment. If its surface is weathered, it must be 
removed. A sloping surface must be stepped or the foundation designed 
with sufficient toe to prevent sliding. 

The sustaining power of earths depends upon their composition, the 
amount of water which they contain or are likely to receive, and the de¬ 
gree to which they are confined. An approximate idea of the loads which 
may be safely placed upon uniform strata of considerable thickness is 
given by Mr. George B. Francis*: 

There are several classes of strata that are readily definable, such as 
ledge rock, hard pan, gravel, clean sand, dry clay, wet clay, and loam, and 
when these strata are of considerable thickness and uniform for consid¬ 
erable areas, they may be loaded with safety (provided the material 


♦Journal Association Engineering Societies, June 1903, p. 340. 


640 A TREATISE ON CONCRETE 

placed thereon is not of less density than the natural material upon which 
it is placed, viz., concrete or brick work on ledge rock) as follows 

Ledge rock, 36 tons per square foot. 

Hard pan, 8 tons per square foot. 

Gravel, 5 tons per square foot. 

Clean sand, 4 tons per square foot. 

Dry clay, 3 tons per square foot. 

Wet clay, 2 tons per square foot. 

Loam, 1 ton per square foot. 

Mr. Francis, however, calls attention to the many kinds and mixtures 
of materials, and to the consequent impossibility of applying such spe¬ 
cific rules as the above to all cases. He also emphasizes the necessity 
for varied and ample experience when fixing safe allowable pressures. 

If the piles are driven to firm strata, such as rock or hard pan, the 
loading which a pile will stand is determined by the crushing strength 
of the timber. If supported wholly or in part by friction, it is customary 
to calculate the safe loading by a formula based upon factors obtained by 
experiment, or by one based upon the penetration of the pile from the 
blow of the pile driver. 

An engineer experienced in pile driving in a particular locality can 
often determine by judgment whether the piles have reached a firm bearing, 
but it is usually safer to formulate exact specifications. Mr. Joseph R. 
Worcester* advises for piles which meet a hard resistance, a penetration 
of one inch under a 2 ooo-lb. hammer falling 10 feet, and for piles which 
hold by friction, a penetration of 3 inches under a 2 ooo-lb. hammer 
falling 15 feet. He prefers heavier hammers if they are available. 

A mean of the various formulasf gives for approximate average values, 
after applying a factor of safety of 3, a safe load of 16 tons for bearing 
piles and 9 tons for friction piles.* These loads apply to ordinary piles 
of spruce and Norway pine. 

A commonly used formula for determining safe loading on piles with 
reference to the penetration under blows of the hammer is the Engineering 
News formula, which is as follows: 

Let 

P = safe load in tons upon a pile. 

W = weight of hammer in tons. 

h = height of fall in feet. 

p = penetration in inches under last blow. 

♦Journal Association Engineering Societies, June, 1903, p. 285. 

fThe various pile formulas are tabulated and discussed by Ernest P. Goodrich, in Trans¬ 
actions American Society of Civil Engineers, Vol. XLVIII, p. 180. 


FOUNDATIONS AND PIERS 


641 


Then 

p _ 2 Wh 

P +1 

Mr. Worcester states with reference to spacing piles: 

0 

The minimum distance between centers of piles depends upon two 
factors: the hardness of the soil and the size of the butts. Ordinary spruce 
piles may be well driven 24 inches on centers, while large and long piles 
cannot be driven to advantage closer than 30 inches. Another governing 
condition must be taken into account, however, and that is the supporting 
power of the soil as a whole. Where the piles reach a real hard pan, the 
soil will generally resist all the pressure that the piles can bring on it, 
unless it consists of a thin crust overlying a soft material; but when the 
soil is so soft that the piles hold by friction only, and there is enough 
friction to carry all the soil between the piles down with them, in case they 
go together, the spacing becomes a question of how much the underlying 
soil will support per square foot. For example, if the soil can only sup¬ 
port 2 tons per square foot, and the piles could each carry 18 tons, it is 
useless to place them closer than 3 feet on centers. 

CONCRETE CAPPING FOR PILES 

Although some authorities advocate stone capping for piles, even if the 
cost is more, it is generally considered good practise to lay the concrete 
directly upon the head of the pile. The ground is excavated to a depth 
of one or two feet around the piles, and if very soft, a layer of broken 
stone or chips may be spread and rammed hard upon it before laying 
the concrete. The load is distributed by the concrete, and the support¬ 
ing power of the soil between the piles is utilized. 

The thickness of the concrete above the piles must be sufficient to dis¬ 
tribute the superimposed weight, and the reactionary load of the pile head 
acting upwards. If the layer is very thin there may be danger of the pile 
head shearing through the concrete. The objection sometimes raised to 
concrete capping is that the upward crushing stress upon the concrete by 
the head of the pile may be excessive, especially if loaded before the con¬ 
crete is thoroughly hard. In considering this tendency, it must be borne 
in mind that under concentrated loading the concrete will sustain a higher 
stress per unit of area of contact than if the load is distributed. (See 
p. 249.) 

DESIGN OF CONCRETE FOUNDATIONS AND FOOTINGS 

The load upon a building foundation need not always be taken as the 
dead load plus the entire live load for which the superstructure is de- 



642 


A TREATISE ON CONCRETE 


signed, because in most structures the full live load will never be imposed 
upon all the floors at the same time. A conservative suggestion for reduc¬ 
tion in the live load is given on page 611. 

To prevent cracks in a structure, it is not only necessary to select a proper 
unit pressure on the soil but also to see that this pressure is uniform, so that 
if there is settlement it will be the same throughout. To satisfy this con¬ 
dition, the center of the loads from the columns or other portions of the 
structure should coincide with the center of gravity of the base. The area 
of the footing should be proportional to its load. When such an arrange- 



Fig. 2C2. —Typical Column Foundations of Boston Elevated Railway, 

{See p. 643,) 

ment is difficult, the foundations under different columns should be separated 
and the area of base of each be made proportional to the superimposed load. 

Frequently the building line nearly coincides with the property line and 
the foundation must be placed entirely inside the building.. In such cases, 
to prevent eccentric pressure, either cantilever construction may be used for 
transmitting the exterior column loads centrally to the footing, or a com¬ 
bined footing designed as explained on page 647. 




































FOUNDATIONS AND PIERS 


643 


In structures such as chimneys or narrow buildings which are subject 
to wind pressure, the foundation should be designed with due consider¬ 
ation of the eccentricity caused by the wind. 

With vertical loading upon rock or soil whose sustaining power per 
square foot is equal to or greater than the unit load, the dimensions of the 
foundation are fixed by the size of the structure, the safe load which can 
be sustained by the concrete, or by resistance to overturning. If the load 
is greater than an equivalent area of soil can sustain, the area of the base 
of the concrete must be enlarged, and the concrete battered or stepped or 
reinforced. It is a common engineering practice to make the length of 
the projections or steps of plain concrete one-half the height of the block, 
and this usually gives good results in buried foundations where the surround¬ 
ing earth assists to prevent splitting. 

The effect of concentrated loading must be considered when designing 
a footing. (See p. 367.) The pedestal bases for the Boston Elevated 
Railway were designed, when covering one-half the area of the concrete, 
with 25 % higher unit stresses for the concrete in actual contact than when 
covering the entire area. Fig. 202, page 642, shows a typical foundation 
for the columns.* 

The following figures are suggested as conservative safe loads, when the 
surface of the concrete is larger than the loaded area. Lower stresses should 
be used with moving loads or when the area of the foundations is no greater 
than that of a column which it supports. The figures are based on ordinary 
concrete with a factor of safety of 4 at one month and a factor of 5 J at six 
months. 


Safe Loads on Foundations. 


Proportions of Concrete 
by ' r olumet 

Lb. per sq. in. 

Safe Loading 

Tons per sq. ft, 

I :i :3 

700 

50 

1 '.2 14 

650 

47 

1 \2h\S 

575 

41 

1:3:6 

5 °° 

3 6 


For a vibrating or pounding load these values should be reduced from 
1 to J, depending upon the nature of tne loading. 

I-Beam Footings. Formerly, footings were made by imbedding steel 
I-beams, or in some cases old rails, in concrete for column footings. The 
concrete serves to distribute the loads and protect, the steel. A typical foot¬ 
ing, designed by Mr. John S. Branne,t is illustrated in Fig. 203. page 644. 
In this particular case the situation required a cantilever girder connecting 
this foundation with the next, but the footing shown is itself designed for 
a total load of 173 tons, of which 120 tons are dead load and 53 tons live 

load. 

* George A. Kimball in Journal Association Engineering Societies, June, 1903, p. 351. 
f Based on a barrel of packed cement of 3.8 cu. ft., weighing 376 lb. net. 

J Journal Association Engineering Societies, Feb., 1901, p. 142. 


644 


A TREATISE ON CONCRETE 



REINFORCED CONCRETE FOOTINGS 

To distribute the load over a large area of soil without carrying the founda¬ 
tions, by successive steps, to a considerable depth and using a large mass of 
concrete, a single slab may be employed and reinforced with steel to prevent 
the projection breaking. 

This in almost all cases permits a very great reduction in the quantity 
of material and reduces the cost. A footing reinforced with rods is designed 
to utilize the strength of the concrete, and is therefore more economical 
than the I-beam type of design just referred to, and is always to be preferred 
to it. 

A reinforced concrete footing is really a flat slab and should be designed 
as such. The theory of the flat plate, explained on pages 483 to 488, there¬ 
fore applies to it and the formulas on page 485 may be used directly for 
determining the bending moment. The principal formula for the maxi¬ 
mum bending moment is as follows: 

Let 

M = maximum moment causing radial fiber stress 

w = uniform distributed load on surface of the plate in pounds per square 
foot 










FOUNDATIONS AND PIERS 


645 


r 0 = radius of base of column in feet 
r t = radius of footing in feet 
Ci, C 2 = constants to use in formula 
Then 

M = wr 0 2 (0.2 -f" Cj T C 2 ) 

Values of the constants Ci, C 2 are found in the table page 518. 

The application of the formula and principles is best illustrated in the 
example which follows. 

Example /. Find the dimensions of a footing for a column 28 inches square 
carrying 392000 pounds, when the allowable pressure on the soil is 2 tons 
per square foot? 

Solution. The necessary area of footing is found by dividing the total su- 

39 2 000 

perimposed load by the allowable unit pressure on the soil, or is-■ =98 

4000 

square feet, thus requiring an area 10 feet square. The footing may be con¬ 
sidered as a flat slab loaded by the uniformly distributed upward pressure of 
the soil and fixed rigidly to the column. The formulas given above were 
deduced for a circular plate, but may be applied without appreciable error 
to a square footing. The radii to be used in the formulas are the averages 
of the radii of the circumscribed and inscribed circles. 


r, = 


5 + 7 -°° 


= 6.00 ft. 


1.17 + 1.63 

r 0 = - = i -4 

2 


r, 

i 

*0 


= 4-3 


Using the formula and substituting for the constants values found from the 

y x 

table, page 518, corresponding to — = 4.3 and using as Poisson’s ratio, g = 0.1 

r 0 

we have 

M = 4 000 X 1.4 2 (0.2 + 6.7 4- 3.49) = 81600 ft. lb. per foot of width, 
which is equivalent to in. lb. per inch of width. For tension in steel, j s = 
16000; compression in concrete, f c = 650; ratio of elasticity, n — 15; 
ratio of steel, p. = 0.0077; the constant from page 519, C is 0.096 and the 

depth of steel, (p. 418), d = 0.096 \/ 81600 = 27.2 in. 

The amount of steel will be found in the following manner. Find the area 
of steel required for the whole circumference of the inner circle of the plate, 
the radius of which at present is 1.4. Divide this amount by four and place it 
in two directions, at right angles, distributing it over an area slightly larger 
than the base of the column. Double the spacing of rods outside of the 
column, as the bending moment decreases very rapidly as shown in Fig. 204. 

Circumference is 2 X 1.4 X 12 X 3.1416 = 105.5 i n - Area of concrete, 
A = 105.5 X 27.2 = 2870 sq. in. Area of steel, A s = 2870 X 0.0077 = 

2 2.1 

22.1 sq. in. Area of steel to be placed in one direction, A = -= 5.53 sq. 

4 

in. The width of column is 28 in., hence six 1 in. square rods 5 in. on centers 
may be used. The spacing of the lods on the remaining area of the footing 
will be made 10 in. Deformed bars are advantageous because of increased 
bond strength. 







646 


A TREATISE ON CONCRETE 


fsotoi^trrn - r 

(deformed) ' 


r^f-irlaw 


Another method of arranging reinforcement is to place the bars in 4 layers, 
2 of them diagonally. 

The thickness of the footing may be decreased by judgment toward the 
edges without reducing its effective strength. 

Shear Reinforcement. A foot¬ 
ing to resist diagonal tension 
may require shear reinforce¬ 
ment of vertical stirrups or 
bent bars, placed near the 
column, where maximum shear 
occurs and diagonal cracks 
may be expected. 

While the action of the inter¬ 
nal shearing stresses are some¬ 
what complicated, the following 
plan may be adopted. 

Find the unit shear at the 
edge of the column, dividingthe 
loading tributary to the area of 
the footing outside of the col¬ 
umn by the moment arm jd 
(which may be taken at 27 X 
0.87) times the circumference 
4 X 40 in. and we have 
(100 — 5.5) 4000 




7T 


1 


1 

I 

1 

1 

1 


r 

lari 



| 



IOftt 


V = 


= IOO 



. ALC BA RS D EFORM ED SQUARE I PiAM. 


-JOftt 


Fig. 204.—Square Footing. (See p. 645.) 


4 X 40 X 27 X 0.87 
lb. per sq. in. Assuming that 
one-third of it is taken by con¬ 
crete, 66 lb. per sq. in. must be 
provided for by steel. 

Next find by trial the cir¬ 
cumference where the unit 
shear is 40 lb. per sq. in., the 
amount which may be safely 
resisted by concrete, so that the 
shear to be provided for by 

the steel is zero. In this case this circumference has been found by trial 
to be distant 39 in. from the center of column, and is shown on the dia¬ 
gram by dot and dash line. 

Now multiply the horizontal area enclosed between the circumference of the 
column and this newly found circumference by half of the previously deter¬ 
mined unit shear to be taken by the steel (66 lb.) and obtain the total amount 
of shear to be taken by the stirrups, Select the diameter of stirrups in accord¬ 
ance with the discussion on page 453, divide the amount of shear by the area 
of one stirrup and by the unit tensile strength and obtain the number of stir¬ 
rups. In this case the area requiring stirrups is 7s 2 — 28^ = 5300 sq. in., and 
the total amount of shear to be provided for, X 5300 = 174 900 lb. If l- 
inch square stirrups are selected (area 0.25 sq. in.) with a unit tensile strength. 



















































































































































FOUNDATIONS AND PIERS 


647 


f s = 16 000 lb. per sq. in.,- = 44 stirrups in all, or n stirrups 

16000 X 0.25 

each side are necessary. Their spacing is evident from the drawing. 

Bond Stress. The bond stresses must also receive attention. It will 
often be necessary to increase the depth of the footing or the amount of rods 
to provide for the excessive bond stress. The discussion, page 456, and 
formulas given there find here a direct application. Reference may be made 
also to the similar treatment in the design of a retaining wall footing, page 670. 

Combined Footings. Sometimes it is necessary to connect the footings 
of two or more columns. The design of such combined footing differs 
from that of a single one. When the loads carried by the columns are dif¬ 
ferent, the footing to distribute the loading uniformly should have the shape 
of a trapezoid. The following example will illustrate method of figuring: 


Example. Let P, and P 2 be respective loadings of colurns I and II, 30 and 
24 inches square; P, = 400000 lb., P 2 = 580000 lb. The distance between 
centers of columns is 15 ft. and the allowable unit pressure on the soil is 4 
tons, 8000 lb., per square ft. Find the dimensions of footing. (See Fig. 205.) 
Solution. The total superimposed load is 980000 lb., then the necessary 
980 000 

area of footing, - = 123 sq. ft. The magnitude of the parallel sides 

8000 

is unknown, and two equations are necessary for the determination. First 
equation may be obtained from the formula that the area of trapezoid equals 
the average of the sum of the parallel sides multiplied by its length. The 
length of the trapezoid is 15 + 1.75 + 1.50 = 18.25 ft., and the area = 123 = 

a x 18.25. Hence a + b = 13.5 ft. The second equation may be found 
2 

from the requirement, that the center of gravity of the trapezoid coincide 
with the center of gravity of the combined column loading. The distance 
from A of the center of gravity of column loadings O, found by taking moments 
of loads, is 6.1 ft. and l = 6.1 + 1.75 = 7.85. Using the common equation 

18.25 a + 2b 

for the center of gravity in a trapezoid gives l = 7.85 = - 1 -—— 

0 3 a + o 

Solving the two equations for a and b, a = 9.6 ft., b = 3.9 ft. 

To facilitate the finding of bending moments, the length of b, the width of 

the footing on the center of gravity line, may be computed from the relation 

a Z .b — a ~ kj anc j t he length l v from the common formula for the distance 
18.25 7- 8 5 

of the center of gravity b l = 7.15 ft. l v = 3.74 ft. and l 2 = 7.85 — 3.74 = 
4.11 ft. 

Assuming the maximum moment* at center of gravity, M= 580000 X 6.1 X 
_ | 9 ' 6 + 7 • x 7.85 X 8 000 X 4. nXnj = 16 550 000 in. lb. for the width 

16 550 000 

of beam equal to b v The moment for one inch of width, M = -- - 

193 000 in. lb. 

* Maximum moment is actually at section of zero shear but the error is inappreciable. 


12 











648 


A TREATISE ON CONCRETE 


For tension in steel, f s = 16000, compression in concrete, f c = 650, ratio 
of steel, p = 0.0077, and C = 0.096 (see p. 421) then depth to steel, d = 
o.og6\/ 193000 = 42.2 in. As A s = 42.2 X 12 X 0.0077 X 7.15 = 27.9 sq. 
in. for the whole width, 18, 1^ inch deformed bars will be used. 

To prevent bending of the projections of the footing, transverse reinforce¬ 
ment will be introduced. The projections are assumed to act as cantilevers, 
loaded by half of the column loading multiplied by a ratio of the difference 
between the width of the footing, a, and the diameter of the column to the 




width of footing, or 


9-6 - 2.5 
9.6 


The moment arm equals half of the length 


of the projection, and the moment, M 


580000 9.6 - 2.5.I 3.55 

' X --- X - X 12 

2 9.6 2 

= 4 57 ° 000 in. lb. . . ..._y 

Assuming a width of the distributing beam equal to 4 ft., the depth will be 


d = 0.096 


4 57 ° 000 _ 
MX12 


29.6 in. The depth . is smaller than the depth of 


the whole slab. Since a larger depth is used, the percentage of steel will 
be found as follows: 

































































































FOUNDATIONS AND PIERS 


649 


C 


=V— 

* a c 1 r 


X 48 


.137 from formula (1) (p. 418) and p = 0.0033 from 
4570000 \ -T / r 00 

table on page 520; A s = 42.2 X 48 X 0.0038 = 7*70 sq. in., hence i3|in. 
square bars will be used. 

Note. —The required depth of the distributing beam may be sometimes 
larger than the depth of the whole slab. In such case the footing may be 
either thickens I under the column or steel introduced at the top and bot¬ 
tom. The latter scheme should be adopted only when additional excava¬ 
tion for the beam cannot be made readily. 

In a similar way the distributing reinforcement for column II is found, 
w 400 000 3.9 — 2 0.95 

-X - X - X 12 = 555000 in. lb. Assume a width 

2 3.9 2 


)f imaginary beam equal to 3 ft., then d = 0.096 -\ / 5 ° —° = 12 in. As 


\ 36 

arger depth is used, the percentage of steel will be found as in previous case. 
_ /42.2 2 X 36 

\ -• = -334- For this value of C less than 0.1% of steel 

x 555ooo 

is needed, and will be taken arbitrarily. 


SPREAD FOOTINGS 


When the allowable pressure on the soil is very small or when the build¬ 
ing is supported by piles sustained by friction, it may be necessary to spread 
the foundation over the whole area of the building, either using a thick mass 
of plain concrete or a thinner slab of reinforced concrete design as a flat 
plate, or a beam and slab system. 

Flat Slab Foundations. A flat slab may be designed by the method of 
flat plates explained on pages 483 to 487. The slab is considered as an 
inverted flat plate loaded by the reaction of the ground and supported by 
the columns. 

Special provision should be made in the design where there is unequal 
loading. 

Since the distributed pressure acts upward, the bottom of the plate under 
the columns is in tension and the top of the plate between the columns; 
hence the steel must be in the bottom of the slab under the columns, and 
should be bent up to the top of the slab between columns. The column 
base must be large enough to prevent excess loading or too great moments 
and shears in the concrete. 

Baam and Slab Foundation. For a combination of beams and slabs die 
principles of floor design are followed except that the distributed load acts 
upward. The beams or ribs may be built either above or below the slab, 
the former method permitting a T-beam design, but, on the other hand, 
requiring an extra fill and separate floor surface in the basement. The 
formulas and discussion relating to floor design in Chapter XXI apply. 











650 


A TREATISE ON CONCRETE 


FOUNDATION BOLTS 

It is often difficult to locate bolts in concrete with sufficient exactness for 
setting a machine. To obviate this difficulty, the head of the bolt should 
be provided with a large washer* to give a good bearing surface, the bolt 
placed in its approximate position, with washer down, and an iron pipe or 
a light wooden box placed around the bolt resting upon the washer. When 
the machine is set, to prevent the bolt from rusting, the iron tube or box 
should be filled with mortar. In any case the tube or box should be filled 
with sand before the machine is poured up with sulphur or cement grout, 
in order to keep these materials from running down the bolt holes. 

CONCRETE PILES 

Concrete piles may be employed in place of wood where the loading is 
excessive, and where the durability of timber piles is questioned either 
because of probable worm action or the rotting of the timber. If the bearing 
is frictional and the piles are driven through ground which is continually 
wet, there is usually no advantage in concrete over timber piles unless in 
certain instances where the low level of the ground water or the tide water 
is so far beneath the structure that the concrete piles permit the commence¬ 
ment of the foundation at a considerably higher level and thus save excava¬ 
tion and material. 

Concrete piles are formed (1) in place, or (2) are molded above ground 
and driven with a pile driver. 

Various methods have been suggested for forming the hole into which 
the concrete is to be placed. One of the patented processes consists in 
driving a double shell of metal into the ground, removing the inner one, 
and leaving the outer to form a mold for the concrete. The two shells 
and pile driver are shown in Fig. 207, page 652. The inner shell or pile 
core, which is of heavy sheet steel and constructed so that it can be made 
to collapse for removal from the ground, is placed within the other thinner 
shell, and driven like an ordinary pile. The core is then collapsed and 
withdrawn, leaving the outer shell, which is closed at the bottom, to be 
filled with concrete. By providing considerable taper, additional support 
is obtained from the soil. 


* The washers, which are used for transmitting the pressure of large bolts to the concrete or other 
foundations, should be carefully designed with heavy ribs so as to transmit a uniform pressure per 
square inch of area. Neither wrought nor cast iron plates should be used for washers under large 
bolts. 


FOUNDATIONS AND PIERS 


Another system, illustrated in Fig. 
206, consists in driving a single shell 
with either a concrete or a steel 
point, then slowly withdrawing it, 
and filling the space which it occu¬ 
pied with concrete whose surface is 
kept far enough above the lower 
end of the tube to maintain the 
head necessary to resist the pressure 
of the ground. 

In still another method, which is 
especially adapted for underpinning, 
the tube is washed down with a 
water jet to firm strata, and the 
bottom of the excavation is enlarged 
by an expanding arrangement to 
form a base, as shown in Fig. 208. 

Piles made in situ may be rein¬ 
forced if desired. 

Cast Piles. Reinforced piles 
which are formed above ground are 
designed like columns with vertical 
reinforcement connected at inter¬ 
vals with horizontal wire rods. 

The pile* used in a foundation 
for the Boston Woven Hose & Rub¬ 
ber Company, Cambridge, Mass., 
is illustrated in Fig. 209. These 
piles averaged about 30 feet long. 
The hammer weighed 4700 pounds 
and the blows were cushioned by a 
head consisting of a plate iron collar 
16 inches square on the inside and 3 
feet in height, which incased an oak 
block 16 by 16 by 18 inches, to the 
bottom of which six thicknesses of 
rope and four layers of rubber belt¬ 
ing Were nailed. The piles were 

* For full description of piles and driving 
see “Cast Reinforced Concrete Piles,” by 
Sanford E. Thompson and Benjamin Fox, 
Journal Association of Engineering Societies, 
Vol. XLII, 1909. 


651 



OAK HEAD 





AIR INLET 




Fig. 206. — Concrete Piles. (See p. 651,) 




















652 


A TREATISE ON CONCRETE 



Fig. 207, — Cores for Concrete Piies. (See £.650.) 














FOUNDATIONS AND PIERS 653 

driven at the age of thirty to forty days. The usual drop was 3 feet, 
but in some cases this was increased to 10 feet without injuring the pile. 

The designs drawn up in 1903 for the Pennsylvania Railroad Tunnel* 
under the Hudson River call for a shell of cast iron surrounded by con¬ 
crete and supported at intervals by steel screw piles filled with concrete. 

Sheet Piling. Poling boards of concrete 
were employed by Mr. Howard A. Carson, 
Chief Engineer in the construction of the 
approaches to the East Boston Tunnel. 
These are described! as follows: 

The excavation was through gravel and 
clay, and through sand containing some 
water. Trenches 16 feet long and 16 feet 
apart were dug to about the level of the 
bottom of the building foundation. Below 
the foundation one-half of each trench, or 
8 feet in length, was carried down to grade. 
The bank below the foundation was held 
in place by means of concrete slabs used 
as sheet piling, as illustrated in Fig. 210. 
These slabs were from 6 to 8 feet long, 
6 inches wide, and 2 inches thick, and each 
was reinforced with six square steel rods 
running the entire length of the slab and 
shown in Fig. 211. If wooden sheeting 
had been used, it would have been neces¬ 
sary either to have concreted directly 
against it and left it in place, or to have pulled the planks as the con¬ 
crete was filled in. If the first method had been used, the planks would 
in time have become rotten, leaving a vacant space. If the planks had 
been pulled, there would have been danger that some of the earth under 
the building would run and a settlement of the building follow. In 
order to guard against any slight voids which might have been left in 
driving, grout was poured in behind the sheeting. This sheeting served 
not only to hold the bank in place, but was used, in place of a back 
wall, to waterproof against. The sheeting was not disturbed, and the 
wall of the Tunnel was built directly against it. 



Fig, 208. — Concrete Pile with 
Enlarged Footing. ( See p. 

651-) 


*Engineering News y Oct. 15, 1904, p. 331. 

fNinth Annual Report, Boston Transit Commission, p. 41. 

















654 


A TREATISE ON CONCRETE 


BRIDGE PIERS 

Concrete is employed for bridge piers either 
is filling for ashlar or cut masonry or for the 
entire pier. In the latter case, in which the 
face is also of concrete, the chief question is 
as to its ability to withstand the wear of the 
water, the ice, and floating debris. Mr. Martin 
Murphy* stated as early as 1893 that concrete 
was generally adopted in Nova Scotia, and with 
successful results, for abutments and piers “in 
the most exposed positions, in the midst of 
strong currents, without any external pro¬ 
tection, where exposed to heavy ice floes, to 
blows from timber rafts, and, in many instances, 
to undermining by scour.” In Nova Scotia it 
is the common practise to construct the body 
of the pier of rubble concrete with a 6 to 9-inch 
facing of richer concrete. In answer to in¬ 
quiries, Mr. Murphy wrote the authors in 1904: 
“The concrete piers erected in this Province 
for the last eighteen or twenty years have with¬ 
stood the action of the weather, and fulfilled 
all that was claimed for them in mv paper, 
read before the International Congress in 1893. 
The erection of such piers and abutments is 
now in almost universal application in Canada.” 

In the Kansas City flood of 1903, the piers 
of solid concrete, although located where they 
were struck by all the heavy debris which 
totally destroyed many of the stone masonry 
structures of the same size, remained practi¬ 
cally uninjured. 

In 1900 a Committee of the Association of 
Railway Superintendents of Bridges and Build¬ 
ings j* made the following inquiry: “For what 
classes of structures do you use Portland ce- 

♦Bridge Substructure and Foundations in Nova Scotia, 
Transactions American Society of Civil Engineers, Vol. 
XXIX, p. 620. 



Fig. 209.—Piles used at 
Cambridge, Mass. (See 
P- 6 5i-) 


BARS, 12'O.C, 


























































































































FOUNDATIONS AND PIERS 


6 55 


ment concrete?” Out of thirty-three replies received, seventeen were in 
favor of employing this material for both the foundation and neat work of 
bridges, piers, and abutments. 

Plastering of concrete piers and abutments should be prohibited. If a 
mortar surface is required, an excellent facing, to be placed next to the 
form as the concrete is laid, is a mixture of one part cement to 2\ parts 
hard broken stone screenings J inch in size and under. Ordinarily, how¬ 
ever, no surface finish is required unless superficial treatment is given for 
the sake of appearance. (See p. 288.) 



Fig. 210. - - Concrete Sheet Piling in Approaches to East Boston Tunnel. (See p. 
653 ») 


Pier Design. Most railroads are substituting concrete for ashlar 
masonry in bridge piers. 

The standard pier of the N. Y. Central R. R., adapted to any height up 
to 40 feet, is shown in Fig. 212, page 657.* The width, which depends 
upon the length of span, is as follows: 


♦Arranged from original drawing, for which the authors are indebted to Mr. Wilgus. 













656 


A TREATISE ON CONCRETE 


Spans up to 40 feet width, A, = 4 ft, o in. 

Spans 40 to 60 feet width, A, = 4 ft. 6 in. 

Spans 60 to 80 feet width, A, = 5 ft. o in. 

Spans 80 to 100 feet width, A, = 5 ft. 6 in. 

Spans 100 to 125 feet width, A, = 6 ft. o in. 

Spans 125 to 150 feet width, A, = 6 ft. 6 in. 

Spans 150 to 200 feet width, A, — 7 ft. o in. 

Spans 200 to 250 feet width, A, = 7 ft. 6 in. 

For skew crossings, increase width, A, if necessary. 


■*- ->-1 


T 


C^O 


0*1 


so 

o 


UJ □ 


□ m 


HORIZONTAL 

SECTION 


Foundation is varied to suit local conditions. Concrete 1:3:6 is em¬ 
ployed for it unless stone masonry is cheaper. The starkweather is carried 
2 feet above high water, and its cap is of 1:1:2 concrete. 

The coping of the pier is reinforced with galvanized wire net¬ 
ting or wire cloth, a somewhat unusual requirement. 

The Illinois Central R. R., in their 1904 design, reinforce 
the surface of piers with vertical and horizontal steel rods, and 
imbed a single I-beam in the pointed nose at each end of the 
pier.* 

The Chicago, Milwaukee & St. Paul Railway Company takes 
the extra precaution to strengthen the noses or starlings of its 
concrete piers only at points where there is considerable ice and 
driftwood.f They build a 7-inch street car rail into the nose of 
the pier, with the head projecting slightly from the concrete. 

Other roads also show no reinforcement in their standard de¬ 
sign. 

It would appear that reinforcement is probably unnecessary 
except in situations where the piers are subjected to unusual 
impact. 

All of the roads named above have piers in streams which 
subject them to considerable wear from ice and drift, and the 
concrete has proved satisfactory. 


ELEVATION 

Fig.211, - 
Sheet Pil¬ 
ing. (See 

P-b 53d 


FOUNDATIONS UNDER WATER 

The best and most durable concrete foundations, especially 
in work in sea water, are laid within cofferdams from which the water 
has been pumped, or in pneumatic caissons. However, because of the 


*From drawing kindly furnished by H. W. Parkhurst, Engineer. 
^Authority of C. F. Loweth, Engineer. 














FOUNDATIONS AND PIERS 


657 


difficulty and expense of these methods, they cannot usually be followed. If 
the bottom is prepared by dredging, and, if necessary, driving piles, good 
practise permits the use of a single line of sheeting, suitably supported with 
rangers, to prevent the wash of the water and keep the concrete from 
spreading.* Permanent metal cylinders are sometimes sunk in place of 
the sheeting. 

Methods of laying concrete under water are described in Chapter XV, 
page 301, and the effect of sea water upon concrete is discussed by Mr. 
R. Feret in Chapter XVI. 


BASE OF RAIL 



SIDE AND UP-STREAM ELEVATIONS 



Fig . 2I2 .— Standard Concrete Bridge Pier, N. Y. C. & H. R. R. R., W. J. Wilgus, 
Chief Engineer. (See p.^SS) 


♦See Foundations for New Cambridge Bridge, Boston, by Sanford E. Thompson, Engineering 
News , Oct. 17, 1901, p. 28-}. 



























































6 5 8 


A TREATISE ON CONCRETE 


For under-water work, a larger factor of safety should be employed than 
for work above ground, the concrete should be slightly richer in carefully 
selected cement, and the aggregate so proportioned as to give a dense and 
impervious mixture. 

Concrete for the foundations of walls and piers for high office buildings 
is usually laid in oblong or circular caissons of steel or wood,* after exca¬ 
vating under air pressure. Steel pipes are sometimes sunk with the aid of 
the water jet, and afterwards filled with concrete, j* 


^■Engineering News, Sept. 26, 1901, p. 222. 

tJules Breuchaud, Transactions American Society of Civil Engineers, Vcl. XXXVII, p. 31. 


DAMS AND RETAINING WALLS 


659 


CHAPTER XXVI 

DAMS AND RETAINING WALLS 

For walls to resist the pressure of earth or water, concrete frequently 
possesses marked advantages over other classes of masonry. With proper 
management, in most localities its cost may be brought below that of rubble 
masonry. Its adaptability for thin walls and for certain classes of face 
work often make it a suitable substitute in complicated designs for first- 
class masonry, with a consequent large saving in cost. In combination 
with steel its possibilities for special designs are almost unlimited, and the 
future will see marvelous advances in its use for ordinary engineering and 
hydraulic construction. 

Water-tightness, often an essential element for this class of structures, has 
received general treatment in Chapter XIX, page 338. Portland cement 
concrete may be made water-tight more readily than stone masonry laid in 
mortar of similar proportions to the cement and sand in the concrete, since 
large voids or stone pockets in the concrete are more easily prevented than 
the “rat-holes” so frequently found in the bedding of stones in mortar. 
Moreover, skill in laying combined with special treatment of the surface or 
the addition of certain ingredients permits construction in concrete— 
strengthened with steel reinforcement—of thinner walls for resisting the 
flow of water than is possible in stone masonry. 

Reinforced concrete retaining walls cannot be designed by “rule of thumb,” 
and therefore a careful consideration of the forces acting and of the stresses 
in the concrete is presented in this chapter. Since the earth pressure is the 
controlling factor, it has been necessary to introduce a practical discussion 
of this before taking up the details of the design and examples of the two 
principal types 

RETAINING WALLS 

Retaining walls to support the pressure of earth may be designed: 

(1) of gravity section with plain concrete or stone masonry; 

(2) of thin reinforced concrete section of the inverted T type with 

spreading base or footing; 

(3) of thin section, reinforced and supported by buttresses or counter- 

1 

forts. 

Another plan sometimes adapted to cellar wall construction (see p. 619) 
consists in embedding the base and supporting the top of the wall with tim- 


66o 


A TREATISE ON CONCRETE 


her, steel or reinforced concrete beams, so that the concrete forms a vertical 
slab supported at top and bottom. 

Reinforced concrete retaining walls are almost always more economical 
than a gravity section of either plain concrete or masonry. In walls of 
gravity section the materials cannot be fully utilized because the section 
must be made heavy enough to prevent overturning by its own weight, 
counterforts or buttresses being of comparatively little advantage because, 
in stone masonry, the wall is liable to break away from them. In reinforced 
concrete retaining walls, on the other hand, a part of the sustained material 
is used to prevent overturning, and the section need be made only strong 
enough to withstand the moments and shears due to the earth pressure. 
Since the wall is lighter, exerts smaller pressure on the soil, and may be 
made if necessary with a very broad base, the special foundations or piling 
which are often necessary for a gravity wall frequently may be avoided. 
Reinforced concrete properly designed can be depended upon as absolutely 
reliable. 

The economy of a reinforced concrete wall over one of gravity section for 
either stone masonry or plain concrete is obvious because of the saving in 
material. The cost of forms is practically the same for gravity section and 
reinforced designs. 

Whether the T-section of reinforced wall or the wall with counterforts 
is the more economical depends upon certain conditions. The principal 
condition is the height of the wall, but the intensity of the earth pressure and 
the relative cost of concrete and steel and forms also enter into the considera¬ 
tion. The construction of the T-section is simpler and the placing of steel 
easier, so that it is preferable where skilled labor is scarce. The form con¬ 
struction in the counterforted wall is considerably more expensive. Com¬ 
parative studies of the two types indicate that the counterfort type is scarcely 
ever economical when the height is less than 18 feet. Rules for designing 
walls of gravity section are first given and then, after the discussion of earth 
pressure, the designs of both aT-type and a counterforted section are treated. 

FOUNDATIONS 

A firm foundation is essential whatever the type of the design. Piles 
may be necessary, or to avoid sliding, a stepped base may be required. 
Unequal settling is more dangerous for a retaining wall than for many 
other structures, because if it is thrown out of plumb, the earth will move 
and produce forces much in excess of the calculated ones. Allowable pres¬ 
sures on different soils are referred to on page 640. 


DAMS AND RETAINING WALLS 


661 


The depth of foundation must be sufficient to prevent heaving of the 
material in front of the wall, and to protect it from frost. A depth of 3 
feet may be given as a minimum, while 4 or 5 feet is necessary in temperate 
or very cold climates. 

DESIGN OF RETAINING WALLS OF GRAVITY SECTION 

The thickness of base of a retaining wall of gravity section, that is, one 
in which the earth pressure is resisted by the weight of the masonry, is 
generally taken without mathematical calculation as a certain ratio of the 
height of the wall. An easily remembered rule is to make the base § of the 
height. The table of empirical values adopted by Mr. Trautwine* for 
thickness of base of wall to resist earth pressure under average conditions 
is in accordance with good engineering practice. While he gives no values 
for concrete, they may safely be assumed equivalent to those for cut stone 
laid in mortar, which are as given in the following table. The earth is 
assumed to slope up from the top of the wall till it reaches a level at the 
height indicated by the ratio in the first column. 


Thickness of Retaining Walls of Gravity Section with Earth Surcharge. 
By John C. Trautwine. (See p. 661.) 


Ratio of 

Height of Earth 
to Height of Wall. 

Thickness of Base 
as ratio to 
Height of Wall. 

Ratio of 

Height of Earth 
to Height of Wall. 

Thickness of Base 
as ratio to 

Height of Wall. 

1 . 

0 • 35 

2 . 

0.58 

1 . 1 

0.42 

2-5 

0.60 

1.2 

O . 46 

3 - 

0.62 

1 -3 

O.49 

4 - 

°.6 3 

1.4 

O.51 ■ 

6. 

0.64 

1-5 

O.52 

9 - 

0.65 

1.6 

o -54 

14. 

0.66 

!-7 

o- 5 S 

25 - 


1.8 

0.56 

or more 

0.68 


The height of the wall is assumed to be measured above the surface c? 
the ground in front of it. 

The batter of the face of a retaining wall is customarily limited to ij 
inches to the foot, and the back is usually vertical. This fixes the width 
on top. 

The values in the table may be employed for long walls of concrete with 
no reinforcement. In many cases, because of the monolithic character 
of concrete, a ratio of thickness to height from 10% to 20% less may be 
adopted with safety, if the character of the filling back of the wall precludes 

* Trautwine’s “Civil Engineer’s Pocket-Book”, 1902, p. 606. 












662 A TREATISE ON CONCRETE 

excessive pressure, and if the base is slightly spread. For more accurate 
determinations of gravity sections, the principles which follow relating to 
reinforced designs are applicable. 

Angle of Internal Friction. The selection of the angle of internal friction 
is of much importance as it affects largely the magnitude of the earth pres¬ 
sure. For ordinary cases the values given on page 665 may be used, but 
for very important structures, where the additional cost is warranted, special 
experiments may be advisable. 


WEIGHT OF EARTH 

In the calculation of retaining walls, and many other structures, the weight 
of earth in place is a prime factor. The weights of dry material, based upon 
experiments by the authors, are represented in the following table. Most 
of the figures for weights of earth give the weights per cubic foot after 
excavation in a loose or a compacted condition. In the authors’ experi¬ 
ments the excavation was measured, so that the weights represent the 
material in place. As fills will eventually assume much the same charac¬ 
teristics as earth in original excavation, the figures may be employed for 
either natural earth or filled material. The weight of earth containing 
water varies with the character of the material and with the conditions. 
Gravel containing ordinary moisture weighs about 2% more than dry gravel 
and sand may weigh from 3% to 10% more, depending upon its fineness, 
since fine sands absorb the most water. Wet muck weighs about 75 lb. 
per cubic foot. These percentages assume that the bank is provided with 
natural drainage; if the earth is literally filled with water which cannot run 
off, its weight will be increased by a quantity of water nearly equal in volume 
to the voids in the material, which vary with the character of the material 
from 20% to 50% of the bulk of the earth in the bank. 

Many of the values appear high, but they are the result of careful tests. 


Average Weight of Ordinary Earth before Excavation. 

Pounds per cu. ft. 

Sand. 105 

Gravel. x^ 

Gravelly clay. x^o 

Loam. qo 

Hard pan. x^o 

Dry muck. 40 


BACKING 

Since the weight of soil saturated with water is much larger than when 
it is dry, the pressure increasing with the amount of water so that it may even 








DAMS AND RETAINING WALLS 


663 


exceed the hydrostatic pressure, the backing should be provided with ade¬ 
quate drainage. For this, a filling of gravel or crushed stone may be placed 
directly against the wall with weep holes at suitable distances apart. 


EARTH PRESSURE 

The principal force governing the dimensions of any retaining wall is the 
earth pressure. Its magnitude varies largely with the character and wet¬ 
ness of the soil, the inclination of the back of the wall, and the slope of earth 
above it. 

Of the numerous theories, all of which are based on some assumptions not 
always met with in practice, Rankine’s theory seems to be the most reliable 
yet developed, and although it does not always represent the true conditions, 
it gives safe results. It is based upon the assumptions that the earth is com¬ 
posed of granular homogeneous particles without cohesion, held only by 
friction developed between them, and that the mass of earth extends 
indefinitely. On a vertical plane the resultant pressure always acts parallel 
to the slope of the earth and at a point one-third of the height from the base, 
when the surface of the earth is level with the top of the wall or slopes back 
from it. 

The following table of pressures determined by Rankine’s formula gives 
horizontal earth pressures for different heights of wall, based on an angle 
of repose of earth of 35 0 —a fair assumption under average conditions— 
and also average unit pressures for the same assumptions. For other 
heights of wall, the horizontal unit pressures with the same angle of repose 
are directly proportional to the heights, and the total pressures are propor¬ 
tional to the squares of the height. 

Total Earth Pressure and Average Unit Pressure upon Vertical Walls of Dif¬ 
ferent Heights (See p. 663 .) 


Height of Wall in Feet. 


Total pressure 

P, in lb . 

5 

10 

15 

20 

25 

3 ° 

35 

40 

35 ° 

1400 

3 I 5 ° 

5600 

875° 

12600 

17150 

22400 


Average unit 
pressure in 
lb. per sq. ft. 

70 

140 

210 

280 

35 ° 

420 

49 ° 

560 

















664 


A TREATISE ON CONCRETE 


The table assumes ( a ) horizontal surface of earth, ( b ) vertical back of 
wall, (c) weight of earth per cubic foot, ioo pounds, (d) angle of repose, 
35 0 . For other weights of earth the values in the table are proportional to 
the weight per cubic foot. 

Passive pressure, that is, the resistance of a mass of earth against mov¬ 
ing, is many times as great as the active pressure but because of the shrink¬ 
age of filling as ordinarily placed it cannot be counted on for its full value 
unless the earth is in its natural state. 

The general formulas evolved by Mr. Rankine from the assumptions 
given above and which apply both to gravity walls and to reinforced walls, 
are presented below. 

Wall with Vertical Back. Let 

P = resultant earth pressure in pounds on a vertical surface for a length 
of wall equal to one foot. 

H = total height of wall in feet. 

H 1 = depth below top of wall of any point in feet. 
h = height of surcharge in feet. 
w = weight of earth per cubic foot. 
d — angle of inclination of earth behind the wall. 
o = angle of internal friction of the earth. 

C p = constant depending upon d and <p. (See table on page 665.) 


Then* 




P = ^ wH 2 cos d 


P’or known values of the angle of inclination and internal friction, the 
terms embracing them become constant and 


P = C v wH 2 

The intensity of pressure at any point the depth of which is H is 

Unit pressure = 2 C p wH x 

and its direction is parallel to the direction of the total pressure.* 



( 3 ) 


* For walls with horizontal filling, d = o, hence 



1 —sin <p 


Unit pressure at any depth, H i is wH x 1 - Sln ^ and acts horizontally. 

i + sin <p 

If angle of slope equals angle of internal friction, i. e., if d — cp, 

P = £ wH 2 cos d and Unit pressure is wH i cos ft 


( 5 ) 


Formulas (2) and (3), however, apply to these cases by using the proper value of Cp given in the 
table. 











DAMS AND RETAINING WALLS 


665 


The values of the constant C p are given in the table below. 

Data for Determining the Earth Pressure. 

Ride: To find the earth pressure on a vertical wall without surcharge, H 
ft. high, multiply the proper value of C p by the square of H in feet and by 
the weight of the filling per cu. ft. P = C p wH 2 (see p. 664.) For formulas 
for inclined walls and walls with surcharge, see pp. 665 and 666. 


►4 

< 

z 

K 

W-Q. 

f 

VALUES OF CONSTANT C p IN RANKINE’s FORMULA ( 2 ), p. 664 

Slope with horizontal 

Z z 









0 

&■ H 

0 H 

I to I 

I to 

1 to 2 

I to 2l 

i to 3 

1 to 4 

Level 


a £ 

0 

z 

Corresponding angle of slope d 

< 

A ~° 

45 

33 ° 4 o' 

26° 30' 

21° 50' 

18 0 30' 

14 0 0' 

0 

<0 

t 

_ r o 

o. 09 

0.07 

0.06 

O . 06 

0.05 

0.05 

0.05 

0 .29 

50 ° 

0.15 

0.09 

0.08 

O. 07 

0.07 

0.07 

0.07 

0.32 

45 ° 


0. 13 

0.11 

O . IO 

0.09 

0.09 

0.09 

0 • 35 

O 

O 


0.18 

0.14 

O. 13 

0.12 

0.12 

0.11 

0.38 

35 ° 


0.29 

0.19 

O.17 

0.16 

0.15 

0.14 

0.41 

3 °° 



0.27 

0.22 

0.20 

0.18 

0.17 

o -43 

25 ° 




O.3O 

0.26 

0.23 

0.20 

o -45 

20° 





0.36 

0.29 

0.25 

0.47 


Note: If the angle of internal friction of the earth is unknown, the fol¬ 
lowing average values may be used: Coal, shingle and broken stone, 50°; 
earth, 35 0 ; clay, 30°; sand dry, 30°; sand moist, 35 0 ; sand wet, 20°. 


As stated above, the pressure is assumed to act 
parallel to the slope of the surface of the earth, 
and for walls without surcharge acts at one-third 
of the height of the wall from the base. The 
maximum unit pressure is at the base, and is equal 
to twice the average, while the minimum at the 
top equals zero, so that the variation of the unit 
pressures may be represented by a triangle. 

Wall with Inclined Back. The earth pressure, 
R, on an inclined plane ah (Fig. 213) is the re¬ 
sultant of P, the horizontal pressure on the vertical 
plane ac, and W , the weight of the prism of earth 
abc, and acts at one-third the height from the 
bottom. 


b 



Fig. 213. —Earth Pres¬ 
sure on Inclined Back 
of a Wall. (Seep. 665.) 




















































666 


A TREATISE ON CONCRETE 


Surcharge. When the earth behind the wall is loaded in any way, for 
example, when a highway or a railway track runs along the wall, or when 
the embankment is used as a storage for material—then this loading causes 
additional pressure on the wall, which may be provided for by replacing 
the load by an equivalent surcharge of earth. The height of this surcharge, 
h, is the extra load per square foot divided by the weight of a cubic foot of 
earth. Thus a load of 500 pounds per square foot is equivalent to a sur¬ 
charge of 5 feet if the earth weighs 100 pounds per cubic foot. 

Vertical Back of Wall with Surcharge. The earth pressure on a retain¬ 
ing wall with surcharge equals the pres¬ 
sure on the surface ab less the pressure on 
bd. Using a constant from the table, page 
665, 

P = wIP C p — ivh 2 C p = 

w ( H 2 - h 2 ) C p (6) 

and this may be represented by the trape¬ 
zoid aced (see Fig. 214). The distance of 
the point of application of this force from 
below the middle point in the height of the 
wall, 

(H - h ) 2 



x = 


6 (H + h) 


( 7 ) 


Fig. 214. —Earth Pressure on 
Vertical Back of Wall with 
Surcharge. {See p. 666.) 


Wall with Inclined Back with Sur¬ 
charge. For an inclined back, the pres¬ 
sure, as in the case of a wall with inclined 


back without surcharge, is the resultant 
of P, the pressure on the vertical projection of the wall found by formula 
(2) and W , the weight of the prism of earth one foot of length, the cross- 
section of which is a trapezoid. Equation (7) gives the vertical distance 
of the point of application of the resultant below the middle point in the 
height of the wall. 


DESIGN OF REINFORCED RETAINING WALLS 

A properly designed retaining wall, whether of reinforced concrete or of 
plain masonry, must fulfil the following conditions: It must be stable (1) 
against overturning, (2) against sliding, (3) against settling, (4) against 
crushing or overstressing of the material. 








































DAMS AND RETAINING WALLS 


667 


To prevent failure by overturning, the moment of downward forces about 
the outer edge of the base, M x — W x / x + W 2 E, must be greater than that of 
the overturning moment, M 2 — Pl 3 (see Fig. 215). The ratio of those two 
M 

moments, —is called the factor of safety. For reinforced concrete walls, 

M 2 

the factor of 1.5 to 2 may be considered as ample, because the stability 
of wall is increased by the resistance of earth to shear along the line ab , 
Fig. 215, and the passive pressure of the filling in front of the wall, which 
two items are not considered in figuring the factor of safety. 

I he horizontal component of the resultant pressure on the foundation 
causes the tendency of the wall to 
slide. This force is opposed by 
the resistance to compression of 
the earth on the plane (see Fig. 

215) and by the friction F. The 
friction is equal to the vertical 
pressure multiplied by the tangent 
of friction between concrete and 
earth, or, if 

F — total friction, 

W j + W2 = weight of concrete 
and earth, 

$ = angle of friction between 

earth and concrete 

Then 

F = (W t + W 2 ) tan 0 

If the wall slides, the cohesion of the earth along the line ab (Fig. 215) must 
be destroyed, which item increases the stability against sliding. The tan¬ 
gent of the inclination of the resultant pressure, that is, the ratio of its hori¬ 
zontal to vertical component, should not be larger than the tangent of the 
angle of friction. 

Sometimes a vertical projection of the base may be needed, which may 
be placed in the middle of the base or at either end. 

Having determined the earth pressure as explained in preceding pages, 
the design of a reinforced concrete retaining wall resolves itself primarily 
into the determination of the thickness and reinforcement of concrete slabs 
to be obtained by the principles outlined in Chapter XXI on Reinforced 
Concrete Design. The methods to follow can be illustrated best by prac¬ 
tical examples, which are given in full below. 



Fig. 215. —Forces Acting upon a Retain¬ 
ing Wall and their Moment Arms. 
{See p. 667.) 






















668 


A TREATISE ON CONCRETE 


A retaining wall is especially subject to temperature stresses. To locate 
the stresses at specially prepared joints, contraction joints may be placed at 
stated intervals. In an unreinforced wall, a spacing of 20 to 30 feet between 
joints is necessary to prevent intermediate cracks. By introducing steel 
to prevent the formation of visible cracks, no joints are necessary. Steel 
reinforcement for shrinkage and temperature contraction is treated on page 

499 - 

EXAMPLE OF T-SHAPED RETAINING WALL 

Example 1. Design a retaining wall 12 ft. high above ground to support 
a sand filling. Angle of internal friction of sand, which weighs 100 lb. per 
cu. ft. is 35 0 , and the fill slopes back at the same angle. Working stresses: 
for the 1 : 2\ 15 concrete in compression, f c = 500 lb. per sq. in.; steel in 
tension, f s = 16 000 lb. per sq. in.; ratio of moduli of elasticity, n = 15; 
allowable shear involving diagonal tension, v = 32 lb. per sq. in.; bond of 
steel to concrete, u — 80 lb. per sq. in. 

Solution. If base is imbedded 4 ft. to protect from frost, and if the footing 
is assumed 18 inches thick, total height of wall is 16 ft. and height of stem 
14 ft. 6 in. The design is shown in Fig. 216, page 669. 

Lpright Slab. Earth pressure on stem from formula (2), page 664, 
taking value of C p from the table, P, = 0.41 X 100 X 14.5 2 = 8600 lb. 
This acts at J the height. Horizontal component, H x = P x cos 35 0 = 7040 
lb., and since the weight of wall and-vertical component of earth pressure 
do not affect the vertical slab, the moment, M = 7040 X | X 14.5 X 12 
= 408 000 in lb. 

Thickness of vertical slab at bottom, using formula (9), page 421, and table 
of constants, page 519, and adding 1.7 in. to the depth to steel to properly 

imbed it, is d + 1.7 = 0.29 X o. 118 \/408000 +1.7=23.5. Ratio of steel is 
p = 0.005 (t° correspond to working stresses), hence area of steel is A s =1.31 
sq. in. per foot of length of wall. This is satisfied by | in. round bars placed 
vertically 5.5 in. on centers. (See table, p. 507.) The thickness of wall at 
top may be selected as 12 in. The moment decreases from the bottom 
upwards so the steel may be reduced as shown in Fig. 216, page 669. 

Since total shear, V = 7040 lb., unit shear involving diagonal tension, is 
7040 

v = ----— = 30 lb. per sq. in. (See p. 447-) As this does 

12 X 21.8 X o.894 

not exceed working stress, no stirrups are needed. 

• 7040 

Bond stress is u = -- = 60 lb. per sq. in. (see 

21.8 X .894X 2.18 X 2.75 4 

P- 457 )- 

Length of bar to imbed in footing to prevent pulling out is 50 X l = 43.8 
in. (see Table on page 454) , hence the vertical bars must extend into the 
base this distance, or else be provided with bent ends (see page 466). 

* A table of dimensions and reinforcement for T-shaped and for counterfort retaining walls of 
different heights, compiled by Sanford E. Thompson, is given in “Concrete in Railroad Construc¬ 
tion,’’ published by The Atlas Portland Cement Co, 





DAMS AND RETAINING WALLS 66 g 

To obtain this bond, the vertical rods frequently are bent into the right 
cantilever of the footing. If instead they are bent to run into the left canti ¬ 
lever, they may form the horizontal reinforcement there, as shown in Fig. 216. 

Footing. In a correctly designed wall the resultant force should intersect 
the base within the middle third of its length. This determines the ratio of 
length of footing to height of wall, and can be obtained only by trial for any 
particular case. A study of different conditions shows that this ratio is gen- 




Fig. 216.—Design of T-shaped Retaining Wall. (See p. 669.) 

erally 0.4 to 0.6, depending upon the inclination of earth pressure, the weight 
of the fill, and finally upon the ratio between the length of the projecting toe 
and the total length of the base. The length of base best suited for our ex¬ 
ample was found after several trials to be 8 ft. 9 in. 

The forces acting on the footing are P 2 , the earth pressure on the plane ab, 
Wj, the weight of prism of sand, bcde, and W 2 , the weight of the retaining 
wall itself. The distance from the toe to the line of action of the resultant R 





























































A TREATISE ON CONCRETE 


b 70 


of W x and W 2 may be obtained as follows: Find center of gravity of earth and 
center of gravity of concrete; multiply the distance from A to these centers 
of gravity by the respective weight, and thus obtain the statical moment. 
Divide the sum of these moments by the sum of the weights, IF, + W 2 , and the 
location of the center of gravity of the combined weight is obtained. The 
line of pressure drawn for P and R intersects the base just inside of the 
middle third. 

Normal component of resultant, N = 21 990 lb. and horizontal component, 

TT 

H — 12 900lb. Hence, ratio — = 0.587, which is smaller than the tangent 

of the angle of friction, hence there is no danger of the wall sliding. 

Maximum unit pressure on soil (from formula (36), p. 562) is 5000 lb. 
per sq. ft., while the minimum equals nearly zero. 

The graphical method of finding the distribution of forces on the base is 
explained on page 586. 

Left Cantilever. Omitting weight of slab and of earth above it as neg¬ 
ligible, the forces acting on this part of the footing are represented by trap¬ 


ezoid fghi. Total force is 


5000 + 3530 


X 2.58 


11 000 lb. and moment 


arm from the diagram is 1.36 ft.; hence bending moment, M — 11 000 X 
1.36 X 12 = 179 500 in. lb. per ft. of width. 

The minimum depth to steel from formula (1), p. 418, using Table 10, 
page 519, is d = 14.5 in., and the area of steel, A s = 0.868 sq. in. How¬ 
ever, this depth may be too small to satisfy the bond stress, which is below 
considered. 

Further, if vertical steel in the vertical wall is all bent and carried into the 
left cantilever of the footing, we should have 1.30 sq. in. of steel per foot of 
width or $ in. round bars spaced 5^ in. cc., which for a depth of 14.5 in. gives 
a ratio p = 0.0075, or greater than is necessary. If desired, therefore, a 
part of this steel may be carried only far enough into the footing to prevent 
its pulling out, or if bond stress were not excessive, the depth, d, might be 
reduced below 14^ in. The bond for the suggested depth must be considered. 


Unit bond, u =-= 140 lb. per sq. in. (see p. 457). 

14.5 X 0.9 X 2.75 X 2.18 

The bond is excessive unless deformed bars of known worth are used, when 
the depth, d, of 14^ in., or to properly protect the steel a total depth of 16 in., 
may be permitted. To decrease the bond stress, for round bars the depth 
of the chntilever must be increased as follows: Assume the decreased ratio, 
p, for the increased section of concrete at p = 0.0045. Then the correspond¬ 
ing values from Table 12, page 521, k = .300, j = .900. 

V V 

From page 457 u — — hence d =— : —Substituting values, 

]dlo u]lo 


d = 


11000 


25.5 in., and total depth 27 in. 


80 X 0.9 X 218 X 2.75 

The depth of beam must be increased to 27 in. in order to decrease thfc 
bond stress to 80 lb. per sq. in. 










DAMS AND RETAINING WALLS 


67I 

Right Cantilever. It is evident from Fig. 216, page 669, that three 
forces act on the right cantilever: the upward pressure of the soil, the down¬ 
ward weight of the earth filling, and the vertical component of the earth 
pressure. Ihe resultant of these forces acts downward, hence the moment 
is negative. 

The computations for amount of steel and the shear and bond stresses 
are similar to that for the left cantilever. 

The length of imbedment necessary to prevent .slipping is not treated in 
the previous case, so it may be given here in detail. 

Area of concrete, A = 12 X 27 = 324 sq. in.; area of steel, = 1.07 

sq. in. and ratio of steel, p = -—- = 0.0033. From table 10, p. 519 find 

3 2 4 

the corresponding k and /, k = .268, j = .911. From formula (8), p. 420, 

since 1 VL = 329000 inch pounds, f s = - i2 5oopounds. 

27 X .91 X 1.07 

For this stress in steel, the length of imbedment from table on page 
454 is 39 X | = 29 in. 

Both cantilevers may be tapered toward the end to a minimum practicable 
depth, since the moments decrease from the support to zero at the end. 

Horizontal Reinforcement for Temperature . Temperature reinforcement 
is treated on page 499. 


EXAMPLE OF RETAINING WALL WITH COUNTERFORTS 

Example 2. Design a reinforced concrete wall with counterforts to support 
a sand filling 20 ft. high above ground, using same assumptions as in Exam¬ 
ple 1, page 668. 

Solution. In this type of wall the vertical slab acts as a slab supported by 
the counterforts, the principal steel being horizontal. The projecting toe 
of the footing is a cantilever and the footing below the earth is a slab supported 
by the counterforts. The counterforts tie the imbedded footing to the ver¬ 
tical slab and act as cantilevers fixed to the footing. Design is shown in Fig. 
217, p. 672. 

The slabs may be considered as partly continuous, using the moment 

wl 2 . r . wl 2 

M = - . If carefully designed for negative moment M = - might be 

10 12 

permissible. (See p. 428.) 

Instead of forming a projecting toe as a cantilever, it is sometimes more 
economical when the projection is large to introduce small buttresses and 
construct this part of the footing also as a partly continuous slab. 

The first step in the operation of design is to determine the length of base 
and the relation between the projecting toe and the base by trial, the allow¬ 
able pressure on the soil and the minimum angle of inclination of the result¬ 
ant earth pressure being the determining factors. The method is the same 
as for a T-type wall, as outlined on page 670. 






t>72 


A TREATISE ON CONCRETE 


Spacing of Counterforts. The spacing of counterforts or ribs may be 
found on the basis of minimum material*, from which 8 feet may be adopted. 

Vertical Wall. The vertical wall must be considered in narrow horizon¬ 
tal strips as slabs supported by the counterforts, partly continuous, and 
loaded uniformly. The earth pressure changes with the height, so that the 
pressure upon the different strips decreases from the bottom up. The pressure 
against the bottom strip as given on page 672 is 1480 lb. per sq. ft., or 123 

wl 2 , „ 123X64X12 

lb. per ft. of width for 1-inch of height. Using M = — , M = - = 

10 10 

9500 inch pounds per inch of width. Hence (p. 418) d = .118 V9500 = n -5 
in.; thickness of wall is thus 13 in., and area of steel, A s = 0.005 X n-5 X 12 
= 0.69 sq. in. per ft. of height. Round bars f in. diameter spaced 5J inches 
on centers may be used. 

For convenience in construction the thickness of the wall may be 
made uniform, and the spacing of rods increased with the decreasing earth 
pressure, as shown on the drawing. The negative bending moment may be 
provided for by introducing short rods in front of buttresses, or by bend¬ 
ing the rods. (p. 428.) 


* For full discussion, see “The Design of Retaining Walls,’’ by H. A. Petterson, Engineering 
Record, Vol. LVII, 1908, p. 777; for practical purposes the following demonstration illustrates 
the necessary steps. Use notation page 529, also let ,x = spacing of buttresses in feet; £?=the 
maximum horizontal unit pressure on vertical wall, which occurs at the bottom of the wall. £), from 
f ormula(3),page 6644s 1480 lb. per sq. ft. Taking a strip of the vertical slab one ft. in height, whose 

1480 X x 2 X 12 

span is the spacing of the counterforts, the bending moment is then M = ~ = 1780.x 2 ; 

the depth to steel, (p. 421), d— .29 X.118 \A780 * = 1.43*, and the volume per foot of 


. i- 43 * 


length of wall is X 1 X 22 = 2.6.x cu. ft. Maximum unit weight acting on horizontal footing 

, . 5 3 2 5 X 12 X x 2 - 7-- 

slab is 5 325 pounds per sq. ft. Hence M = ~-, d = .29 X .118 53 2 5 X 1.2.x- 


2.72.x 

= 2.72X, and volume per foot of length of wall is —X 1 X 8.25 = 1.9.x 

The thickness below steel is a constant for any spacing and therefore need not be considered in 
fixing the volume. 


Assume the thickness of counterfort as 16 in., and volume will be- 


22 X 8.25 X 16 
2X12 


= 121 


121 


cu. ft., and for one foot of length of wall,-. Because of the greater cost, per unit of volume, 


of the counterforts over that of the slab work in a wall of this type, the quantity representing 
the counterfort volume may be increased by, say, 100%. The expression for this quantity then 

121 I 21 

becomes - X 2. Hence total volume, = 2.6* + 1.9X + - X 2 

x x 


242 dQ 

or 3 . = 4 - 5 * + V and 4 ’ 5 


24.2 


o (for minimum, first derivative equals zero). 


x = 


242 


4-5 


7.3 ft. For practical purposes, say 8 ft. 















DAMS AND RETAINING WALLS 


673 


Horizontal FootingSlab. 

This slab may be con¬ 
sidered as composed of 
narrow strips uniformly 
loaded and supported by 
the counterforts. The 
loading is the difference 
between the weight of the 
earth above it plus the 
vertical component of 
the earth pressure, and 
the upward pressure of 
the soil. As indicated 
in the drawing, this dif¬ 
ference is a maximum 
at a and decreases to¬ 
ward b. In this case 
the maximum unit load¬ 
ing is 5566 - 241 =5325 
lb. per sq.ft. The max¬ 
imum bending moment in 
this slab, considering it as 
partly continuous is 

M = 5325 X 64 x 12 

I o 

= 40 800 in. lb. Depth 
of steel, d = 0.29 X 
o.ii8\/ 40800 = 21.75 in., 
hence thickness may be 
taken as 23.25 in. The 
area of concrete is then 
261 sq. in., hence area of 
steel required is = 1.31 

sq. in., which is satisfied 
by i-in. bars spaced 5 § Fig - 217-—Design of Retaining Wall with Coun- 

, T , terforts. (Seep. 671.) 

m. on centers. The v r - 

thickness of this founda¬ 
tion slab may be made uniform, and the spacing of the rods increased as 
the loading decreases. 

The negative bending moment must be provided for by introducing at 
the top of the slab, under the counterforts, short rods of equal size and spac¬ 
ing to the bottom ones or else these bottom rods must be bent down at each 
counterfort. (See p. 428.) 

Counterforts. A counterfort is really an upright cantilever beam sup¬ 
ported by the horizontal foundation slab and carrying as its load the vertical 
slab of the wall, which, in turn, takes the earth pressure. The thickness of 
the counterfort, which must be sufficient to insure rigidity and resist unequal 
pressures during construction, may be selected by judgment. 






































































674 


A TREATISE ON CONCRETE 


To determine the quantity of steel required in the counterfort, we find the 
horizontal component of the earth pressure per foot of wall to be (from for¬ 
mula (2), p. 664) .41 X 22 X 22 X 100 X .819 = 16 200 lb.; hence, the total 
force transmitted to the counterfort, since they are spaced 8 ft., is 8 X 16 200 
= 129 600 lb. The bending moment, since the force acts at one-third the 

22 

height, is then M = 129 600 X— X 12 = 11 400 000 in. lb. The thickness 

3 


of the counterfort is taken at 16 in., the depth to steel, 
mula (1), p. 418, C 


I bd 2 I 11 
\ M = \ 7i 


6 X no 2 


= I 3°- 


400 000 


d = no in. From for- 
By interpolation in the 


Table 11 on page 520 between items 3 and 4, the ratio of steel, p — 0.00416 
and area of steel i 8 = no X 16 X .00416 = 7.36 sq. in. Six i|-in. round 
bars will satisfy this. 

The portion of the counterfort receiving the greatest tension is the inclined 
edge, so these bars are placed near to this surface. Besides these bars, 
horizontal and vertical bars are necessary to tie the vertical and horizontal 
slabs to the counterfort, to transfer the forces and provide for diagonal ten¬ 
sion. These bars should be bent into the slabs to obtain as good a bond as 
possible. The principal tension bars in the counterforts also must be well 
imbedded in the horizontal foundation slab, and bent so as to attain their 
full strength in tension. The value of hooking is discussed on page 466. 


COPINGS 


A coping may be formed on a concrete retaining wall, which will shed 
water and look nearly as well as cut stone, by sloping the top back from the 
face and treating surfaces by methods described on pages 288 to 293.* 


DAMS 

Concrete is a suitable substitute for stone masonry (a) in gravity 
dams, where the masonry is laid in large masses, whenever the cost per 
cubic yard of concrete rubble is cheaper than stone masonry of equal 
quality, and (b) in curtain or arch dams of thin section reinforced with 
steel. 

Concrete of cement, sand, and crushed stone cannot always compete in 
price with rubble masonry laid in cement mortar, because, although the 
labor cost of laying concrete is less, more cement is required per cubic yard; 
but by introducing large stones into the concrete, the percentage of cement 
per cubic yard may be reduced to the same quantity or even less than in 
water-tight rubble masonry. Therefore, the concrete rubble is apt to be 
the cheaper, since the cost of crushing the stone for the concrete is small 

* See illustration of form construction in Engineering News, July 9, 1903, p. 37. 





DAMS AND RETAINING WALLS 675 

compared with the difference in expense of employing skilled masons or 
unskilled labor. 

Methods of laying rubble concrete and the calculation of the quantity 
of cement per cubic yard are discussed in Chapter XV, pages 300 and 
2984 As is there stated, the concrete must be of soft, mushy consistency 
so that the large stone may be properly imbedded. 

The relative cost of rubble concrete and stone masonry depends upon 
the price of cement at the work and local conditions. The dam at Boonton, 
N. J., a section of which is shown in Fig. 219, p. 676, contains 240,000 
cubic yards of concrete rubble, and was built at a contract price, not 
including the cement, of $1.98 per cubic yard. Only 0.6 barrels Portland 
cement were used per cubic yard, although the proportions of the concrete 
matrix were i:2j:6j. This small quantity of cement was due to the 
large proportion of stones which averaged from one yard to 2% yards 
each and occupied 55% of the total volume. The contract price men¬ 
tioned includes the preparation of the large stones and the crushed 
stone, and their transportation from a quarry three miles away. It is 
believed by the authors that the price and also the quantity of cement 
per cubic yard represent minimum figures in first-class construction, but 
the force account showed that the contractor was making a fair profit, 
and inspection of the work and its water-tightness prove that there was 
no skimping in the use of cement. On this particular job the quotation 
of the highest bidder was nearly double the accepted price. 

With reinforced concrete the engineer is able to branch out into special 
types whose design may be applicable to local conditions. 

Design of Gravity Dams. A foundation must be secured which 
will resist the pressure upon it and prevent percolation of water under 
the masonry. The end connections with the adjacent soil or rock must 
also be carefully considered. The section of the dam must be of such 
thickness and design as to prevent (1) leakage, (2) overturning, and 
(3) sliding. 

Leakage through a concrete dam of gravity section need only be con¬ 
sidered to the extent that no careless work be allowed. 

To avoid tension in the foundation it is necessary that the resultant of all 
the forces of pressure and weight shall pass through the middle third of 
the base. Dangerous sliding need not usually be feared if the dam is de¬ 
signed to resist overturning. In considering the resistance of friction, Mr. 
Joseph P. Frizell* states that smooth stone slides on smooth stone 

* Frizell’s “Water Power”, p. 19. 

fTables of Quantities are given on pp. 236, 237. 


676 


A TREATISE ON CONCRETE 


under a horizontal force of two-thirds its weight, and to slide on gravel 01 
clay, stone requires a force nearly equal to its weight. 

The pressure of the water upon any submerged surface is equal to the 
area of the surface in square feet times the weight of a cubic foot of water 
times the depth of the center of gravity of the surface below the water 
level. This pressure tends to overturn the dam, and is resisted by the 
weight of the dam, and in some cases, where the up-stream face slopes, by 
the weight of the water upon the dam. 

The treatment in Frizell’s Water Power of the location of the center of 
pressure, and the moment produced by it, is especially clear and practical. 



Fig. 219. —Section through Overflow of Boonton, N. J., Dam. (See p.676.) 

Fig. 219 represents a section through the overflow of the concrete dam 
t Boonton, N. J., the construction of which is described on page 300. 












DAMS AND RETAINING WALLS 


677 

The extreme height of the dam at the highest point above the foundations 
is no feet. An interesting practical test of the water-tightness of concrete 
occurred when the reservoir was filled. A vertical well was left in the dam 
in order to provide access to two drainage gates, and although the water in 
the reservoir is 100 feet deep, and is separated from the well by only 5 feet 
6 inches of concrete mixed in the proportions 1: 2f: 6f, the well remains 
entirely dry. 

Reinforced Dams. The aim in reinforced dams is to reduce the quan¬ 
tity and cost of materials, and at the same time to permit a much broader 
base, and a sloping water-tight deck for the up-stream face. The water 
pressure is thus made to increase instead of oppose stability. 

A section of such a dam at Schuylerville, N. Y., 250 feet long and 25 feet 
high, is shown in Fig. 220. The buttresses are on io-foot centers, and support 
a deck tapering from 8 inches to 12 inches thick, while the overfall apron is 8 
inches thick. A foot-bridge lighted by electric lights passes through under 
the crest, giving access from the mill to the railway platform on the other bank. 


TO RELEASE:- GO underneath 

THE DAM;- TURN THE ROD HALFWAY 
HOUND, AND DROP HOOK. INTO SOCKET, 
flush with crest, the flash 


BOARDS DRIFT AWAY AND ARE 
RECOVERED. 

TO SET:-reversf the oper¬ 
ation, HANDLING THE ROD 
FROM BELOW OR ABOVE 
AS IS MOST CONVENIENT. 





Wk 

CUT-OFF WALL 


Fig. 220. — Section of Reinforced Concrete Dam at Schuylerville, N. Y. (See p. 677.) 


Arched Dams. Curved dams, designed in plan as a single arch, convex 
up-stream, are considered by foremost authorities to be of doubtful economy, 
as the extra length requires more material than is saved by the reduced 
cross-section. 

Recently, a type of dams consisting of a series of arches supported by 
piers or steel lattice work has been suggested, and this idea may receive 
further development through the introduction of reinforced concrete. 








































































A TREATISE ON CONCRETE 


678 

A dam in the form of a buttressed wall with a vertical up-stream surface 
has been suggested by Mr. George L. Dillman,* the dam in plan consisting 
of parabolic arches. 

The design for a dam at Ogden, Utah,f consists of a number of piers, 
triangular in vertical section, forming buttresses to support an up-stream 
sloping face composed of circular concrete arches from 6 to 8 feet thick. 
The arches are designed to be covered on their upper surface with J-inch 
steel facing. The top of the dam, which is also formed by arches between 
the piers, carries a roadway. 


CORE WALLS 

Concrete is largely superseding rubble masonry for core walls in earth 
dams and dikes. The forms can be roughly made without reference to 
the appearance of the faces, while a thin wall of concrete may be built 
water-tight more easily than one of rubble masonry. Unless reinforced, 
core walls are generally of the same thickness as those of rubble masonry. 
The Natural cement concrete core wall of the Sudbury Dam, built by the 
Boston Water Commissioner and his successor upon the work, the Metro¬ 
politan Water Board of Massachusetts, is 2 feet thick at the top, with a batter 
of one in fifteen on both faces, until it reaches a maximum width of 10 feet. 
At Spot Pond Reservoir, several dikes with core walls of Portland cement 
concrete, of 15 to 18 feet average height, are 2\ feet in thickness throughout. 

The dike for the Jersey City Water Supply Company at Boonton, N. J., 
is designed for a total height of 54 feet. The lower 30 feet is 4 feet 8 inches 
thick, and at this height it begins to batter, so as to reach a width of 3 feet 
at the top. 

Although core walls may often be economically built of rubble concrete, 
the stones must be of smaller size, and cannot occupy so large a volume of 
the mass as in gravity dams, since the sections are thinner. In the construc¬ 
tion of the Boonton Dike, mentioned above, one contractor was placing rub¬ 
ble to the extent of 20% of the total mass, while another was placing 33%. 
In the former case the stones were loaded on to derrick skips and unloaded 
by hand; in the latter case, they were hooked by the derrick. This 33% 
probably represents a maximum for a wall 5 feet thick or less. 

Since a thin wall of reinforced concrete may be made equally strong, and 
more elastic than a thick wall of plain concrete, reinforcement may event¬ 
ually be employed to reduce the section, and therefore the quantity of 
material. 

♦Transactions American Society of Civil Engineers, Vol. XLIX, p. 94. 

fHenry Goldmark in Transactions American Society of Civil Engineers, Vol. XXXVIII, d. 290 


CONDUITS AND TUNNELS 


679 


CHAPTER XXVII 

CONDUITS AND TUNNELS 

Since the principal stresses in arches are compressive, concrete is pe¬ 
culiarly suitable for all classes of arched structures. Eccentric loading 
may be provided for by increasing the thickness of the concrete at the 
points of greatest stress, by steel reinforcement, or by both. The steel may 
also prevent failure of thin sections of the arch from excessive stresses 
due to suddenly applied loads or to settlement of the foundation. 

Concrete is supplanting cut stone in arch bridges because of its rela¬ 
tive cheapness. Although not entirely acceptable from an architectural 
standpoint because of the difficulty in obtaining a satisfactory surfacing, 
several methods of treating the face have been used with fair success. 
(See p. 288.) This objection may also be met by facing the arch with cut 
stone. Methods of arch design are treated in Chap. XXII. 

Concrete arches and conduits are likely to be cheaper than brick even 
at the same price per cubic yard, because the greater strength of the con¬ 
crete makes a thinner section possible. 

Tunnels (see p. 689) and subways (see p. 692) are now built almost 
exclusively of concrete, or of combinations of concrete and steel. 

CONDUITS 

Sewer and water conduits of almost any size or shape may be built of 
concrete. In the larger sizes, and in conduits under pressure, steel rein¬ 
forcement occasionally may be advisable from the standpoint of safety 
and economy. 

Concrete was first used in conduits to form in bad ground a foundation 
for a brick invert. Later it was adopted instead of brick for the entire 
arch, and finally, in many instances, the brick invert lining has also been 
replaced by concrete. 

While concrete may not be preferable to brick in all localities and under 
all conditions, its advantages are sufficient to always warrant a very careful 
investigation of its adaptability to the work in question. 

As far back as 1850 sewers and aqueducts of beton or beton-coignet 
(see p. 1) 8 feet in diameter were constructed in France. The materials 
consisted of J part heavy Paris cement, one part hydraulic lime, and 5 


68 o 


A TREATISE ON CONCRETE 


parts sand.* Some of these structures, notably the viaduct of La Vanne, 
are said to have cracked and flaked.f Not until the beginning of this 
century, however, was concrete extensively used for conduit construction, 
although in the extreme western part of the United States for a number 
of years it had been employed to a certain extent upon irrigation works 
for lining both canals and tunnels, a thickness of 4 or 6 inches corre¬ 
sponding to 8 inches or two rings of brickwork. J 

Comparison of Brick and Concrete Conduits. Even with no reinforce¬ 
ment Portland cement concrete is unquestionably stronger, when properly 
proportioned and laid, than brickwork of equal thickness. Therefore, 
even if the cost per cubic yard of the two materials, including centering, 
is practically the same, the concrete is made more economical than brick 
by the adoption of a thinner ring, or a ring of varying thickness propor¬ 
tioned to suit the actual stresses. 

A comparison of data shows that concrete conduits can be built at one- 
fifth to one-third less cost than brick conduits of equal diameter. Williams¬ 
port^ Pennsylvania, furnishes an example where bids were obtained for 
brick, plain concrete, and reinforced concrete. The contract bids on the 
plain concrete section averaged considerably less than the brick, and the 
bids on reinforced construction the lowest of the three. 

Referring to the reconstruction of sewers necessitated by the New York 
Subway, Mr. William Barclay Parsons, Chief Engineer, makes the fol¬ 
lowing statement in his report to the Board of Rapid Transit Commis¬ 
sioners: || 

During the year 1901 an experiment was made to construct sewers in 
situ in concrete. The first experiment gave such satisfactory results that 
the principle has been extended to other sewers in a similar manner during 
the year, except that instead of building the arch of brick, as was done at 
first, the whole sewer in many cases has been built of concrete. The ad¬ 
vantages of this form of construction are that a perfectly smooth surface 
is obtained without joints, with all connections, curves, cut-waters and 
other details molded to perfect lines, and that construction can be car¬ 
ried on more rapidly. 

♦Leonard F. Beckwith in Transactions American Society of Civil Engineers, Vol. I, p. 108. 
Mr. Beckwith also gives a table of strength of beton from Michelot. 

fO. Chanute in Transactions American Society of Civil Engineers, Vol. X, p. 307. 

JWilliam Barclay Parsons in Transactions American Society of Civil Engineers, Vol. XXXI, 
p. 314. See also description of the lining of a water works tunnel with concrete in Massachusetts, 
by Desmond Fitzgerald, Transactions American Society of Civil Engineers, Vol. XXXI, p. 394. 
Sec also References, Chapter XXXI. 

§Engineering News Supplement, Sept. 11, 1902, p. 92. 

||Report for 1902, p. 271 


CONDUITS AND TUNNELS 


681 


It is reported that these concrete sewers have cost one-third less than 
brick sewers of the same size.* 

Concrete, especially if reinforced, has another great advantage over 
brick, in that it is able to withstand internal water pressure. 

Water-Tightness of Conduits. Water-tightness is to a certain extent 
dependent upon the proportion of cement to sand. If for a concrete 
.conduit the sand and cement are mixed in the same proportions employed 
for the mortar between the joints in a brick sewer, the structures ought to 
be equally impervious. For example — a i: 2\: 5 concrete should be as 
water-tight as brick laid in 1: 2\ mortar. 

If the concrete invert is laid in separate sections, these may be connected 
by a stepped joint similar to one of the many joints between the different 
courses in brickwork. A conduit to resist water pressure without leakage 
must be longitudinally reinforced. 

The best proof, however, of the practicability of laying concrete conduits 
which will prevent the percolation of water, is the fact that sections 4 
inches and 6 inches in thickness, which satisfactorily withstand water 
pressure, have been and are still being built.f 

Lime thoroughly hydrated or slaked, or Puzzolan cement, may event¬ 
ually prove to be the most satisfactory ingredient to mix with Portland 
cement concrete as a substitute for a portion of the cement, its extreme 
fineness assisting in filling the minute voids and thus increasing the im¬ 
perviousness. 

The general subject of water-tightness is discussed in Chapter XIX. 

Durability of Concrete Inverts. Concrete inverts have proved in 
practise to be equal, if not superior, in durability to the best hard-burned 
brick. 

The hardness and smoothness of surface obtainable with concrete 
reduce the friction to a minimum and render it less liable to erosion than 
are other materials. Concrete sewers built at Duluth, Minnesota, furnish 
a practical example of the ability of Portland cement mortar to resist 
erosion. After twenty years of wear, they show no appreciable deteriora¬ 
tion or enlargement in diameter, while brick sewers laid at the same time 
required rebuilding after six or seven years. A section of the Duluth 
drains, about 2 000 feet long and 4 feet in diameter, was built on a 13 per 
cent, grade where the velocity of the water was 42 feet per second, with an 
invert of flat granite flags laid with 1: 1 Portland cement joints. The 
flow of water during heavy storms was tremendous, carrying down with 
it quantities of sand and boulders, but after two years of wear the invert 

*Engineering News , March 6, 1902, p. 201. 
fSee Sewers and Conduits in References, Chapter XXXI. 


682 


A TREATISE ON CONCRETE 


showed ridges of mortar between the granite flags, indicating that the 
Portland cement mortar was more durable than the granite. 

Experiments by Mr. Eliot C. Clarke indicate that Portland cement 
mortar in proportions i: 2 will withstand erosion better than either richer 
or leaner mortar. (See p. 125.) 

Design of Concrete Conduits.* The selection of shapes and sizes of 
conduits suitable for different flows of water and sewage is treated in 
literature on hydraulics and sewerage. If the material adopted is concrete, 
it should be of a minimum thickness consistent with good workmanship, 
strength, and durability. Steel reinforcement reduces the quantity of 
concrete required for the larger sizes, but for a diameter of 3 feet or less 
there is no practical advantage in its use unless the conduit is under pres¬ 
sure, because the minimum thicknesses which can be advantageously placed 
in a sewer trench are sufficient to withstand all strains. Even in larger 
conduits the use of steel reinforcement is not usually advisable under ordi¬ 
nary conditions, because of the cost and the difficulty of properly placing 
the metal. 

In preference to an entire concrete section, many engineers advocate 
an invert of one or sometimes two rings of brick laid in a concrete founda¬ 
tion and surmounted with an arch of either brick or concrete. Others 
favor a concrete invert paved with a granolithic wearing surface, — 
thoroughly troweled, — from one-half to one inch thick. 

The design of a conduit is dependent upon the depth and character of 
the material through which it passes, but a few typical illustrations may 
afford hints for special cases. The proportions of the concrete should be 
carefully determined by an examination of the aggregate at hand. (See 
Chapter XI, page 183.) A mixture of one part packed cement, 2 parts 
sand, 4 parts stone or gravel, is rich enough for important work, while 
proportions as lean as 1: 4: 8 may sometimes be employed for sub-founda¬ 
tions or backing. In most cases the selection will lie between these two 
extremes. Natural cement, because cheaper than Portland, is especially 
adapted for foundations and filling which are not subject to stress or to 
wear. Puzzolan cement is also suitable in many instances. 

The Weston Aqueduct of the Metropolitan Water Works, Massachu¬ 
setts, built on a gradient of one in 5 000, has in loose earth a typical section 
shown in Fig. 221. In compact earth the excavation is narrower, and 
the width of base is reduced as shown by one or the other of the dotted 
lines, AB or CB. In embankment, the foundation is carried lower and 
horizontal reinforcing rods are sometimes placed at intervals just below 
the brick invert lining. 


♦Earth pressure on conduits is discussed on page 693. 


CONDUITS AND TUNNELS 


683 

In the Chicago Clearing Yards* drainage is accomplished by concrete 
sewers. The 36-inch and 42-inch diameter mains are 8 inches thick, 
the 48-inch diameter are 10 inches thick, and the 84 and 90-inch mains, 



Fig. 221. — Typical Section of Weston Aqueduct in Loose Earth. (See p. 682.) 

12 inches thick. The ring in each size is of uniform thickness, and 
the lower portions of the interior surface are covered with a ^-inch coat of 
plaster. 

In large concrete conduits, even when of circular shape, and passing 
through material which needs no foundation, it is good practice, whether 
or not reinforcement is employed, to thicken the walls at the spring of the 
arch. At Williamsport, Pennsylvania, a n-foot concrete sewer, suggested 
as a possible substitute for a 4-ringed brick sewer, was designed 13 inches 
thick at the crown and invert, and 19J inches thick at the haunches with 
no reinforcement. 

The Jersey City Water Supply Company constructed in 1903 a conduit 
reinforced with twisted steel. A typical section, taken through a manhole, 
is shown in Fig. 222, as designed by Mr. William B. Fuller. Longitudinal 
reinforcement consists of fV-inch rods spaced about 18 inches apart, and 
circumferential reinforcement is formed by rings of f-inch rods pbout 12 
inches apart. Through rock open cut the metal was placed only in th fi 

♦See article by E. J. McCaustland, Cement , Sept., 1902, p. 265. 




















A TREATISE ON CONCRETE 


684 

arch, and as far down on each side as the filling would extend. The open- 
cut conduit is shown in process of construction in Fig. 97, page 278. 

At Kalamazoo, Michigan, Mr. George S. Pierson adopted for a creek 
culvert* a section shown in Fig. 223. 


COVER 



-2 FT.6 

n* n " 


2 2 

• • 



SQUARE MANHOLE 


p- 5 -FT 78 --5 FT.8- 

Fig. 222.— Typical Section of Jersey City Water Sup- 


5 FT.8 


ply Conduit in Loose Earth. (See p. 683.) 


At Grenoble, France,f in 1902, a concrete-steel penstock was built to 
withstand a pressure of 65 feet head of water. The thickness of wall is 


from 8 to 10 inches, reinforced with longitudinal bars | to J inch diameter 
and circular hoops f to J- inch diameter, forming a mesh about 4 inches 
square. 


Thickness of Conduits. Mr. Fuller’s general rulej for determining 

the thickness of concrete in conduits is as follows: 

If concrete is not reinforced and ground is good, — able to stand without 
sheeting, — make crown thickness a minimum of 4 inches, and then one 


# 


♦Described in Engineering News, Feb. 12, 1903, p. 163. 
■\Engineering Record, Mar. 7, 1903, p. 249. 

^Personal correspondence. 


































CONDUITS AND TUNNELS 


685 


inch thicker than diameter of sewer in feet. Make thickness of invert same 
as crown plus one inch except never less than 5 inches. Make thick¬ 
ness at haunches two and a half times thickness of crown, but never less 
than 6 inches. This rule is expressed in the following table: 


Thickness of Conduits. 


Diameter of Conduit. 

Thickness of Crown, 
inches. 

Thickness of Haunch, 
inches. 

Thickness of Invert, 
inches. 

2 

4 

6 

5 

6 

7 

18 

8 

12 

13 

33 

14 


If ground is soft or trench is unusually deep, these thicknesses must be 
increased according to experienced judgment. 

If reinforcement is used, the thickness for conduits of ordinary sizes is 
usually determined bv the minimum thickness of concrete which can be 
laid so as to properly imbed the metal. This minimum for the large diam¬ 
eters where steel is advisable may be taken as 6 inches. 

Methods of Conduit Construction. There are four general methods 
of construction of concrete conduits: (1) The lower portion of the invert is 
laid by template and the remainder of the circle by centering. (2) The 


K 

! \ 

I \ 

I \ 



Fig. 223.— Creek Culvert at Kalamazoo, Mich. ( See 

p. 684.) 

invert is formed by an inverted center, and the arch by an upright center. 
(3) A center the size of the entire sewer, but with a removable bottom, is 
placed, the sides and arch are built, and then the bottom of the center is 
removed, and the invert is laid. (4) The entire sewer is formed as a 
monolith. The size of the sewer and the character of the work influences 
the choice of method. 


















686 


A TREATISE ON CONCRETE 


If the invert is to have a brick lining or a granolithic finish, after exca¬ 
vating the material to the required grade and shape, profiles or templets 
are placed in advance of the finished concrete, and the surface is formed 
with the aid of a straight-edge placed longitudinally from the finished 
concrete to the nearest template. If the sides run up sharply, as in a small 
sewer, the concrete may be held in place by strips of lagging, 2-inch by 
2-inch for a very small sewer, or wider for a larger size. This lagging 
rests at one end on the finished concrete, and at the other end on the tem¬ 
plate, and is placed as the work progresses. In horseshoe sewers the in ¬ 
vert may be shaped with templates and straight-edge, and the side walls 
laid back of plank forms. 

One of the simplest methods of constructing a small sewer whose invert 
is to be entirely of concrete, without reinforcement, is that adopted by the 
New York Transit Commission.* The process is described as follows: 

Previous to setting the invert form in place for constructing a length of 
invert, concrete was placed on the bottom of the trench in a layer thick 
enough to bring its top surface up to within from |-inch to ^-inch of flow¬ 
line grade. To insure the accuracy of this work and also to insure the 
accurate alignment of the form a template was suspended from the trench 
timbering and adjusted to line and grade. After placing the bottom layer 
of concrete the form (a center 12 feet in length) was accurately set in posi¬ 
tion by resting its rear end on the end of the last completed invert and 
supporting its forward end on a foundation accurately set in grade. The 
flow-line was then accurately formed by filling the space between the 
bottom of the form and the concrete foundation layer with a mortar of one 
part Portland cement to one part sand. The form was then firmly braced 
in position by struts nailed to the trench sheeting, and vertical planking 
was set up to form the outside of the spandrel. The concrete was then 
placed and carefully rammed against the form so as to insure a smooth 
surface. The invert concrete was composed of one part Portland cement, 
two parts sand and four parts broken stone to pass a i-inch ring. This 
mixture was placed (not dropped) into position and carefully rammed. 
The ends of each successive section of invert were mortised to insure a 
firm and intimate connection with the next section, and 2 by 4-inch strips, 
laid longitudinally along the center of the tops of the side walls of the invert 
section, formed mortises for bonding the arch ring to the invert. The 
forms were left in place at least 24 hours to allow the concrete to set. 
After the invert was set and the form withdrawn a thin cement wash was 
brushed over its surface to smooth any slight roughness. This work gave 
a surface almost polished in comparison with the best brickwork. 

This method of procedure affords no opportunity of troweling the surface, 
but in a sharply curved invert it is difficult to use a trowel. The plan 

*Engineerin% News , Mar. 6, 1902, p. 199. 


CONDUITS AND TUNNELS 


68 7 


described is not suitable for a large reinforced sewer because so much time 
is required to set the center and the steel that the layer of concrete in the 
bottom sets too hard to unite with the mortar finishing coat. 

In a large conduit the smoothest and best wearing surface is obtained by 
laying a comparatively narrow strip of invert by means of profiles or 
templets and straight-edge, and troweling it. If desired, a granolithic (or 
mortar) finish may be given, but with thorough troweling, excellent 
results are secured with concrete. The arch center, which in such cases 
must be nearly a complete cylinder, is placed after the strip of invert 
concrete has set, mortar is spread on the edges of the invert strip already 
laid, and the circle is completed with fresh concrete. A longitudinal groove 
also assists in forming a tight joint. 

To avoid this joint, a similar plan has been followed to that just de¬ 
scribed, except that the form, which is a complete cylinder open at the 
bottom, is placed, before laying any concrete, upon concrete blocks pre¬ 
viously prepared in' molds and then laid in the bottom of the trench. 
The lowest strip of invert is not laid until after the sides and arch are in 
place, the concrete for it being let down through holes left in the crown 
for the purpose, and troweled as thoroughly as the obstructions of the 
forms will permit. 

It would at first appear that the sewer could more readily be made 
monolithic by placing a complete cylinder and pouring concrete around it 
for the invert arch. The objection to this, however, is the great difficulty 
in placing the concrete in the extreme bottom, and also the tendency of 
the center to “float” from the upward pressure of the concrete. This 
difficulty is also encountered to a less extent in the method described in 
the preceding paragraph. 

In a sewer whose invert and arch are constructed separately, the arch 
centers are made and placed as for brick, except that a smoother and 
tighter surface is necessary, and the forms are oiled to prevent adhesion. 
A covering of sheet metal has often been successfully used. In order to 
lay the concrete of the arch sufficiently wet to obtain a smooth surface, an 
outside set of forms, open at the crown, is usually essential. 

The laying of a large water conduit for the Jersey City Water Supply 
Company is illustrated in Fig. 97, page 278. 

If a plaster finish is required by the specifications, the mortar may be 
spread upon the arch center before placing the concrete, or troweled on to 
the intrados after the completion of the work. In the aqueduct of the 
Metropolitan Water Works, Massachusetts* (see Fig. 221, p. 683), a 

♦Third Annual Report, Metropolitan Water Board, 1898, p. 56. 


688 


A TREATISE ON CONCRETE 


Portland cement wash was first used on the Portland concrete arch, but 
it was afterwards found that thin plastering gave better results. The 
plastering was put on to increase the water-tightness and to make a smoother 
surface. As a rule, the authors do not consider it necessary or advisable to 
plaster the arch. 

Conduit Forms. The construction of forms* so that they may be readily 
“struck” and removed requires considerable ingenuity and design. Invert 
centers for a small sewer, designed by Mr. William G. Taylor and em¬ 
ployed in the Medford, Massachusetts, sewers, are illustrated in Fig. 224. 



Fig. 224. — Center for Invert of 30-inch Sewer at Medford, Mass. {See p. 688.) 


Conduits in Tunnel. The methods of construction, except as regards 
the handling of the concrete, are substantially the same in tunnel as in 
open-cut. It is generally necessary, however, to provide loose longitudi¬ 
nal lagging for the arch, and place it stick by stick as the concrete is laid. 
The extreme crown or key for a width, say, of 2 feet, is most easily laid 

♦Various styles are referred to under “Forms” in References, Chapter XXXI. 






CONDUITS AND TUNNELS 


689 


upon cross strips or short segments in the same way that a brick arch in 
tunnel is keyed. The concrete for the key must be mixed fairly dry, and 
rammed lengthwise of the tunnel. 

The tunnel section of the conduit of the Jersey City Water Supply 
Company is similar in inside dimensions to the open-cut section. (Fig. 
222, p. 684.) It is plain concrete with no reinforcement. The thickness 
of the arch and sides is 8 inches and of the invert 6 inches, but points of 
rock are allowed to jut into this section “provided a minimum thickness 
of 6 inches is maintained in the arch, and of 3 inches in the sides and bot¬ 
tom.” 

TUNNELS 

The general principles of design and methods of construction for large 
railway tunnels are similar to those for sewer and water conduits. The 
external strains are of course greater and must be provided for according 
to local conditions. In some cases water-tightness is essential; in others, 
which compose the large majority, the drift is through dry material, and 
the ballast may be laid directly upon the bottom. 

Tunnel Design. The standard section of a double-track tunnel of the 
Pittsburgh, Carnegie & Western R. R.* has an arch 26 inches thick and 
side wall laid on a batter, inside, of one inch to the foot, and of such thick¬ 
ness as to reduce to 26 inches at the springing line. 

The standard section of single archf in the New York Subway for a 
tunnel 25 feet wide is 18 inches at the crown. In rock drift this thickness 
is carried down to the springing line, from which point the inside face is 
battered inward. In deep open-cut construction the arch is thickened at 
the haunches to about 4 feet, and the outside of the wall is waterproofed. 

The East Boston Tunnel, completed in 1904, is shown in section in 
Fig. 225. The sketch also illustrates the general construction of steel 
framework and lagging which, after completion, were entirely removed. 
The invert between A and B was laid after the rest of the section was 
complete. The method of carrying on the work is described on page 691. 

The approaches to the Harlem River Tunnelf of the New York Subway 
were excavated in open-cut, then roofed over, and the tube thus formed 
pumped out. The section of this tunnel under the river is lined with cast- 
iron segments. 

The single-track tubes of the Pennsylvania R. R. tunnels§ under the 

*Engineering News, May 21, 1903, p. 447 - 

•{•Contract Drawing No. C 9. 

^George S. Rice in Journal Association of Engineering Societies, Dec., 1902, p. 224. 

§Engineering News, Oct. 8, 1903, p. 327. 


690 a treatise on concrete 

channel of the Hudson River at New York City are designed with a cast 
iron shell made in segments bolted together and lined on the inside with 
concrete 2 feet thick. 

Methods of Tunnel Construction. Concrete side walls and arches in 
tunnels constructed without the use of compressed air are laid by means of 
forms and centers, whose design varies with the character of the excavation 



Fig. 225.—Section of East Boston Tunnel during Construction. (See p. 691.) 


and the general arrangement of the structural machinery.* To provide 
clearance so that the arch center may be lowered and moved ahead, the 
side walls may be carried up above the springing line. For supporting 
the center, a temporary frame consisting of a timber resting on posts is 
set up close to each side wall, and the center is jacked up to line and sup¬ 
ported by wedges. By placing the side timbers in advance, the arch may 
be hauled ahead on rollers by hand tackle or hoisting engine. 

*In the serial on The New York Rapid Transit Railway, Engineering News , Sept. 18 and 
Oct. 8, 1902, are excellent descriptions with sketches and illustrations of the methods of construc¬ 
tion on one of the sections of the New York Subway and in the Harlem Tunnel. See Reference* 
for further examples. 















































CONDUITS AND TUNNELS 


691 


The East Boston Tunnel, shown in Fig. 225, is an interesting illustra¬ 
tion of a tunnel entirely of concrete built with the aid of compressed air.* 
Two side drifts, solidly timbered, were kept from 60 to 150 feet in advance 
of the shield, so that the concrete side walls, which were built in these to a 
height of about 16 inches below the springing line of the arch, had an op¬ 
portunity to set for about ten days before the shield reached them. The 
shield, resting on rollers, moved along on these side walls, and the main ex¬ 
cavation was made under it. The concrete arch was built under the tail 
end of the shield, in lengths of 30 inches, as soon as the earth was removed. 
The shield was forced ahead by 16 hydraulic jacks, acting against the cast- 
iron cruciform push rods, 3 inches in diameter, shown in the drawing, which 
were placed in the concrete in 30-inch lengths, so as to form continuous 
rods the entire length of the tunnel. The supports for the centering con¬ 
sisted of steel ribs, j* also shown in the figure, placed 2^ feet apart, and sup¬ 
porting 4-inch lagging, against which the concrete was laid. Portland 
cement grout, usually 1 cement to 2 fine sand, was forced in on top of the 
arch so as to form a film about 1J inches thick. The invert was laid as the 
shield progressed. The progress of excavation and lining in May, 1901, 
was about 6 feet in twenty-four hours, about 60 men being then employed 
on each of the two shifts. 

The specifications for the East Boston TunnelJ limited the sizes of the 
gravel to 2 inches, and stated that 5% only should be less than J inch. 
The proportions required that “to each 123 pounds of dry Portland cement 
there shall be 2J cubic feet of sand and 4 cubic feet of gravel, and such a 
proportion of water as the engineer shall from time to time determine. 
The sand and gravel shall not be packed more closely for the above meas¬ 
urements than is done by shoveling in a dry state into a measuring box.” 
Compensation was awarded the contractor when these proportions were 
varied. Crushed stone screenings were largely used instead of sand. 

Closing Leaks. In the East Boston Tunnel a layer of neat cement 
mortar was spread upon a surface of old concrete before laying a new 
section, but even this did not prevent slight percolation of water at these 
joints after the removal of the air pressure. Although the leakage through 
these was almost inappreciable, they gave the walls a somewhat unsightly 
appearance, and to stop them holes 6 inches or less in depth were drilled in 
the concrete, and f-inch pipes inserted, through which neat cement grout 
was forced by a power pump. The leakage in September, 1904, in 1.4 

♦Howard A. Carson in Journal Association of Engineering Societies, Dec., 1902, p. 205. 

-j-Ribs were of wood on one of the sections. 

^Construction Contract, Boston Transit Commission, Section B, East Boston Tunnel, 1900. 



6q2 


A TREATISE ON CONCRETE 


miles of tunnel,—over one-half mile being directly under the harbor,— was 
not more than 7 to 8 gallons per minute. 

SUBWAYS 

Subways are technically distinguished from tunnels as constructions in 
open-cut instead of drift, although portions of a subway are often really of 
tunnel construction. The term subway is applied to accessible conduits 
for water mains, electric cables, etc., as well as to underground passages 
for traffic, but it will be considered here in the latter sense only. 



<1 11 *= 18 >1 it 27 a a =24 ** 1 “ =34 << 

Fig. 226.— Typical Section of Reinforced Concrete Construction in New 
York Subway. (See p. 692.) 

Subway Design. To save the headroom required by a circular arch, 
the roof of the subway is usually made flat. The older portion of the New 
\ ork subway is built with a framework of steel I-beams,-the bents being 
spaced about 5 feet apart and the roof formed by arches of concrete* sprung 

* Concrete has superseded brick for such arches. 




































































































































CONDUITS AND TUNNELS 


693 


between the lower flanges of the cross girders, which are also completely im¬ 
bedded in concrete. The walls are of concrete, 15 inches thick, forming 
arches between and imbedding the posts. 

The typical design of the Philadelphia subway is reinforced concrete 
throughout, except that steel columns incased in concrete are used for the 
supports between the tracks. The walls are longitudinally reinforced to 
prevent shrinkage or temperature cracks with about -fa of 1 % of steel,* and 
this was found sufficient to prevent all except very small cracks, so that the 
structure is practically dry even although the backfilling may retain con¬ 
siderable moisture above the level of the underdrains. 

The more recent portions of the New York subway also are entirely 
of reinforced concrete, the typical designf in 1909 being shown in Fig. 
226, page 692. 

During the course of construction in New York it was decided to widen 
one of the portions already complete. The contractors moved the concrete 
side walls and roof, 275 feet long, bodily, without injury^. 


DESIGN OF CONDUITS 


The external pressure on structures buried in the ground is very indefinite, 
depending not only upon the character of the fill, but also upon the method 
of excavating and filling the trenches and tamping the filling.^ 

For small depths up to 3 feet the sum of the weight of the earth and the 
live load may be taken as acting on the structure. For larger depths, 
however, the sum of these two forces would be excessive, and may be 
decreased. According to Mr. Fruhling§ the effect of the live load decreases 
as a parabola until it is zero at i 64 feet, and may be represented by formula 
(1) using notation below. || 


q x =w {h — 0.06 h 2 + 0.001 2J1 3 ) 



and q 2 = Q 


(16.5 - h ) 2 


269 



The weight of the earth increases only toadepthof about 16 4 feet accord¬ 
ing to formula (2) and is constant for larger depths. 

The sum of the force q, and q 2 thus found gives the working load per 
square foot. Allowance should be made for impact when necessary. 


* Personal correspondence with Mr. Charles M. Mills, Principal Assistant Engineer. 

-f- Presented by courtesy of Mr. Henry B. Seaman, Chief Engineer. 

J See descriptions and illustrations in Engineering News, June II, 1903, p. 515. 

Poi* excellent treatment of this subject with formulas for moments, see T-ests of Cast- 
Iron and Reinforced Concrete Culvert Pipe,” by Arthur N. Talbot, University of Illinois, Bulletin 
No. 22, 1908. 

§ Handbuch fur Eisenbetonbau, Band III, p. 510. 

(j Notation, qi = pressure per sq. ft. due to dead load; q 2 = t pressure per sq. ft. due to live load; 
w = weight of earth per cu. ft.; ^ = unit live load; h = depth in ft. 



694 


A TREATISE ON CONCRETE 


Conduits with Arch Top Only. The computation of the arch is similar 
to that for an arch bridge, and is given in Chapter XXII. The loads 
are carried to the sides of the arch conduit, which act as abutments. Ex¬ 
perience indicates that it is not safe to count to a large extent upon the filling 
at the sides of the conduit to prevent them from cracking. 

Longitudinal bars should be introduced to assist in providing for unequal 
settlement as well as to resist temperature stresses. 

Circular Pipes. Under vertical forces the maximum positive moment acts 
at the top and bottom of the pipe and produces tension on the inside surface, 
and the maximum negative moment acts on the sides, causing tension on 
the outside surface* Double reinforcement however is usually introduced. 

Rectangular Conduits. Square and rectangular conduitsf are designed 
as rigid frames loaded by weight of earth and live load acting on upper hori¬ 
zontal slab, reaction acting on lower horizontal slab, and earth pressure 
acting on sides of conduits. The stresses may be computed as in ordinary 
slabs (see page 421) after determining the moment by formulas given below. 

Let 

M x = negative moment at the four corners and at the center of vertical 
slabs, caused by vertical loads. 

M 2 = positive moment in the center of the lower or upper slab, caused by 
vertical loads. 

IiJh = moment of inertia of horizontal and of vertical slabs, respectively. 
l f h = span of horizontal and of vertical slabs, respectively. 
w = uniformly distributed load. 

Then 

wP ll t f wl 2 

M ' = 77 JI^+hT, (3) and M2 = T " M ' (4) 

The formulas apply to vertical loads as indicated above. 

For earth pressure, assuming it as uniformly distributed, these same for¬ 
mulas may be used, but the earth pressure, which acts at right angles to 
the vertical load, causes positive moment, M 2 , in center of vertical slabs and 
negative moment, M , at corners and also at center of horizontal slabs. For 
the earth pressure moments l and h must be transposed. The moments, 
M x and M 2 , due to earth pressure must be computed separately and then 
may be combined with M 2 and M x , respectively, due to vertical loads. The 
moments to be combined are of opposite signs and their sum may not repre¬ 
sent the most unfavorable condition, which, of course, must be selected. 

* See footnote H page 693. 

t A table of dimensions and reinforcement for square and for rectangular conduits under 
different conditions is given by Sanford E. Thompson in “Concrete in Railroad Construction,” pub¬ 
lished by the Atlas Portland Cement Co. 




RESERVOIRS AND TANKS 


695 


CHAPTER XXVIII 

RESERVOIRS AND TANKS 

A new field has been developed for concrete design in the building of 
covered reservoirs and filtration plants for water purification works. 
Plain or reinforced concrete is now commonly employed for the floors, 
columns, vaulted roofs, tanks, and filter basins. The Filtration Works at 
Little Falls, N. J.,* furnish a modern example of such construction. For 
open reservoirs, concrete is frequently substituted for stone masonry both 
in the retaining walls and core walls, and also is used for lining the bottom. 

Concrete tanks are used not only for water but for chemicals. 

OPEN RESERVOIRS 

The principles of design and construction of retaining walls have already 
been discussed in Chapter XXVI. The contraction cracks, which are 
almost certain to occur in long walls of any class of masonry, may be 
provided for by some form of expansion joint. Cut-off walls of clay| may 
be placed to prevent the passage of water through these vertical joints, or 
open wellsj may be left at intervals in the walls, and after setting for a 
month or more filled with concrete. This concrete filling is placed pref¬ 
erably upon a cold day, when the contraction in the wall is greatest. 

The lining for the bottom depends upon the character of the underlying 
soil or rock. Usually a layer of 1: 2J: 5 concrete 4 to 8 inches thick, if 
properly laid and troweled, will provide a lining sufficiently impervious 
for practical purposes.§ 

In small reservoirs, where earth and rock meet so as to present danger of 
unequal settlement and consequent serious leakage, a strip of reinforcing 
metal may be placed over the line of division. 

COVERED RESERVOIRS 

A common type of design for covered reservoirs consists of a concrete 
bottom, underlaid, where necessary, with 12 to 16 inches of clay puddle 

♦Transactions American Society of Civil Engineers, Vol. L, p. 394. 

-j-See paper by Chas. W. Paine in Journal Association of Engineering Societies, October, 1902, 
p. 151. 

^Transactions American Society of Civil Engineers, Vol. L, p. 406. 

§For other methods of lining see ChapterXIX on water-tightness. 


696 


A TREATISE ON CONCRETE 


and laid in the form of inverted groined arches. Piers of concrete or brick 
rest upon the thick haunches of the arches, and the roof is formed of 
groined arches supported by the piers and covered with a layer of earth. 
For the prevention of leakage, the principles already discussed in Chapter 
XIX,on Water-tightness, are applicable. The contraction of the concrete 
is a common source of cracks, but when comparing concrete with other 
kinds of masonry, it must be noted that concrete is no more liable to tem¬ 
perature contraction than brick and stone, the brick division walls, for 
instance, of the Albany Filtration Plant,* showing cracks similar in num¬ 
ber and appearance to the cracks in the outside concrete walls. 

Reservoir Walls.| Since the walls are supported at the top by a roof, 
there is less danger of overturning, and thinner sections may be used than 
for open reservoirs. This class of structure also presents opportunity for 
thin walls reinforced with steel. 

Walls of plain concrete for shallow reservoirs or filter beds are frequently 
2 feet to 2 feet 6 inches at the top, with a batter on the outside of 1 in 10. 

The wall of a circular reservoir supporting a dome-shaped roof should 
be reinforced at the top with one or more rings of steel to resist the thrust. 

Methods of forming expansion joints for open reservoir walls, described 
on page 695, are also applicable to covered reservoirs. 

Reservoir Piers. The dimensions of the piers are readily calculated 
after designing the roof and determining its weight, and the weight of the 
earth covering. In concrete piers of dimensions suitable for reservoirs, a 
working pressure of 400 pounds per square inch may be safely allowed 
when the proportions of the concrete are 1: 2^: 5. 

A floor of inverted groined arches will distribute the pressure of the piers 
if the soil is unstable. In some cases it may be necessary to place rein¬ 
forcing steel in the footing (see design of column footings on page 644) to 
prevent unequal settlement. 

In ordinary cases no reinforcing steel is needed in the piers. However, 
if the load upon them is extra heavy and the reduction of their dimensions 
is of importance, steel may be introduced to assist in carrying the com¬ 
pression. (See p. 489.) Also, if the columns are of considerable height, 
say, over 12 feet, a small rod near each corner, with occasional horizontal 
hoops, may be placed as described on page 624. 

Reservoir Floors. The floor should be smooth, fairly impervious, and 

♦Transactions American Society of Civil Engineers, Vol. XLIII, p. 282. 

•j-Methods of calculating the wall pressure, the amount of reinforcement required, as well as 
other tables and data relating to covered reservoir construction, are given in a paper on Covered 
Reservoirs and Their Design, by Freeman C. Coffin in Journal Association Engineering Societies, 
July, 1899, P- *• 


RESERVOIRS AND TANKS 697 

strong enough to resist the upward water pressure from the underlying soil 
when the reservoir is emptied. Mr. Coffin* considers a thickness of 3 or 
4 inches sufficient when the soil is so compact that there is no danger, when 
erupt}, of piessure from without. In pervious earth he suggests 6 inches 
of concrete for heads as great as 20 feet. 

Inverted groined arches for the floor not only distribute the pressure of 
the piers, but also present increased thickness of concrete around the piers 
where there is most danger of unequal settlement, give a minimum vol¬ 
ume of concrete, and afford channels for the passage of the water when the 
reservoir is emptied. 

The groined arches are laid in alternate diamonds before the piers are 
built, so that each pier will rest upon the corners of four diamonds. The 

method of laying the floor arches at the Albany Filtration Worksf is 
illustrated in Fig. 227. 



Fig. 227.— Reservoir Floor. (See p, 697.) 

Before the concrete has set, the surface may be covered with a grano¬ 
lithic or mortar finish, as in sidewalk construction (see p. 600), or it may 
be simply troweled. Methods of treating joints between blocks and other 
means of waterproofing are discussed on page 346. 

♦See second footnote on p. 696. 

fAllen Hazen in Transactions American Society of Civil Engineers, Vol XLIII, p. 262. 





















6 g 8 


A TREATISE ON CONCRETE 


Reservoir Roofs. Groined elliptic arches* are especially suited to 
reservoir roofs because requiring the minimum volume of concrete to 
support their own weight and the weight of the earth above them. 

Mr. Coffinf says that the cost per cubic yard of groined arches of 
concrete is about one-half that of brick masonry. Although the centering 
costs more than brick because a tight surface is necessary, the brickwork 
is more expensive on account of the great amount of cutting required. 
He further states that “the cost of the centering, their supports, placing 
and removing them, is from 15 to 20 cents per square foot for the interior 
surface of the reservoir if it is all centered at once.”{ 

Mr. Leonard Metcalf has compiled a table§ of data relating to reservoirs 
in the United States covered with groined arches, which shows a range in 
span of arch from 10 feet 6 inches to 16 feet, a rise varying from one foot 
6 inches to 4 feet, and a thickness at crown, in all cases but one, of 6 
inches. The proportions of the concrete range from 1 : 2\ : 4 to 1:3:5. 

TANKS 

Reinforced concrete is cheaper for tanks than sheet steel, and more 
durable than wood. It is especially adapted for tanks used in paper and 
pulp mills to hold chemicals. When made of wood or other material 
which is affected by acid and bleach liquor, such tanks require constant 
repairs. Concrete not only furnishes a durable material, but one into 
which outlet castings may be readily built, and to which, if properly flanged 
so that the concrete cannot shrink away from the metal, the cement will 
adhere and form a tight joint. The gates and other connections, which 
are usually of brass or bronze, must be so heavy that the corrosion and 
wear upon them will not necessitate removal and therefore repairs to the 
concrete, since it is impossible to form a satisfactory joint between old and 
new concrete in a thin wall. 

There are two distinct methods of concrete and mortar tank construction. 
In one, forms are built and the concrete is laid with metal reinforcement 
in the usual manner, and in the other, a framework of metal lathing, the 
shape of the tank, is constructed, and Portland cement mortar plastered 
upon it, as described on page 627. 

♦Methods of centering and placing the concrete of the vaulting are described in detail and 
illustrated in Mr. Hazen’s paper in Transactions. 

•j-See second footnote on p. 696. 

jMr. Coffin also gives interesting diagrams showing quantities and costs of materials and labor 
for covered reservoirs. 

§See Report of Annual Convention of the New England Water Works Association, 1903, 
Engineering News, September, 1903, p. 238. 


RESERVOIRS AND TANKS 


699 


Methods of Construction. The materials for the concrete must be very 
carefully proportioned so as to give a water-tight wall (see p. 339), and the 
stone should be of such size that a good surface can be readily obtained. 
The concrete should be mixed so wet that it will completely cover the metal 
reinforcement and flow against the form, and it is absolutely essential that 
the entire tank be built in one operation. 

Mr. W illiam B. Fuller’s methods of constructing a thin wall require that 
the concrete be mixed very wet, so that after wheeling 25 feet it will settle 
down to a level in a wheelbarrow. The laborer shovels it from the barrow, 
throwing one shovelful in a place, and goes the entire length of the section 
or around the circumference, thus forming a very thin layer and preventing 
the separation of the ingredients. 

The forms for the Little Falls tank described and illustrated on page 700 
consisted of 2\ by f-inch tongued and grooved boards, planed one side and 
placed vertically. Around the outside of the top of this cylinder of boards 
was placed a horizontal rib consisting of two sets of boards, 8 in each set, 
cut to a circle and laid in two thicknesses so-as to break joints. Below this 
rib, a wire rope was wrapped around the forms spirally, so that the separate 
spirals were about one foot apart. The lower ends of the staves were held 
by the bottom portion already built, otherwise another rib would have been 
required at the bottom. The inside form consisted of three cylindrical 
centers built like ordinary sewer centers and placed upright one above the 
other, each about one foot 3 inches high. These were suspended so that 
the bottom of the lowest allowed for the 3-inch thickness of the concrete 
bottom. They were held temporarily in place sideways by pieces of board 
3 inches long placed between them and the outside forms. As soon as the 
centers were fixed in position the concrete for the bottom was poured down 
through the middle of them and immediately afterward the walls were 
poured. This concrete flowed out slightly under the bottom center, but 
was easily removed after setting. There were no reinforcing angles be¬ 
tween the bottom and the sides. The rods of the bottom extended very 
nearly to the outside lagging, and the side rods extended down almost to 
the lower surface of the concrete bottom. Two tanks were built at once, 
and the contract price of each was $100. 

Examples of Tanks. The Filtration Plant at Little Falls, N. J., whose 
structural features were designed by Mr. Fuller, has a tank or well 41 feet 
high and 10 feet in diameter, which sustains the pressure of water either 
from within or from without. The walls are 15 inches thick at the bottom 
and 10 inches thick at the top. Rings of J-inch Ransome twisted steel 
rods were placed about every 2 feet in the center of the wall, and vertical 


700 


A TREATISE ON CONCRETE 


rods f inch in diameter and about 5 feet apart were also set in the center 
of the wall, thus forming a series of hoops and posts. 

On a platform in the same building is a tank 4 feet high and 4 feet in 
diameter. The walls are 3 inches thick, and contain rings of £-inch twisted 
rods placed about 6 inches apart, and J-inch vertical rods about 2 feet apart. 
The floor of the tank is also 3 inches thick, with J-inch rods spaced so as to 
make a 6-inch square mesh. This tank is shown in section in Fig. 228. 

The Illinois Steel Company, South 
Chicago, employ circular concrete 
tanks* for storing cement. These 
are 25 feet in diameter and 50 feet 
high, with walls 7 inches thick at the 
bottom and 5 inches thick at the top. 

The concrete is reinforced by rings 
spaced 4 inches apart and varying in 
diameter from one inch at the bot¬ 
tom to § inch at the top. 

At Milford, Ohio, is a stand-pipef 
of reinforced mortar 80 feet high and 
15! feet outside diameter. The thick¬ 
ness of the shell for the lower 30 feet 
is 9 inches, for the next 25 feet, 7 
inches, and for the remaining 25 
feet, 5 inches. The outside face is 
vertical. The concrete foundation 
is 20 feet in diameter and 6 feet thick. 

On top of this, T-bars, 1 by 1 by J 
inch, were placed radially from the 
center to within 6 inches of the outer 
edge, and the shell was started di¬ 
rectly from these. The horizontal 
base around and within the shell was 
then strengthened by a layer of 1: 3 
mortar 6 inches thick in the interior 
of the tank and 16 inches thick 
around the outside of it. The shell 
is of 1:3 mortar reinforced with T-bars 1 by 1 by J inch, spaced 18 
inches apart vertically and in horizontal rings varying from 2 inches 

*Engineering News, August, 1902, p. 148. 
fSee Engineering News , Feb. 1904, p. 184. 



Fig. 228. — Concrete Feed Tank for 
Mechanical Filter at Little Falls, N. J. 
(See p.yoo.) 







































RESERVOIRS AND TANKS 


701 

apart at the base to 3 inches at the top. T-shaped steel is not so suit¬ 
able as round for reinforcement because of the lower adhesion. Stone 
with the sand would have produced a denser and cheaper mix. 

STORAGE RESERVOIRS 

Storage reservoirs for waterworks and other purposes are being built of 
reinforced concrete. The design of square or rectangular reservoirs invol¬ 
ves problems similar to those met with in the design of retaining walls (see 
P* 659). In circular reservoirs, the thickness of the walls is usually based 
upon judgment to insure the proper placing of the concrete for water-tight¬ 
ness, while the horizontal reinforcement is designed to resist all the tension 
due to water pressure. The amount of horizontal reinforcement at various 
sections will vary with the water pressure, being zero at the top and increas¬ 
ing toward the bottom, and may be determined thus: 

Let 

H = height of reservoir in feet above section considered. 

D = diameter of reservoir in feet. 

A h = area in square inches of horizontal steel per foot of height at section 
considered. 

f s = allowable unit stress in steel in pounds per square inch. 

At any horizontal section the total tensile force, per foot of height, tending to 
rupture the reservoir on any diameter is 62.5 HD. Since the area of steel 
resisting this force is aA h , we have 2A h f s = 62.5 HD , or 

A __ 3 I -3 HD 

h Is 

A comparatively low unit stress in the steel should be adopted, preferably 
not over 10 000 or 12 oco pounds per square inch, to prevent the formation 
of cracks in the concrete as it stretches. 

Joints require special treatment to prevent leakage. (See page 284.) 

In a high circular reservoir, the thickness of wall and vertical reinforce¬ 
ment should be considered as in chimney design (see p. 630). 

Waltham Reservoir. The reservoir in Waltham, Mass., is 100 feet in 
diameter and 37 feet high, and the walls are 18 inches thick at the bottom 
and 12 inches at the top, the inside surface being vertical. The wall rein¬ 
forcement consists of 1J inch round bars, simply lapped at the ends and 
varying in spacing from the bottom to the top, so as not to stress the steel 
beyond 12 000 pounds per square inch. The aggregates were especially 
graded according to the recommendation of one of the authors, and 5 per 
cent of hydrated lime, based on the weight of the cement, was added to 
increase the water-tightness. 



702 


A TREATISE ON CONCRETE 


CHAPTER XXIX 

MISCELLANEOUS STRUCTURES. 

The more important structures are treated with considerable detail in 
preceding chapters. The uses of concrete and reinforced concrete are now 
so numerous and are increasing so rapidly that only brief reference can be 
made to a few of the smaller and of the less common structures. 

In railroad work, not only for the more important structures like piers, 
abutments and arches, but for the numberless smaller details like telegraph 
poles, ties, bumping posts, and signal posts, is reinforced concrete being 
employed. Roundhouses, stations and terminal warehouses are being 
designed either exclusively or in part of this material. 

In power development, not only the dams are of concrete, but the canals, 
penstocks, flumes, and the power stations themselves. 

In water-works construction the use of concrete has extended to reservoirs, 
Alter basins, tanks and conduits, and, in some of the recent works, concrete 
with its imbedded steel for reinforcement is almost the only structural 
material. 

Even the farmer and the householder are utilizing concrete in various ways 
for barns, garages, chicken houses, floors, fences, silos, tanks, troughs, 
drains and many other of the small details which make for economy, dura¬ 
bility and convenience. By mixing and placing the concrete according to 
the directions laid down in Chapter II and using sufficient reinforcement (in 
some cases ordinary fence wire is suitable), many an inexperienced man has 
built permanent structures of pleasing appearance. For reinforced con¬ 
crete work such as floors, roofs and stairs, an engineer should be called 
upon to design the dimensions and reinforcement. 

Telegraph Poles. Wooden poles are being replaced in many localities by 
poles of reinforced concrete because of their greater durability. The Pennsyl¬ 
vania lines west of Pittsburg* have installed poles from 20 to 28 feet high, 
8 inches square at the bottom, tapering to 6 inches square at the top, with 
corners chamfered 2 inches. Holes are left in the pole for the brace and 
cross-arm bolts and also for the climber steps. The reinforcement maybe 
greatest at the bottom and reduced above to allow for the lessening stress. 


* Concrete Engineering, July 1908, p. 189. 


MISCELLANEOUS STRUCTURES 


1 ° 3 


In 1907 Mr. Robert A. Cummings* made comparative tests of reinforced 
concrete and white cedar poles. The former were 13 inches square at the 
butt and 7 inches at the top, reinforced to withstand the weight of 50 wires 
all coated with ice to a diameter of one inch. These were stronger than the 
wooden poles of substantially the same size. After breaking, the ends of 
the concrete poles were held in a slightly inclined position by the reinforce¬ 
ment, while the wooden poles broke square off and fell to the ground. 

Ties. Concrete ties of varied designsf have proved satisfactory for slow 
speed traffic, especially in yards and on turnouts. They also have been 
used to a certain extent on high speed track. One of the most important fea¬ 
tures is the connection with the rail which is generally made through a 
cushion block of wood. If the tie supports both rails, it must be reinforced 
in the center at the top to resist the negative bending moment. The ends 
of the ties should also be well reinforced to prevent breakage in case of derail¬ 
ment. 

Road Beds. For tunnels, concrete roadbeds have been found economical 
because of the very great saving in maintenance expense. 

Roundhouses. Reinforced concrete affords a durable and inflammable 
material for the structural portions and the roofs of roundhouses, while the 
walls may be built either of concrete or of brick. 

Cinder and Ash Pits. Concrete will stand as high temperature as will 
be given to it by hot ashes and cinders. 

Grain Elevators. By building of reinforced concrete the danger from 
fire is avoided as well as the necessity for constant repairs. 

Coal Pockets. For coal storage the strength and fireproofness of rein¬ 
forced concrete is bringing about its general adoption. 

Boiler Settings. Reinforced concrete boiler settings have been in success¬ 
ful use in several plants for a number of years. The initial cost is prob¬ 
ably not less than brick but greater durability and freedom from repairs is 
claimed by the users of concrete settings. 

Double walls are required with an air space between. The inner wall 
may be about 5 inches thick and the outer about 6 inches, both thoroughly 
reinforced to prevent as far as possible the development of cracks. Bars 
f-inch diameter, spaced 6 inches apart both ways, afford effective reinforce¬ 
ment. The walls may be tied together at intervals with bars. The rein¬ 
forcement permits building the setting to any shape over the boiler, although 
wherever it comes in contact with the boiler, a 3-inch layer of mineral wool 
should be introduced to allow for variation in expansion. 

* Cement Age, Aug. 1907, p. 84. 

f Concrete Review, 1908, published by the Association of American Portland Cement Manu¬ 
facturers. 


7©4 


A TREATISE ON CONCRETE 


A fire-brick lining must be used. A thickness of 8 or 9 inches is more 
economical than a 4^-inch lining because it can be replaced without dis¬ 
turbing the concrete. Spaces must be left at the ends of the fire-brick lining 
to allow for expansion. 

The concrete should be as rich as 1: 2:4 and the best aggregates are quartz 
sand and trap rock about f inch maximum size. For high temperatures 
gravel and limestone aggregates should be avoided. Cinders of first-class 
quality should make durable walls when mixed with sand and cement 
in rich proportions. 

Fences. Fences have been built of solid concrete, of mortar plastered 
on wire lath, of concrete rails set in concrete posts, and of concrete posts with 
galvanized fence wire between them. The last plan is the most common. 
For farm or division fences the length of posts may be 7 feet, allowing 3 feet 
of this to set into the ground, and the size may be 5 or 6 inches square at the 
bottom and 4 or 5 inches square at the top with |-inch rods in each corner. 
Forms are easily made singly or so as to mold several posts at once. 

Silos. Silos of solid monolithic concrete built in circular forms may have 
walls 6 inches thick reinforced with ^-inch bars bent to circles and placed 
12 inches apart. Occasional vertical bars are also necessary. The con¬ 
crete must be mixed wet and placed very carefully so as to give a perfectly 
smooth interior surface, so solid and dense that the ensilage will not be dried 
out next to the wall. 

Greenhouses. Greenhouses themselves, as well as the floors, tables, 
water troughs, hotbeds, and minor appurtenances, are being built of con¬ 
crete. The directions throughout the various chapters in this treatise 
for structures of different classes will be found to apply to these details. 

House Chimneys. Chimneys for residences may be of concrete if 
heavily reinforced, but the expense of forms usually will make them more 
costly than brick. 

Chimney caps of concrete should be well reinforced to prevent cracking. 

Residences. Residences are built of solid reinforced concrete;concrete 
blocks (see p. 629); concrete tile, plastered (see p. 629); and mortar plas¬ 
tered on metal lath (see p. 627). 

Solid or monolithic concrete is especially adapted to fine residences and 
permits unique architectural treatment. Eventually with the development 
and consequent reduction in cost of form construction, reinforced concrete 
may be more generally employed for dwellings of small and moderate size. 


CEMENT MANUFACTURE 


7°5 


CHAPTER XXX 

CEMENT MANUFACTURE 

This chapter contains a short historical sketch followed by a brief out¬ 
line of the processes of modern cement manufacture, illustrated with views 
of typical machinery. 

HISTORICAL 

Lime must have been used by the Egyptians thousands of years before 
Christ, as the stones in the pyramids apparently were laid in mortar of 
common lime and sand. It is even thought by some that these ancients 
understood the principle of mixing lime and clay together to make a real 
cement. 

Concrete was made by the Romans as early as several centuries before 
Christ. For most of their work, they used lime mixed with sand and stone, 
but understanding the value of puzzolana or volcanic ashes to render lime 
hydraulic, they employed these two materials in combination with the 
sand and stone for marine construction. For less important work, they 
often mixed lime and coarsely powdered brick with the aggregate. Vitru¬ 
vius, writing in the first century, describes methods of making concrete 
with lime alone, and also gives as the formula for making it of slaked lime 
and Italian puzzolana: 

12 parts of puzzolana, well pulverized. 

6 parts of quartz sand, well washed. 

9 parts of rich lime, recently slaked; to which is added 
6 parts or fragments of broken stone, porous and angular, when 
intended for a “pise” or a filling in. 

In the Middle Ages concrete was employed, after the Roman fashion, for 
both walls and foundations. In the former it was generally laid as a core 
faced with stone masonry. Large stones were often imbedded in the 
mass. 

The fact that clay contained in certain limes rendered them hydraulic 
was discovered by John Smeaton, when studying the designs for the third 
Eddystone Lighthouse, about 1750. Early in the following century, 
Vicat, by his extended scientific researches in France, earned for himself 
the name of the founder of hydraulic chemistry. 


706 


A TREATISE ON CONCRETE 


In England, in 1796, James Parker made Irom nodules of argillaceous 
limestone, calcined and ground, what he called Roman cement. This 
process he patented, and from it the Natural cement industry was developed. 
It was Joseph Aspdin, of Leeds, England, who really invented Portland 
cement by discovering in 1824 that an artificial mixture of slaked lime and 
clay, highly calcined, formed a hydraulic product. On account of its 
resemblance in color and hardness to the Portland stone which was much 
used in England at that time, he called his invention Portland cement. 
Two patents had been granted in England a few years before his time, 
but as in these the materials were not heated to vitrification, hydraulic 
lime instead of cement was produced. 

The Portland cement industry was not developed to any great extent 
until about twenty years after Aspdin’s discovery, when J. B. White & 
Sons in Kent, England, commenced its manufacture. Later, Mr. John 
Grant gave a great impetus to Portland cement manufacture by experi¬ 
mental studies upon the practical action of cements, mortars and concretes 
under varied conditions. The results of his tests he presented to the In¬ 
stitution of Civil Engineers in 1866, 1871, and 1880. 

The first manufactory for producing Portland cement in France was 
established toward the middle of the last century at Boulogne-sur-Mer. 
In Germany the first factory was erected soon after this, for the production 
of the Stettin Portland cement, and with such successful results that in 
1900 Germany produced more Portland cement than any other country. 

The discovery in the United States of a rock suitable for Natural cement 
was made in 1818 by Canvass White, an engineer connected with the 
construction of the Erie Canal, and Natural cement was made in Madison 
and Onondaga Co., N. Y., in that year. The first Natural cement in 
the Rosendale district was made at Rosendale, Ulster Co., N. Y., about 
1823. Mr. D. O. Saylor was the founder of the Portland cement industry 
in the United States. His discoveries were made in the Lehigh Valley. 
He experimented from 1871 to 1875 and marketed cement in 1875. 

PRODUCTION OF CEMENT 

The total production* of hydraulic cement in the United States for 1908 
was 52 910 925 barrels, of which 51 072 612 barrels were Portland cement, 
1 686 862 barrels were Natural cement, and 151 451 barrels were Puzzolan 
or Slag cement. The average values per barrel were, for Portland cement 
$0.85, for Natural, $0.49 and for Puzzolan, $0.63. 

I he superior quality of Portland over Natural cement and the increasing 

* Edwin C. Eckel in The Cement Industry in the United States in 1908. 


CEMENT MANUFACTURE 


7°7 


economy of its manufacture is evinced by a comparison of these figures 
with those of 1890, when only 335 500 barrels of Portland cement were 
produced against 7 082 204 barrels of Natural cement. The imports of 
cement in 1890 were 1 940 186 barrels, and in 1908, 842 121 barrels. 

The production of Portland cement in the United States by individual 
States is represented in the following table. 


Production of Portland Cement in the United States in 1900 and 1908 by States 


State 


Pennsylvania.. 

Indiana. 

Kansas. 

Illinois. 

New Jersey. . . 

Michigan. 

Missouri. 

California 
Washington . . 
New York. .. . 

Ohio. 

Iowa. 

Kentucky ... 
Tennessee ... . 

Texas. 

Oklahoma . .. . 
South Dakota. 

Colorado. 

Arizona. 

Utah. 

Maryland. 

Virginia. 

Massachusetts. 

Alabama*. 

Georgia*. 

Arkansas - } - 
North Dakota. 


1900 


Producing 
Pla nts 


Quantity 

barrels 


Value 


1908 


Producing 

Plants 


Quantity 

barrels 


Value 


14 

4 

984 

417 

4 

984 

4i7 

17 

18 

254 

806 

13 

899 

807 

I 


30 

OOO 


37 

5oo 

7 

6 

478 

i65 

5 

386 

56,3 

I 


80 

OOO 


100 

OOO 

7 

3 

854 

603 

2 

874 

457 

3 


240 

442 


300 

55 2 

5 

3 

211 

168 

2 

707 

044 

2 

I 

169 

2 12 

I 

169 

212 

3 

3 

208 

446 

2 

416 

009 

6 


664 

75 o 


830 

940 

i5 

2 

892 

576 

2 

556 

215 




56S 




4 . 

2 

929 

5 o 4 

2 

571 

236 

1 


44 


89 

130 

4 


2 

480 

100 

3 

268 

196 

8 


465 

832 


582 

290 

2 

7 


I 

988 

874 

I 

813 

623 

6 


534 

2l5 


667 

769 

8 


1 

52 1 

764 

I 

3°5 

210 








1 


1 

205 

25 I 

I 

1 76 

499 

2 


26 

OOO 


52 

OOO 

2 



917 

977 


924 

039 

1 


38 

OOO 


76 

OOO 

I 



809 

306 

I 

o 57 

433 

1 


35 

708 


71 

416 

2 















1 



5 o 7 

603 


8 o 5 

23S 

1 


70 

OOO 


175 

OOO 

2 








I 


58 

479 


73 

099 

I 



502 

225 


5 ii 

118 








2 



310 

244 


274 

995 

I 


40 

OOO 


70 

OOO 









1 



400 


I 

200 








So 

8 

482 

020 

9 

280 

525 

98 

51 

072 

612 

43 

547 

679 


* Product in 1900 combined with Virginia. fProduct in 1900 combined with Missouri. 

About 40% of the total production in 1908 was in the Lehigh Valley 
of Pennsylvania and New Jersey. In 1900, 73 % came from that district. 


PORTLAND CEMENT MANUFACTURE 


Portland cement is made from a mixture of calcium carbonate and silicate 
<ol alumina. 

The processes of manufacture differ with the natural state in which 





























































A TREATISE ON CONCRETE 


708 

these materials are found, but the operation consists essentially of (1) pul¬ 
verizing and mixing the two ingredients, (2) heating to a temperature 
which is near the melting point, i. e., calcining, (3) grinding to a fine powder. 

If either of the raw materials occurs in a moist state it is generally cus¬ 
tomary to mix them wet, and after a preliminary grinding introduce them 
into the kilns. Dry raw materials for calcining or burning in the old style 
stationary kilns must be formed into plastic bricks with the aid of water, 
but the rotary kiln, invented in 1885 by Mr. Frederick Ransome, has revolu¬ 
tionized the manufacture of Portland cement by making it possible to intro¬ 
duce the mixed substances into the furnace, in either a dry or wet state, with¬ 
out hand labor. 

After calcination, the methods of grinding the clinker are independent of 
the character of the raw materials or the type of kiln. 

The Association of German Cement Manufacturers, to protect the good 
name of German Portland cement, requires that its members shall sign 
the following:* 

The members of this Association are permitted to bring into the market 
under the term of “Portland Cement” only such material as is prepared 
from an intimate mixture of lime and clay materials as essential ingredients, 
burning to sintering and subsequent grinding to the finest of flour. They 
obligate themselves not to recognize as Portland cement any material which 
is prepared otherwise than above stated, or which during or after the burn¬ 
ing has been mixed with foreign bodies, and to look upon the sale of other 
material under the name of Portland cement as deceiving the purchaser. 
These requirements are not to forbid the addition of not more than three per 
cent of other material to the Portland cement for the purpose of regulating 
the setting time. 

The members of the Association further obligate themselves to furnish 
Portland cement which will in all respects meet the requirements of the 
Prussian Minister of Public Works. 

When a consumer requires cement for a particular purpose, coarser grounp 
than the requirements, or colored, its preparation is allowable. 

If a member of the Association offends the above given obligation, he shall 
be expelled from the Association. His expulsion is made known publicly. 

The manufactured product of each member of the Association is tested 
yearly in the laboratory of the Association at Karlshorst near Berlin; and the 
results are given out at the General Meeting of the Association. 

Raw Materials for Portland Cement Manufacture. The raw ma¬ 
terials, as stated above, consist essentially of calcium carbonate and silicate 
of alumina. Their exact proportions are determined by their chemical 
composition. A usual ratio is about 75% carbonate to 25% silicate. 
The two substances occur in nature in so many forms that we have a 


* Quoted in Cement Age, January 1909, p. 24. 


CEMENT MANUFACTURE 


7°9 


large range of choice in raw materials. The following combinations are 
actually used in ditferent cement manufacturing plants in the United 
States: 

Cement rock and limestone 

Limestone and clay. 

Limestone and shale. 

Marl and clay. 

» j 

Chalk and clay. 

Limestone and slag. 

Alkali waste and clay. 

Cement rock is an argillaceous limestone, rather soft in texture, which 
in the Lehigh Valley usually requires from 10% to 20% of limestone to 
give it the correct Portland cement composition. Occasional deposits are 
found which are suitable to use with no admixtures, or from which the 
desired proportions may be obtained by mixing two different strata in the 
same quarry. Several other States, among them the Virginias, Alabama, 
Colorado, and Utah, have a geological formation similar to that in the 
Lehigh Valley from which Portland cement is made. 

In the Hudson River Valley, near Catskill, New York, are situated 
large manufactories employing a hard limestone which is nearly pure 
carbonate of lime, requiring 20% to 25% clay or shale and producing a 
fine quality of cement. A somewhat similar mixture is used in California 
and in scattered localities in the Central States. 

The marl used for cement is a wet, calcareous earth, in some localities 
of organic origin from shell deposits, and in other places of chemical for¬ 
mation. There are large cement plants using marl and clay in western 
New York, Ohio, Indiana, and Michigan. 

Chalk and clay deposits resembling those in England are worked in 
South Dakota, Texas, and Arkansas. 

Certain blast furnace slags similar to those used in the manufacture of 
Puzzolan cement, when combined with a suitable admixture of limestone, 
produce, after calcination, a true Portland cement. 

The waste from the manufacture of soda, when employing the ammonia 
soda process with suitable raw materials, is substantially a precipitated 
chalk, and is burned with clay to produce Portland cement.* 

In Germany the Alsen and Stettin brands are made from chalk and 
clay, the Dyckerhoff and Mannheimer brands from limestone and clay, 
while the Germania and Hanover works use marl and clay. In England 


*B. B. Lathbury, Engineering News, lune 7, 1900, p. 372. 


710 


A TREATISE ON CONCRETE 


raw materials consist principally of chalk and clay. Belgium manufac¬ 
turers use chalk and clay, and a Portland cement from natural rock is also 
manufactured in that country. In France, marl and clay, and chalk and 
clay, are the chief raw materials for true Portland cements. 

The character and proportioning of the raw materials and the processes 
of chemical combination are discussed by Mr. Spencer B. Newberry in 
Chapter VI. 

The following table illustrates the composition of various classes of 
materials which are used for Portland cement, and also the resulting 
analysis of the cement in each case: 


Comparative Analyses of Raw Materials and Portland Cements. 



Cement Rock and 
Limestone. 

Limestone and 
Clay. 4 

Marl and 

Clay. 

Chalk and 
Clay* 

Cement Rock. 1 

Limestone. 2 

W . 

a 

<D 

E 

4 ) 

u 

Limestone. 

>3 

0 

Cement. 

aj 

S 

CO 

>» 

. 1 

u 

Cement. 7 

00 

A 

T 3 

CJ 

Oi 

c 3 

0 

O 

H 

G 

<L> 

E 

V 

U 

Silica 

Si o 2 

19.06 

1.98 

19.92 

3-3 0 

55-27 

21.50 

i -75 

62.10 

22.52 

o -35 

60.30 

22.10 

Alumina 

Al 2 O3 

4 - 44 ] 


983] 




( 

20.09 

6.69 

o -75 

11.07 

1 



\ 

0.70 

\ 

1-30 

28.13 

10.50 

1-571 





pi.32 

Iron Oxide 

P e 2 O3 

1. raj 


2.63J 




{ 

7.81 

3-54 


8.13 

1 

Calcium Oxide 

CaO 

38.78 

53-31 

60.32 

52-15 

5-84 

63-50 

49.24 

0.65 

63.82 

54-95 

4 4 ° 

60.76 

Magnesian Oxide Mg O 

2.01 

0.97 

3.12 

1.58 

22.5 

1.80 

0.44 

0.96 

0 69 


1.27 

I.IC* 

Sulphuric Acid 

S0 3 



1 -13 

0.30 

0.12 

x.50 

0.15 

0.49 

0.98 


2.5O 

1.40 

Carbonic Oxide 

C 0 2 

32.66 

42.94 


40.98 



39-i61 



43-17 

1 














1 7-47 

1-94 

Water 

h 2 o 




8-37 



► 

8.oo' 



J 


Organic Matter 








7-5° 




4.06 


Other Constituents 





• 


0.40 



1.08 

0.85 

0-45 

1.38 


Note.— Carbonates in raw materials, given in some of the analyses, have been transformed into oxide. 

1 Cement Rock. Lehigh Valley District, Penn. 21st Annual Report, U. S. Geological Survey. Pt. 6, 
p. 404. 

2 Pure Limestone, Lehigh Valley District. W. E. Snyder, Analyst. 

3 Lehigh Valley Cement. Booth, Garrett & Blair, Analysts. 

4 Hudson River Valley. Mineral Industry, Vol. 6, p. 97. 

6 W. H. Simmons, Analyst, 22d Annual Report, U. S. Geological Survey, Pt. 3, p. 650. 

6 Shale. Mineral Industry, Vol. 6, p. 99. 

7 Michigan. W. H. Simmons, Analyst, 22d Annual Report, U. S. Geological Survey, Pt. 3, p. 680. 

8 Water, 23%. Analysis from David B. Butler, England. 

9 Estuary Mud. Roughly dried, lost 333%. Analysis from David B. Butler, England. 

10 English Portland Cement. Analysis from David B. Butler, England. 


Processes in Portland Cement Manufacture. The method of mixing 
the materials in preparation for their introduction into the kilns has led tG 

♦The authors are indebted for these analyses of chalk and clay to David B. Butler, of Eng’ 
land, who prepared them for this Treatise. 




































CEMENT MANUFACTURE 


711 


a classification of processes into (1) wet process, and (2) dry process. 
The former is often subdivided into wet and semi-wet, depending upon 
the quantity of water added at the time of the mixing. 

The wet process is employed with soft or wet materials, such as chalk 
and clay, or marl and clay. The carbonate of lime and the clay are 
mixed in a vat or wash-mill with a large excess of water. Agitators break 
up the lumps and so finely reduce the particles that they are held in sus¬ 
pension in the water and flow off over the top of the vat. In another basin 
the stub is allowed to settle, the water is drawn off, and the “slurry” 
becomes hard enough to handle in barrows and then form into bricks to 
be dried, and finally calcined in stationary kilns. 

By using a smaller quantity of water, say 40 or 45%, the settling process 
and consequent hand-labor is avoided, and the material is made only 
fluid enough to handle in pumps. After grinding, it may be pumped 
directly into the rotaries, or, if stationary kilns are used, the pumps throw 
it to the drying room to be made into bricks. This process is called in 
England the semi-wet process, but as it is practically the only wet process 
used in the United States, it is here simply termed the wet process. 

The dry process was first used in Germany as a result of the sub¬ 
stitution of limestone for the chalk of England. The two ingredients 
are ground and mixed in a dry state. If the kilns are stationary, the 
mixed material must be moistened with sufficient water to form plastic 
bricks, which are then dried, but for rotary kilns no water is added, the 
mixture of dry materials passing, after being ground, directly into the kiln. 

Dry Process with Rotary Kilns. The introduction of rotary kilns into 
new cement plants is universal, while many of the older mills are sub¬ 
stituting them for their stationary kilns. Where rock, or rock and clay, 
form the raw materials, they are mixed and ground, and introduced into 
the rotary in the form of a dry powder. If marl or chalk furnish the 
carbonate of lime, the wet process of mixing and grinding is usually em¬ 
ployed, as described on page 720, although in a few plants each of these 
materials is dried when entering the mill, and the operations are similar 
to those described below for rock mixtures, except that driers and dis¬ 
integrators are substituted for stone crushers. 

The process of manufacturing Portland cement from rock, or rock and 
clay mixtures, in plants equipped with rotary kilns, consists essentially of 
crushing the materials, — either separately or after mixing them, — dry¬ 
ing, grinding, calcining in the rotaries, cooling, grinding to powder, and 
packing. 

The details of the process will be best understood by briefly describing 


712 


A TREATISE ON CONCRETE 


the typical machinery shown in the illustrations. Various types and 
makes of grinding machinery will produce similar results, those selected 
being merely representative. 

If two stones of fairly similar texture and each of uniform composition 
form the raw materials, they may be carefully weighed and thrown to¬ 
gether into the breaker. Otherwise, they are treated separately, and mixed 
just before the grinding which precedes the calcination. A common type 
of breaker is the gyratory crusher shown in Fig. 78 on page 244, No. 5 or 
No. 6 being the usual size employed. This reduces the stone to a size 
varying from dust to about 2^-inch diameter. A further reduction in 
size to about J-inch is accomplished in plants of modern design by crack¬ 
ers of the coffee mill type (see Fig. 229), or similar machinery. 

Clay, if used, is dried in broken lumps, and 
then may be pulverized by passing it through a 
disintegrator consisting of two horizontal rolls, 
one corrugated or toothed and the other smooth. 

An economical form of dryer for clay or stone 
consists of a long revolving steel tube about 4 
feet in diameter, provided with shelves on its 
interior surface, formed by horizontal Z-bars. 
The hot gases from the kiln may be made to 
pass through the tube and meet the raw mate¬ 
rial. 

By treating the two materials separately up 
to this point, an extremely accurate mixture is 
obtained by weighing the ingredients in a pair 
of automatic weighing machines (see Fig. 230), 
so arranged that one of the pair will not dump 
until both are charged. 

Samples of the two materials are taken, just 
before mixing, at definite periods throughout 
the day, and analyzed to determine the correct 
proportions. A partial analysis showing the quantities of the principal 
constituents may be all that is necessary except at occasional intervals. 
The maintaining of correct proportions is one of the most essential ele¬ 
ments in the manufacture. 

Another grinding of the mixed materials in tube mills, Kent Mills, 
Griffin Mills, Fuller Mills (pp. 716, 717), or similar machines, to a fineness 
which will pass a screen having 20 to 30 meshes per linear inch, com¬ 
pletes the preparation for the rotary kilns. The actual fineness of the 









































CEMENT MANUFACTURE 713 

ground stone at this point is such that 90% to 95% or even a higher per¬ 
centage will pass a screen having 100 meshes to the linear inch. Fine 
grinding before burning is one of the secrets of successful manufacture. 

I he best type of rotary kiln (see Fig. 231) used for calcining dry 
matetials, consists ot an inclined steel tube from 60 to 200 feet long. 
I he diameter is generally 6 to 12 feet, though occasionally smaller than this 
t the upper end and tapering to the larger size at a point about one- 



Fig. 230.—Tandem Automatic Weighing Machine. (See p. 712.) 

third of its length from the upper end. The lining may be of U-shaped 
fire-brick in order to present, as a non-conductor of heat, a hollow sur¬ 
face against the shell of the rotary. The low T er end of the rotary is 
closed by a stationary brick wall, and through the center of this passes 
a pipe which feeds the petroleum, or more frequently the powdered 
coal which in a separate building is crushed to pea size and pulverized in 
tube mills, or other pulverizing machines, so that about 90% passes a 1 oo- 
mesh screen; the finer the coal the greater its efficiency. 

The ground stone may be fed into the upper end of the rotary by a spiral 
conveyor enclosed in a pipe which is water-jacketed so that the material 
will not cake. The degree of calcination is governed by the supply of raw 
material, the speed of rotation of the rotary, which rests on rollers geared 
to a speed-changing device, and the quantity of fuel. If coal is used for 
fuel, it is fed by a blast from a fan, and the quantity is regulated by a spiral 







714 


A TREATISE ON CONCRETE 


conveyor running at 
changeable speed. The 
heat in the kiln is so intense 
that the coal burns as a gas 
without apparent smoke or 
cinder. The proper tem¬ 
perature, which is said to be 
2700° to 3000° Fahr., is de¬ 
termined by the appearance 
of the burning stone. At a 
certain point in its descent 
the material becomes semi- 
vitrified and forms into 
irregular balls or clinkers, 
^ which roll around and 
*7* finally fall out red-hot at 
^ the lower end in particles, 

So 

w most of which range in size 
fi from sand to i-inch diame- 
£3 ter. The clinker, when 
properly burned, is of a 
^ greenish black color with 
I. a faint glisten, and contains 
but few large pieces. It 
o slightly resembles in ap- 
^ pearance the clinker often 
found among the ashes of 
hard coal. 

The output of a rotary 
varies with the length and 
diameter from 150 to 200 
barrels per 24 hours for a 
60 foot kiln to 1000 to 1200 
barrels, for a 158 to 200 foot 
kiln with a smaller coal con¬ 
sumption per bbl. 

The clinker, after being 
cooled in some form of 
cooler, is crushed by pass¬ 
ing between horizontal rolls 







CEMENT MANUFACTURE 


7 J 5 


or through some other form of crusher, and is then ready for the fine 
grinding, or, if desired, it may be stored either out of doors or under cover 
until needed. Strangely enough, wetting the cinder does not injure it 
provided it is dry when it enters the fine grinders. 

The fine grinding is generally accomplished by passing the clinker 
through ball mills and then through tube mills, or by a single operation in 
such machines as the Griffin, Kent or the Fuller Mill. A section of a ball 



mill is shown in Fig. 232. It consists essentially of a cylindrical drum, 
lined with castings of hard, tough steel, and containing forged steel balls 
8 or 10 inches in diameter. Rotation of the drum grinds the stone or 
clinker between the balls and the plates, and the powder passes through 
sections of screens — which for clinker have usually 20 to 28 meshes to 
the linear inch — into the hopper below. A single ball mill, such as is 
shown in sketch, running on clinker, should give an output of, say, 5 500 
to 7 500 pounds per hour. 

A tube mill (see Fig. 233) consists of a long horizontal cylinder filled 























































































































































716 


A TREATISE ON CONCRETE 



nearly to its axle with flint pebbles imported from Europe, which average 
about 2 to 3 inches in diameter. The cement is ground by rolling around 
with the flints. It is then thrown by centrifugal force against the screen, 
which regulates the fineness of grinding and prevents the passing of pieces 
of flint. A tube mill which passes, say, 250 barrels of cement per day, 


Fig. 233.—Tube Mill. (Seep. 715.) 


will require the renewal of the flint pebbles at the rate of about 600 lb. 
per week. More tube mills than ball mills, usually twice as many, are 
required for the finish grinding. 


The Griffin mill (see Fig. 234) is used 



Fig. 234.—Griffin Mill. (See p. 716.) 


by many manufacturers in prefer¬ 
ence to ball and tube mills. The 
mill is driven by a horizontal 
pulley, from the center of which, 
by a universal joint, is suspended 
a vertical shaft having fixed at its 
lower extremity a crushing roll, 
which revolves on its axis at a 
speed of about 200 revolutions 
per minute, and also rotates by 
centrifugal force against the ring 
or die where the pulverizing is 
accomplished. The material to 
be ground passes first into the 
pan below the crushing roll, upon 
the under side of which are shoes 
or plows which stir it up and force 
it up between the roll and the die. 


































CEMENT MANUFACTURE 717 

The cement or stone is so finely powdered that, held in suspension by 
the moving air, it passes through a cylindrical screen above the roll, and 
falls through slots in the circumference of the pan into the hopper below, to 
be carried off by a conveyor. The screen in mills for grinding clinker is 30 
to 32 mesh to the linear inch, but as it is placed vertically, it lets through 
only cement of such fineness that 75 to 80% of it will pass a soo-mesh sieve. 
The Kent pulverizer, shown in Fig. 235, which is used in a few plants, 



Fig. 235.—Kent Mill (See 17.) 


consists essentially of an upright circular case containing within it three rolls 
surrounded by a revolving ring. The material is ground by passing be¬ 
tween the internal circumference of this ring and the rolls, which are 
pressed against it by springs. 

The Fuller-Lehigh mill, illustrated in Fig. 236, has come to the front dur¬ 
ing the past few years as a fine grinder for grinding coal, raw material 
and clinker. The material to be reduced is fed to the mill from an overhead 
bin by means of a feeder mounted on top of the mill. This feeder is driven 
direct from the mill shaft by a belt running on a pair of three-step cones, 
which permits the operator to accommodate the amount of material enter¬ 
ing the mill to the nature of the material being pulverized. 

The grinding is done by means of four unattached steel balls 12 inches 
in diameter, which are propelled by four equidistant horizontal arms or 












A TREATISE ON CONCRETE 



pushers radicating from a vertical central shaft. The material discharged 
by the feeder falls between the balls and the die and is reduced to a finished 
product in one operation. Above the die and the balls and attached to the 
yoke propelling the balls, is a fan with two rows of fan blades, one above the 
other. The lower set of blades lifts the finished product from the pulver¬ 
ising zone into the chamber above the die, where it is held in suspension until 
it is floated out through 
a screen by the fanning 
action of the upper row 
of blades. The finished 
product is then dis¬ 
charged through a spout 
which may be placed at 
any one of four quarters 
of the mill. When the 
mill is in operation, it is 
continually handling 
only a limited amount 
of material at any one 
time. As soon as the 
material is reduced to 
the desired fineness, it 
is lifted out of the pul¬ 
verizing zone and dis¬ 
charged from the mach¬ 
ine. 

It is customary to 
store the cement in bulk 
and weigh it out into 
bags or barrels as re¬ 
quired for shipment. 

An automatic weighing Fig. 236. —Lehigh-Fuller Mill. {See p. 7 17.) 

machine similar to that 

shown in Fig. 230, page 713 (except that it is single instead of 
double), is a convenient apparatus for bagging. With this machine a 
weighing gang consists of three men. The nominal capacity of a single 
machine is 3 000 bags in ten hours, and the authors have known as many 
as 3 900 bags to be filled in this time. 

In outlining the cement machinery, no reference has been made to*the 
methods for conveying the material from one machine to another. Bucket 








CEMENT MANUFACTURE 


719 


conveyors, belts and spiral conveyors are all more or less used. A. spiral 
conveyor is a helical blade on a revolving shaft, set in a square 01 circular 
trough or tube of larger size than the spiral, so that the material packs 
around the circumference, and the blade comes in contact only with the 
powdered material. 

Plaster of Paris (calcium sulphate CaS 0 4 ), or gypsum (CaS 0 4 -f 2 H 2 0 ) 
the same substance in crystalline form, is an important addition to cement 
as a regulator of its setting, and from 1 to 2% is used in nearly all Port¬ 
land cement manufactories. The gypsum must be added after the calci¬ 
nation and before the final grinding, in order to insure the proper result 

The laboratory of a cement plant is an important feature. Not only 
must the chemical composition of the raw materials and the finished 
product be analyzed (see Appendix I) at frequent periods, but the cement 
must be mechanically tested for fineness, time of setting, tensile strength 
at seven and twenty-eight days, and, perhaps most important of all, for 
soundness. Most manufacturers use some form of the accelerated or hot 
test. This is not only due to the fact that many engineers require the ce¬ 
ment to pass an accelerated test for reception, but because the chemists in 
the cement factories consider this test of great value in checking up the 
quality of cement. 

Wet Process with Rotary Kilns. The rotary or Ransome kiln was 
first used in England on wet materials Rotaries have been widely, in fact 
almost universally, adopted in the United States for calcining dry materials, 
and more recently this field has been extended to use with slurry containing 
as much as 40% of water, which is pumped into the end of the rotary and 
dried bv the same flame used for calcination. With kilns of ordinary 
length, Mr. Henry S. Spackman states* that at least 25% more fuel is re¬ 
quired for burning than with dry materials, and the temperature of the gases 
in the chimney is about 400° Fahr., one-third to one-half that from dry 
kilns. The product per kiln, according to Mr. Spackman, is not much more 
than 100 barrels per kiln, or about one-half the output with dry materials. 

Higher production than this has been attained by lengthening the kilns 
so as to utilize more thoroughly the heat of the flame. Lengths of 70 to 
too feet are used, or a cylindrical kiln about 60 feet in length and 6 feet 
in diameter, lined with firebrick, is connected at its upper end with an 
independent drying tube 40 to 50 feet long of slightly smaller diameter 
and with no lining. A kiln 6 feet in diameter by 60 feet long, with a 54-inch 
by 50-foot dryer extension, working on wet materials, has been known in cer¬ 
tain cases to give an average capacity of from 135 to 140 barrels per day.f 

♦Proceedings Philadelphia Engineers’Club, April, 1903. 

■^Statement of Allis-Chalmers Co. to the authors. 


720 


A TREATISE ON CONCRETE 


In the United States the raw materials most commonly employed in the 
wet process are marl and clay. The marl as it comes to the mill is broken 
up in some form of a disintegrator. The clay is dried and pulverized and 
is then mixed with the marl, which is about of the consistency of thick 
cream, in a pug mill, or an edge-runner. (See Fig. 237.) 



Fig. 237.—Edge Runner. ( See p. 720.) 


In some cases the clay is ground and water is added to it before mix¬ 
ing with the marl. 

The mixed materials must now be ground wet before burning. This 
is often accomplished in mill stones, consisting of a pair of horizontal 









CEMENT MANUFACTURE 72 1 

stones the upper one of which revolves upon an upright shaft, or in wet 
tube mills closely similar to that shown in Fig. 233 on page 716. 

From the mills, it may be run into tanks, where it is sampled and its 
chemical composition exactly determined, and from there pumped into the 
ends of rotary kilns, which, as stated above, are usually made longer than 
those used in the dry process. 

Centrifugal pumps may be employed for conveying the wet material, or 
if it is too thick for these to handle, plunger pumps may be resorted to. 
A more recent system of handling is by compressed air. 

After calcination the treatment is similar to that in mills where dry raw 
materials are used. 

Stationary Kilns. Before the introduction of rotary or revolving kilns 
all cement was burned in stationary kilns. Stationary kilns are of two 
general types: (1) intermittent kilns, which are completely charged and 
then burned, and (2) continuous kilns, where the fire is maintained con¬ 
tinuously and the exhaust heat used to dry and heat the raw materials 
before burning them. 

The most common form of intermittent kiln is the Dome or Bottle 
Kiln. This consists of a single shaft into which alternate layers of moist 
bricks of cement slurry and coke are placed by hand and burned. After 
cooling, the clinker is drawn out by hand through a door at the bottom, 
picked over to remove under-burned clinker, — which is of a yellowish 
shade instead of black,.— and clinker which has fused to fragments of the 
firebrick lining. 

The Johnson Kiln is a more economical form of intermittent kiln. The 
slurry is placed in chambers, and dried by the exhaust gases from the 
burning of the previous charge before being placed in the kilns. 

Of the continuous kilns, the Hoffman Ring Kiln consists of several 
chambers or furnaces around a central chimney. As the material in one 
furnace is burned, the heat passes around through the other furnaces so as 
to raise the temperature of the bricks in them and utilize the exhaust 

heat. 

In the Schoejer Kiln , which is also of the continuous type, the 
bricks and fuel are loaded from time to time into the upper end of the 
shaft, and pass down, increasing in temperature, through the flame, 
where the area is contracted, to be cooled below and drawn out at the 
bottom. 

The Dietzsch Kiln is of a somewhat similar type of construction, except 
i^at hand-labor is required in passing the dried material into the heating 
tnamber. 



722 


A TREATISE ON CONCRETE 


Comparison of Rotary and Stationary Kilns. Mr. Frederick H. Lewis* 
compares the three classes of kilns as follows: 

Quantity of Fuel 

. 15 to 30 bbls. per day 

. 40 to 80 bbls. per day 

. 120 to 250 bbls. per day 

Fuel in Terms of Clinker Produced 

Intermittent kilns require . 25 to 35% of fuel (coke) 

Continuous shaft kilns require . 12 to 16% of fuel (coal) 

Rotary kilns require . 22 to 40% of fuel (coal) 

The chief difference in cost between rotary and stationary kilns is for 
labor. In a rotary plant one sees the machinery running with only an 
occasional attendant, as no handling of the materials is required from the 
time they enter the mill until the cement is packed in bags or barrels for 
shipment. In the stationary kiln plant, even if brick machines are used 
for molding the slurry, a great deal of hand labor is required, as the 
kilns must be loaded and emptied by hand. Mr. Lewis estimates the 
labor cost with continuous kilns to range from three to live times the cost 
with rotaries. 

NATURAL CEMENT MANUFACTURE 

The process of manufacture of Natural cement consists, in brief, of 
burning a natural argillaceous limestone at low heat and grinding it to 
powder. The stone used in England is very soft, in fact nearly as disin¬ 
tegrated as marl. 

Raw Material. Many of the limestones used for Natural cement con¬ 
tain a high proportion of magnesia and an excess of clay, while others are 
nearly free from magnesia. It must be calcined at a temperature much 
below that required for Portland cement or it will fuse to a slag which 
after grinding has no hydraulic properties. Suitable formations occur in 
many parts of the United States, one of the most noted being that found in 
the region of eastern New York where Rosendale cements are made. 
Sometimes the stone is taken entirely from one ledge, while in other cases 
mixtures of two strata are employed. Little attention is paid to the analysis 
of the rock, as there is a wide range in the required chemical composition 
of the product (see p. 47), and the price at which Natural cement is sold 
does not warrant great refinement. 

Process of Manufacture of Natural Cement. There is less variety in 
the methods employed for producing Natural cement than for Portland. 


Intermittent kilns _ 

Continuous shaft kilns 

Rotarv kilns . 

¥ 


*Engineering Record, Dec. 17, 1898, p. 47, and personal correspondence. 








CEMENT MANUFACTURE 


7 2 3 


In a typical plant, the stones, of about the size that would be required 
for a large crusher, are brought from the quarry in carts or cars and 
dumped directly into the top of the kilns, which are of boiler iron lined 
with firebrick. They have no chimneys, but are open at the top and of 
the same size throughout. Thick layers of stone are alternated with thin 
layers of pea coal. The clinker is drawn out at the bottom as it is burned. 

In the older plants the burned clinker is crushed and then ground be¬ 
tween mill stones, while the newer mills use grinding machinery similar to 
that in Portland cement plants. When burnt, Natural cement rock is 
more readily powdered than Portland cement clinker. 

PUZZOLAN CEMENT MANUFACTURE* 

Puzzolan cement is made in the United States from blast furnace slag 
mixed with slaked lime. In Europe, natural puzzolanic materials have 
been employed. 

The process of manufacture consists essentially of cooling the slag, 
mixing it with slaked lime, and grinding to a very fine powder. 

Slag for Puzzolan Cement. For making pig iron a blast furnace is 
charged with a mixture of iron ores, fluxes (consisting of limestone, either 
calcite or dolomite) and fuel, in the proper chemical proportions to pro¬ 
duce, after reduction by heat, products of definite chemical composition. 
These resulting products are pig iron and slag. Any one unacquainted 
with metallurgy naturally thinks of blast furnace slag as a compound of 
iron. This is incorrect, as iron forms only a very small impurity. 

All slags are not suitable for Puzzolan cement, as they ordinarily con¬ 
tain too high a percentage of magnesia and are often too high in alumina. 
The specifications for slag used in the manufacture of Steel Portland ce¬ 
ment are as follows :f 

Slag must analyze within the following limits : 


Per cent. 

Silica plus alumina, not over. 49 

Alumina. 13 t° 16 

Magnesia, under . 4 


Slag must be made in a hot furnace and must be of light gray color. 

Slag must be thoroughly disintegrated by the action of a large stream of cold water 
directed against it with considerable force. This contact should be made as near the 
furnace as is possible.” 

Mr. E. Candlot sayst ‘‘'The slag must be basic; according to Mr. Tet- 

*An investigation of the manufacture and properties of Puzzolan cement is given in Report of 
Board of Engineers, U. S. A., 1900, on Steel Portland cement. 

fReport of Board of Engineers, U. S. A., 1900, on Steel Portland Cement. 

JCiments et Chaux Hydrauliques, 1898, p. 157. 





7 2 4 


A TREATISE ON CONCRETE 


majer, when the ratio -- falls below unity the slag is useless; the 

Si 0 2 

ratio of alumina to silica must be between 0.45 and 0.50. According to Mr. 
Prost, the composition of slags habitually used in the manufacture of Puz- 
zolan cements must be nearly represented by the formula 2 Si 0 2 , A 1 2 0 3 , 
3 CaO.” 

Mr. E. C. Eckel* gives the following analyses of slag and slag cement: 
Analyses 0} Slags in Actual Use and Composition of Slag Cements 


SLAG CEMENT 


CONSTITUENT. 

Choindez, 1 
Switzerland. / 

\ 

Saulnes, > 
France. / 

6 

bO 

rt —1 

23 

O 

Choindez, \ 

“fl 

s_, l 

France. > 

1 

Chicago, 1 

1111 

Si 0 2 . 

26.24 

3 ^- 5 ° 

32.20 

i 9-5 

22.45 

28.95 

Al 2 O3. 

24-74 

16.62 

I 5-50 

J 7-5 

13-95 

11.40 

FeO. 

0.49 

0.62 



3 - 3 ° 

0-54 

CaO . 

46.83 

46.10 

48.I4 

54 -o 

5 1 - 10 

50.29 

MgO. 

0.88 


2.27 


i -35 

2.96 

CaS. 

o -59 






CaS 04 . 

0.32 






S . 






i -37 

SO3. 





°-35 


I. oss on ignition. 





7-50 

‘ 3-39 

Ca r > | 







SiCC j 

X) 

M 

1.46 

1.49 




A 1 O3 1 







Si 0 2 ( 

o -93 

0.52 

O.48 





Process of Manufacture of Puzzolan Cement. No kilns are required 
except for burning the lime. Molten slag as it flows from the blast furnace 
is granulated by coming in contact with a stream of cold water. This 
renders the product more strongly hydraulic, and most of the sulphur is 
removed as it strikes the water. As sent to the cement plant, it usually 
contains from 30% to 40% of water, and the first operation is to pass it 
through a dryer. The dried slag may or may not have a preliminary 
grinding before adding the slaked lime. 

The lime is produced by burning a pure limestone, and then slaking it 
with water to which has been added a small percentage of caustic soda or 
other similar material, to make the resulting cement quicker setting. 
After drying, the slaked lime is mixed with the slag and ground in ball 
mills and tube mills, or in other forms of fine grinding machinery, and 
is ready for packing in bags or barrels for shipment. 


♦Mineral Resources of the United States, 1901. 


































REFERENCES TO CONCRETE LITERATURE 


7 2 5 


CHAPTER XXXI 

REFERENCES TO CONCRETE LITERATURE 

While this chapter is not a complete bibliography of concrete literature, 
it presents a comprehensive list of valuable books and articles relating to 
the subject. 

Under General References the names of authors are arranged alpha¬ 
betically. The various subject headings under Subject References are 
also arranged alphabetically, and the references are printed in order of 
dates, the latest first. Articles are usually described by their subject-mat¬ 
ter instead of giving their titles verbatim. In the case of similar articles 
printed in two or more periodicals, preference is generally given to the one 
bearing the earlier date. For references to this treatise see the Index. 


ABBREVIATIONS 

The following abbreviations (most of which correspond to those adopted 
by the Engineering Index) are employed: 

Ann. de Ponts et Chauss. —Annales des Ponts et Chaussees. m. Paris. 
Arch. Rec. —Architectural Record. New York. 

Beton u. Eisen. —Beton und Eisen. Vienna. 

Can. Eng. —Canadian Engineer. Montreal, Canada. 

Cement and Eng. News. —Cement and Engineering News. Chicago. 
Comptes Rendus —Comptes Rendus de 1 ’Academic des Sciences. Paris. 
Con. Eng. —Concrete Engineering. Cleveland, Ohio. 

Deutsche Ban. —Deutsche Bauzeitung. Berlin. 

Eng. Contr. —Engineering Contracting. New York. 

Eng. Mag. — Engineering Magazine. New York & London. 

Eng. News. — Engineering News. New York. ' 

Eng. Rec. — Engineering Record. New York. 

Gen. Civ. — Genie Civil. Paris. 

l ns. Eng. — Insurance Engineering. Boston. 

l nt. Eng. Cong. — International Engineering Congress, St. Louis, 1904. 
Jour. Am. Chem . Soc. — Journal American Chemical Society. Easton, 

Pa. 

Jour. Assn. Eng. Socs. — Journal of the Association of Engineering So¬ 
cieties, Philadelphia. 

Jour. Fr. Inst. — Journal Franklin Institute. Philadelphia. 

Jour. W. Soc. Engs. — Journal of the Western Society of Engineers, 
Chicago. 

Mimic. Engng. — Municipal Engineering. Indianapolis. 

Oest. Monaischr. j. d. Oefj. Baudienst. — Oesterreichische Monatsschrift 
fiir den Oeffentlichen Baudienst. Vienna. 


726 A TREATISE ON CONCRETE 

Pro. Am. Soc. Civ. Engs. — Proceedings of the American Society of Civil 
Engineers. New York. 

Pro. Am. Soc. Test. Mat. — Proceedings of American Society for Testing 
Materials. Philadelphia. 

Pro. Assn. Ry. Snpts. — Proceedings of the American Association of 
Railway Superintendents of Bridges and Buildings. New York. 

Pro. Engs. Club oj Phila. — Proceedings Engineers’ Club. Philadelphia. 
Pro. Engs. Soc. oj W. Penn. — Proceedings of Engineers’ Society of 
Western Pennsylvania. Pittsburgh. 

Pro. Inst. Civ. Engs. — Proceedings of the Institution of Civil Engineers. 
London. 

Ry. Eng. Rev. — Railway & Engineering Review. Chicago. 

R. R. Gaz. — Railroad Gazette. New York. 

Rept. Chief oj Engs., U. S. A. — Report of Chief of Engineers, U. S. A. 
Rept. Eng. Dept. — Report of Engineering Department, Washington, D. C. 
Rept. Met. W. dr 3 S. Board. — Report of Metropolitan Water & Sewerage 
Board, Massachusetts. 

Revue Gen. des Chemins de Per. — Revue Generate des Chemins de Fer. 
Paris. 

Rev. Tech. — Revue Technique. — Paris. 

Schw. Bauz. — Schweizerische Bauzeitung. Zurich. 

Tech. — Technograph. University of Illinois. Champaign, Ill. 

Tech. Qr. — Technology Quarterly. Boston. 

Trans. Am. Soc. Civ. Engs. — Transactions American Society of Civil 
Engineers. New York. 

Trans. Am. Soc. Mech. Engs. — Transactions American Society of Me¬ 
chanical Engineers. New York. 


GENERAL REFERENCES 

*An asterisk precedes the references which are especially noteworthy. 


Andrews, H. B. Practical Reinforced Con¬ 
crete Standards for the Design of Rein¬ 
forced Concrete Buildings. Simpson 
Bros. Corporation, Boston, Mass. 

Balet, Joseph W. Analysis of Elastic Arches. 
Three-hinged, Two-hinged and Hingeless, 
of Steel Masonry and Reinforced Con¬ 
crete. Engineering News PublishingCo., 
New York, 1908. 

*Eckel, Edwin C. Cements, Limes and Plas¬ 
ters. Their Materials, Manufacture and 
Properties. John Wiley & Sons, New 
York, 1905. 

*Feret, R. Etude Experimentale du Cement 
Arm6. Gauthier-Villars, Paris, 1906. 

*Feret, R. Chimie Appliqude. Baudry et 
Cie, Paris. 

Gillette, H. P. Concrete Construction, Meth¬ 
ods and Costs. M. C. Clark Publishing 
Co., Chicago, Illinois. 

Gilbreth, F. G. Concrete System. Engineer¬ 
ing News Publishing Co., New York, 
1908. 

Hawkesworth, J. Graphical Handbook for 
Reinforced Concrete Design. D. Van 
Nostrand, New York, 1907. 


Heidenreich, E. Lee. Engineers’ Pocketbook 
of Reinforced Concrete. M. C. Clark 
Publishing Co., Chicago, Illinois. 
Kersten, C. Brucken in Eisenbeton. 2 vol¬ 
umes, Wilhelm Ernst & Sohn, Berlin, 

r 909- 

*/Vtarsh, C. F., and Dunn, Wm. Reinforced 
Concrete, Third Edition. D. Van Nos¬ 
trand, New York, 1907. 

*Morsch, Emil. Der Eisenbeton ban-Seine 
Theorie und Anwendung. Konrad Witt- 
wer, Stuttgart, Germany, 1908. 

Reid, Homer A. Concrete and Reinforced 
Concrete Construction. M. C. Clark 
PublishingCo., New York, 1906. 
Reuterdahl, Arvid. Theory of Practice of 
Reinforced Concrete Arches. M. C. 
Clark Publishing Co., Chicago, Illinois, 
1908. 

Taylor, W. Purves. Practical Cement Test¬ 
ing. Myron C. Clark Publishing Co., 
New York, 1905. 

Taylor, Frederick W. and Thompson, Sanford 

E. A Treatise on Concrete, Plain and 
Reinforced, 2d edition, John Wiley & 
Sons, New York, 1909. 


REFERENCES TO CONCRETE LITERATURE 


*Turneaure, Prof. F. E., and Maurer, Prof. E. R. 

Principles of Reinforced Concrete Con¬ 
struction. John Wiley and Sons, New 
x ork, 1909. 

Twelvetrees, W. N. Concrete Steel. Mac¬ 
millan Co., New York. 


Alexandre, Paul. Etude sur la resistance des 
mortiers de ciment. Annales des Ponts et 
Chaussees, 1888, I, p.375. 

*-— Recherches experimentales sur les mor¬ 

tiers hydrauliques. Annales des Ponts et 
Chaussees, 1890, II, p. 277. 

Baker, Ira (). A Treatise on Masonry Construc¬ 
tion. John Wiley & Sons, New York, 1899. 

♦Berger, C. et V. Guillerme. La construction en 
ciment arme. Applications generates theories 
et septemes divers. Du nod, Paris, 1902. 

Boitel, C. Les constructions en fer et ciment. 
Berger-Levrault, Paris, 1896. 

Bonnami, H. Fabrication et controle des chaux 
hydrauliques et des ciments: theorie et 
pratique. Gauthier-Villars et Fils, Paris, 
1888. 

Brown, Charles C. Directory of American Cement 
Industries and Hand-Book for Cement Users. 
Municipal Engineering Co., Indianapolis, 
Ind. 

Buel, A. W. and C. S. Hill. Reinforced Concrete. 
Engineering News Publishing Co., New York, 
1904. 

*Burr, William H. The Elasticity and Resist¬ 
ance of the Materials of Engineering. John 
Wiley & Sons, New York, 1903. 

*But!er, David B. Portland Cement, Its Manu¬ 
facture, Testing, and Use. Spon, London, 
1899. 

Cain, William. Theory of Steel-Concrete Arches 
and of Vaulted Structures. Van Nostrand’s 
Science Series. New York, 1902. 

♦Candlot, E. Ciments et chaux hydrauliques: 
fabrication — proprietes — emploi. Baudry 
et Cie, Paris, 1898. 

Castanheira das Neves. Estudos sobre resistencia 
de materiaes. Lisbon, 1892. 

*Cement Industry, The. The Engineering Record, 
New York, 1900. 

♦Christophe, P. Beton arme et ses applications. 
Ch. Beranger, Paris, 1902. 

Coignet, E. et de Tedesco. Du calcul des ouvrages 
en ciment avec ossature metallique. Societe 
des Ingenieurs Civils, 1894. 

♦Commission des methodes d’essai des materiaux 
de construction. Vol. I et IV. Paris, 1893 
and 1895. 

♦Congres International des methodes d’essai des 
materiaux de construction. Vo . II, 2d Part. 
Dunod, Paris, 1901. 

♦Considere, A. Resistance a la compression du 
beton arme et du beton frette. Dunod, Paris, 
Genie Civil, 1902. 

-Experimental Researches on Reinforced 

Concrete, translated and arranged by Leon 
S. Moisseiff. McGraw Publishing Co., New 
York, 1903. 

Cummings, Uriah. American Cements. Rogers 
& Manson, Boston, 1898. 

Daubresse, P. De l’emploi des ciments Portland 
dans les constructions civiles et industrielles. 
Bruxelles, 1897. 

♦Durand-CIaye, Derome et R. Feret. Chimie ap- 
pliquee a Part de l’Ingenieur. Baudry et Cie, 
Paris, 1897. 

Faija, H. Portland Cement for Users. London, 
1884 

Falk, Myron S. Cement. Mortars and Concretes, 
their physical properties. M. C Clark, New 
York, 1904. 


727 


Vacchelli, Giuseppe. Le Construzioni in Cal- 
cestruzzo ed in Cement Armato. Ulrico 
Hoepli, Milan, 1906. 

Von Emperger, F. Handbuch fuer Eisen- 
betonban. Wilhelm Ernst and Sohn, 
Berlin, 1907. 


Feret, R. Sur la compacite des mortiers hydrau¬ 
liques. Annales des Ponts et Chaussees, 
Paris, 1892, II, p. 1. 

•-(See Durand-CIaye.) 

French Commission. (See Commission des me¬ 
thodes d’essai des materiaux de construction.) 

German Association of Portland Cement Manufac¬ 
turers. Der Portland Cement und Seine An- 
wendungen im Bauwesen, Berlin, 1892. 

Gillmore, Q. A. Practical Treatise on Limes, 
Hydraulic Cements, and Mortars. D. Van 
Nostrand Co., New York. 

■-— Notes on the Compressive Resistance of 

Freestone, Brick Piers, Hydraulic Cements, 
Mortars and Concretes. John Wiley & Sons, 
New York, 1888. 

-- Report on Beton Agglomere or Coignet- 

Beton and the Materials of Which it is Made. 
Professional Papers, U. S. A., No. 19, Wash¬ 
ington, D. C., 1871. 

*Golinelli, L. How to Use Portland Cement (Das 
Kleine Cement-Buch). Translated by Spen¬ 
cer B. Newberry. Cement and Engineering 
News, Chicago, 1899. 

Grant, John. Portland Cement: Its Nature, Tests, 
and Uses. Institution of Civil Engineers, 
Vols. XXV, p. 66, XXXII, p. 266, and LXII, 
p. 98. London. 

Guillerme, V. (See Berger.) 

Hill, C. S. (See Buel.) 

Jameson, Charles D. Portland Cement: Its Man¬ 
ufacture and Use. D. Van Nostrand Co., 
New York, 1898. 

♦Johnson, J. B. The Materials of Construction. 
John Wiley & Sons, New York, 1903. 

Lavergue, Gerard. Etude des divers systemes de 
constructions en ciment arme. Le Genie 
Civil. Baudry et Cie., 1899. 

♦Le Chatelier, H. Proced6s d’essai des materiaux 
hydrauliques. Annales des Mines, 1893. Du¬ 
nod, Paris, 1893. 

Leduc, E. Chaux et Ciments. J. B. Bailliere & 
Fils, Paris, 1902. 

Lefort, L. Calcul des poutres droites et planchers 
en beton de ciment arme. Baudry et Cie., 
Paris, 1899. 

Mahiels, Armand. Le Beton et son emploi. Ma¬ 
teriaux— chautiers — coffrages—■ prix de re- 
vient — applications. Benard, Liege, 1893. 

Marsh, Charles F. Reinforced Concrete. D. Van 
Nostrand Co., New York, 1904. 

*Morel, Marie-Auguste. Le ciment arme et les 
applications. Gauthier-Villars & Masson et 
Cie, Paris, T902. 

Newberry, Spencer B. (See Golinelli.) 

Newman, John. Notes on Concrete and Works in 
Concrete. Spon, London, 1887. 

Noe, H. de la. Ciment arme. Annales des Ponts 
et Chaussees, I, 1899, p. 1. 

♦Potter, Thomas. Concrete: Its Use in Build¬ 
ing. B. T. Botsford, London, 1894. 

Redgrave, Gilbert R. Calcareous Cements: Their 
Nature and Use. With Some Observations 
upon Cement Testing. Charles Griffin & 
Co., London, 1895. 

Sabin, Louis Carlton. Cement and Concrete Mc¬ 
Graw Publishing Co., 1905. 

♦Schoch, C. Die Moderne Aufbereitung und 
Wertung der Mortel Materialen. Berlin, 1896. 

♦Spalding, Frederick P. Hydraulic Cement: Its 
Properties, Testing, and Use. John Wiley & 
Sons, New York, 1903. 


*An asterisk precedes the references which are especially noteworthy. 








728 A TREATISE ON CONCRETE 


Sutcliffe, George L. Concrete: Its Nature 
and Uses. Crosby, Lockwood and Son, 
London, 1893, 

*Taylor, Fredrick W. and Thompson, Sanford 

E. A Treatise on Concrete, Plain and 
Reinforced. John Wiley & Sons, New 
York, 1905. 

Tedesco, N. de. Traitd thdorique et pratique 
de la resistance des matdriaux appliquee 


au bdton et au ciment armd. Ch. 
Beranger, Paris, 1904. 

Thompson, Sanford E, (See Taylor.) 

Vicat, L. J. A Practical and Scientific Trea¬ 
tise on Calcareous Mortar and Cements, 
Artificial and Natural. Translated from 
the French by Capt. J. T. Smith. John 
Weale, London, 1837. 


SUBJECT REFERENCES 
Bond of Steel to Concrete 


Berry, H. C. Tests of Bond of Steel Bars 
Embedded in Concrete. Eng, Rec., 
July, 1909, p. 93. 

Van Ornum, J. L. Tests of Bond between 
Concrete and Steel. Eng. News, Feb. 
1908, p. 142. 

Withey, Morton O. Tests of Bond in Rein¬ 
forced Concrete Beams, Proc. Am. Soc. 
Test. Mat., Vol. VIII, 1908, p. 469. 
Shuman, Jesse J. Tests of Cold Twisted Steel 
Rods. Eng. Rec., July, 1907, p. 77. 


Noble, C. W. Choice of Steel for Reinforcing 
Concrete. Eng. News, May, 1907, p. 5 16. 

Boost, Von H. New Tests of Bond of Steel 
to Concrete, Berlin. Beton u. Eisen, 
Heft II, 1907, p. 47. 

Withey, M. 0 . Variation of Bond with Com¬ 
pressive Strength. Univ. of Wisconsin 
Bulletin No. 175, 1907. 

Talbot, A. N. Tests of Bond. Umv. of 
Illinois Bulletin, No. 8, 1906 . 


*Schaub, J. W. Some phenomena of adhesion. 
Eng. News, June, 1904, p. 56 i. 

*Spofford, Chas. M. Tests of adhesion of 
concrete and steel at Mass. Inst. Tecnol- 
ogy. Beton <fc Eisen, III Heft, 1903, p. 
200. 

*Christophe, Paul. Adhesion of metal Bdton 
Armd, 1902, p. 476. 

Mensch, Leopold. Adherence of concrete and 
steel. Jour. Assn. Eng. Socs.,Sept. 1902, 
p. 101. 


Hatt, W. K. Tests of rods imbedded in con¬ 
crete. Pro. Am. Soc. Test Mat., 1902. 

Carson, H. A. Adhesive resistance of steel 
bars in concrete. Tests of Metals, U. S. 
A., 1901, p. 620. 

Kurtz, C. M. Tests of bolts imbedded in con¬ 
crete. Jour. Assn. Eng. Socs., Feb. 1901, 
p. 109. 


Bridges 



Max. 

span 

Max. 

rise 

Crown 

thickness 


Location 

ft. 

ft. 

ft. 

Reinforcement 

Switzerland 

259 

87' 

4 ' 

Longitudinal & trans¬ 
verse bars 

42d St., Phila. 

C. B. & Q. R. R. 

25 o 

53 

3 

Double steel arch 
ribs 

Trestles 

Delaware River 

i 5 o 

40 

6 


D. L. & W. R. R. 

Paulins Kill 

120 

60 

6 


D. L. & W. R. R. 

Grand River 

L. S. & M. S. Ry. 

160 

7 1 2 

7 

Longitudinal & trans¬ 
verse bars 

Cumberland Valley 

100 

32 

5 

None 

Ry. 

Wyoming Ave., Phila. 

90 

28 

2 2 

Horizontal longitudinal 
rods in spandrel 
walls. No other 
reinforcement 


Authority 
Eng. News, Aug., 
1909, p. 133. 

Eng. News, May, 
1909, p. S40. 
Eng. A r ews, May, 
1909, p. S46." 
Eng. Rec., Apr., 
1909, P- 542. 


Eng. Rec., Apr., 
1909, p. 541. 
Eng. Rec., Apr. & 
May, 1909. 

Eng. News, Apr., 


1909, p. 377 - 
Eng. Rec., Feb. 
1909, p. 233. 


Harrisburg, Pa. 
Viaduct 

Maumee, Waterville, 
Ohio 

Sandy Hill, N. Y. 


Walnut Lane 
Phila. 

Paterson, N. J., 
Plain well, Mich., 
Waterloo, Iowa, 
Yellowstone River, 


90 

25 

2 

60 

8J 

ij 

233 

70 

5 \ 

54 

2.5 

1.8 

54 

8 

1.25 

72 

7.2 

1.18 

120 

1 5 

2.0 


Longitudinal & trans¬ 
verse rods 
Ribs, angle bars, 
latticed 

9 

None 

11 ribs about 
4 ft. apart 
4-inch 6-lb. chan¬ 
nels 1.9 ft. apart 
Steel Ribs 

Lattice girders 


Eng. Rec., Aug., 
1908, p. 228. 
Cement, Aug., 
1908, p. 116. 
Trans. Am. Soc. 
Civ. Engrs., Vol. 
LIX . p. 195. 
Eng. News, Jan., 

1907, p. 117. 

Eng. Rec., Sept., 1904, 
P- 303 

Eng. A rws. May, 1904, 
p. 456 

Eng. Rec., Feb., 1904 
p. 1 85 

Eng. News, Jan., 1904, 
p. 2 5 


*An asterisk precedes the references which are especially noteworthy. 



REFERENCES 


TO CONCRETE LITERATURE 


7 2 9 


Location. 

Max. 

span 

Max. 

rise 

Crown 

thickness 



ft. 

ft. 

ft. 

Reinforcement. 

Authority 

Plano, Ill., 

75 

38^ 

3 

4" and V cor¬ 

Eng. Rec., Jan., 1904, 

3rd St., Dayton, Ohio, 

no 

14.25 

2.1 

rugated bars 
Melan, 4 angles, lat¬ 
ticed 

p. 18 

Edwin Thacher, 1904 

Newark, N. J., 

132 

16.2 

3 

Melan, 4 angles, lat¬ 
ticed 

Thacher, rods near 
top and bottom 

Edwin Thacher, 1904 

Kankakee, Ill., 

73 

8.4 

i -33 

Edwin Thacher, 1904 

Mishawaka, Ind., 

no 

14 

2 

Melan, 4 angles, lat¬ 
ticed 

Edwin Thacher, 1903 

Prospect Ave., N. Y, 

85 

82 

2.25 

Corrugated bars 

Eng. News, Dec., 1903, 

Riverside, Cal., 

87 

369 

3-5 

None 

p. 588 

Eng. News, Oct., 1903, 

Leominster, Mass., 

45 

6.25 

1.1 

Round rods 
anchored 

P- 353 

J. R. Worcester, 1903 

Des Moines River, 

100 

28 

1.67 

Melan 

Cement, July, 1902, 
p. 200 

Zanesville, Ohio, 

122 

ii-S 

2-5 

f"x 5" bars 

Eng. News, March, 
1902, p. 261. 

Concord, Mass., 

66 

7 

1.1 

None 

J. R. Worcester, 1901 

Lansing, Mich., 

120 

23 

2 

Melan, 4 angles, lat¬ 
ticed 

Edwin Thacher, 1901 

South Bend, Ind., 

100 

n 

2-5 

Melan, 4 angles, lat¬ 
ticed 

Edwin Thacher 

Chatellerault, France, 

164 

15-7 

i -7 

Hennebique 

Revue Gen. desChemins 
de Fer, Dec., 1901 

Kirchheim, Germany, 

124.6 

18 

2.6 

None 

Eng. News, Oct., 1899, 
p. 246 

Eng. News, Sept., 1899, 

p. 179 

Germany, 

132 

14.7 

0.82 

Monier 

Switzerland, 

128 

n 

0.56 

Monier 

Eng. News, Sept., 1899, 
p. 179 

Southern Ry., Austria, 

32.8 

3-3 

o -5 

Monier 

Eng. News, Sept., 1899, 
P -179 

Topeka, Kan., 

125 

12 

1.8 

Melan beams 

Eng. Rec., April 16, 1898 

Inzigkofen, Germany, 

140 

14-5 

2-3 

33 000 lb. cast iron 

Eng. News, Sept., 1896, 
p. 178 

Munderkingen,Germany, 164 

16.4 

3-3 

None 

Inst. Civ. Engs., V. 119, 
p. 224 

Cincinnati, Ohio, 

70 

10 

1.25 

Melan beams 

Eng. News, Oct., 1895, 
p. 214 

Maryborough, Queensl’d 

50 

4 

1-25 

Steel rails 

Engng., London, May 
10, 1895, p. 395 

Neuhausel, Hungary, 

55-78 

3-7 

0.82 

Skeleton girders 

Inst. Civ. Engs.,V., 114, 
p. 402 

Philadelphia, Penn , 

25-39 

6-5 

3 

ii" mesh, i" wire 
netting 

Eng. News, Sept., 1893, 
p. 189 


Buildings 


Reinforced Concrete Dome of Porto Rico 
Capitol. Eng Rec., May 1909, p. 578. 
Baxter Building, Portland, Me. Eng. Bee., 
Apr., 1909, p. 49 2 * 

Bradford, A. M. Mill Building of Cement 
Brick, Plymouth Cordage Company. 
Average Cost 12 per cent Less than Clay 
Brick. Eng. News. Mar., 1909, p. 288. 
Perry, J. P. H. Cold Storage Warehouses. 

Eng. News, Feb., 1909, p. 209. 

Mill of Androscoggin Pulp Company. Eng. 
Rec., Feb., 1909. P- *90. ... _. 

Christopher Warehou.se, Jacksonville, rla. 

Eng. Rec., Jan., i 9 ° 9 > P- 72. 

Mason, W. H. Methods and Costs with 
Separately Molded Members. Nat. Assn. 
Cem. Users, Vol. IV, 1908, p. 48. 

Repairs at Pumping Station, Evansville, Ind. 

Eng. Rec., Dec., 1908, p. 719. . 

Great Western Railway Freight Terminal, 
England. Eng. News, Dec., 1908, p. 

629. 


Cost of Walls at Camp Perry, Ohio. Cone. 

Eng., Sept., 1908, p. 249. 

Torrey Building, Boston, Mass. Eng. Rec., 
Sept., 1908, p. 319. 

Sugar Warehouse, Detroit, Mich. • Eng. Rec., 
Sept., 1908, p. 269. 

Construction with Reinforced Concrete Joints. 

Con. Eng., Aug., 1908, p. 214. 

Reinforced Concrete Mausoleum. Cone. Eng. 
July, 1908, p. 183. 

New Orleans Court House. Eng. News, July, 
1908, p. 1. 

Chimney of Colusa-Parrott M. & S. Co., Butte, 
Mont. Eng. Rec., June, 1908, p. 735. 
Chimney at Cumberland Mills, Me. Eng. 

Rec., May, 1908, p. 593. 

Hostetter Building, Pittsburg, Pa. Eng. 

News, May, 1908, p. 521. 

First National Bank Building, Oakland, Cal. 

Eng. Rec., May, T908, p. 648. 
Bostwick-Braun Building, Toledo, O. Eng. 
Rec., May, 1908, p. 57S. 


*An asterisk precedes the references which are especially noteworthy. 


73 ° 


A TREATISE ON CONCRETE 


Cantilever Girders in the Boyertown Build¬ 
ing, Philadelphia. Eng. News, Apr., 
1908, p. 447. 

Phelps Publishing Co. Building, Springfield, 
Mass. Eng. Rec., April, 1908, p. 459. 
Burr, W. H. Thirty-ninth Street Building, 
New York. Trans. Am. Soc. Civ. Engr., 
Vol. LX, p. 443 • 

Harwood, S. G. Wisconsin Central Railway 
Depot, Minneapolis, Minn. Eng. Rec., 
March, 1908, p. 394. 

Foundry Building at Moline, Ill. Eng. Rec., 
March, 1908, p. 297. 

Cement Stock House near Montreal, Canada. 

Eng. Rec., Feb. 1908, p. 159. 

Westport Power House, Baltimore, Md. 

Eng. Rec., Feb., 1908, p. 116. 

Terrell, C. E. Garage, White Plains, N. J. 

Eng. News, Dec., 1907, P- 633. 

St. Mark Hotel, Oakland, Cal. Eng. Rec., 
Dec., 1907, p. 686. 

Newark Warehouse Co., Newark, N. J. Eng. 

Rec., Aug., 1907. p. i 52 . 

Chateau des Beaux Arts on Huntington Bay, 
Long Island. Eng. Rec., Aug., 1907, p. 
186. 

Separately Moulded Members Edison Portland 
Cement Co. Building, New Village, N.J. 
Eng. News, July, 1907, p. 5 . 

R. H. H. Steel Laundry Building, Newark, 
N. J. Eng. Rec., June, 1907, p. 677. 
Burleigh, W. F. Murphy Varnish Co. Build¬ 
ing, Newark, N. J. Eng. Rec., May, 
1907. P- 555 . 

Holy Angels School, Buffalo, N. Y. Eng. 

Rec., April, 1907, p. 491. 

Ketterhnus Lithographic Manufacturing Co. 
Building, Phila. Eng. Rec., Feb., 1907, 
p. 128. 

♦Stadium. Athletic field of Harvard University. 
L. J. Johnson, Jour. Assn. Eng. Socs., June, 
1904, p. 293. 

♦Store building, Chicago, Ill. Eng. Rec., June, 
1904, p. 713- . 

Chimney reinforced with T-bars, Zeigler, Ill. 

Eng. Rec., May, 1904, p. 661. 

♦Kelly & Jones Company’s factory building. Eng. 

Rec., Feb., 1904, pp. 153 and 195. 

Lighthouse at Nicolaieff, Russia. Eng. Rec., 
Jan., 1904, p. 100. 

♦Factory building, Long Island City, N. Y. Eng. 
Rec., Jan., 1904, p. 67. 

College of Music, Cincinnati, Ohio. Eng. Rec., 
Nov., 1903, p. 666. 

♦The Filtration works of the East Jersey Water 
Supply Company, Little Falls, N.J. G. W. 
Fuller, Trans. Am. Soc. Civ. Eng., Vol. L, p, 
394 - 

♦Ingalls Building, Cincinnati, O. Eng. Rec., May, 
1903, p. 540. 

Robert A. Van Wick Laboratory, New York. 

Cement, Sept., 1901, p. 203. 

Elevator, Buffalo, N. Y. C. R. Neher, Jour. 

Assn. Eng. Socs., April, 1901, p. 275. 

Nassau County Jail, Long Island. Cement, 
March, 1901, p. 37. 

Mediaeval Castle of Badajos, Spain. G. L. Sut¬ 
cliffe, Concrete, 1893, p. 5, 

St. James’s Church, Brooklyn, N. Y. Cement, 
Nov., 1900, p. 196. 

Singer Manufacturing Co’s. Buildings and Chim¬ 
neys. Cement, Sept., 1900, p. 162, and May, 
1901, p. 88. 

Office Building, Washingon, D. C. A. L. Harris, 
Cement, Sept., 1900, p. 155. 

Library Building at University of Virginia. Ross 
F. Tucker, Cement, March, 1900, p. 26. 

*An asterisk precedes the references which < 
•{•Engineering Index. 


Eagle Warehouse and Storage Co. Building 
Brooklyn, N. Y. Eng. Rec., Jan., 1907 
p. 19. 

Marlborough Apartment House, Baltimore, 
Md. Eng. Rec. Jan., 1907, P- 99 - 
Derfel Ing. Rob. A Print Mill Building, 
Briinn, Germany. Beton u. Eisen, Heft 
1, 1907, p. 10. 

Hotel Traymore, Atlantic City. N. J. Eng. 

Rec., Nov., 1906, p. 523. 

Cadillac and Packard Automobile Shops, 
Detroit, Mich. Eng. Rec., Nov., 1906, 
p. 544. 

Traders Paper Bond Co. Building, Bogota, 
N. J. Eng. Rec., Oct., 1906, p. 45 7 - 

A. T. & S. F. Railway Station. Eng. News, 

Sept., 1906, p. 246. 

Marlborough Hotel Annex, Atlantic City, 
N. J. Eng. News, March, 1906, p. 25 1. 
Taylor & Wilson Manufacturing-Co. Building, 
McKees Rocks, Pa. Eng. Rec., Dec., 
1905. p. 695. 

B. T. Babbit Works, Jersey City, N. J. Eng. 

Rec., Dec., 1905, p. 747. 

North West Knitting Co. Building, Minne¬ 
apolis, Minn. Eng. News, June, 1905, 
p. 593. 

Concrete Medical Laboratory, Brooklyn, Navy 
Yard. Eng. News, March, 1905 p. 31°- 
Masonic Temple Building. Toledo, Ohio. Eng. 

News, March, 1905, p. 287. 

United Shoe Machinery Shops, Beverly, Mass., 
Eng. Rec., March, 1905, p. 257. 

Bilgram Machine Shop, Philadelphia. Eng. 

Rec., Feb., 1905, p. 136. 

ChapM of the United States Naval Academy, 
Annapolis. Eng. Rec., Jan., 1905, p. 36. 


♦Chimney of Pacific Electric Rv., Los Angeles, 
Calif. J. D. Schuyler, Cement, March, 
1903, P- 30 - 

Chimney of the Laclede Fire Brick Manufacturing 
Co., St. Louis, Mo. Cement, March, 1903, 
P- 37 - 

Dome on Yale University Building, New Haven, 
Conn. Cement, March, 1903, p. 15. 

Strasburg Music Hall, Strasburg. Beton & 
Eisen, III Heft, 1903, p. 149. 

Salvation Army Building, Cleveland, Ohio. Ce¬ 
ment and Eng. News, Jan., 1903, p. 10. 

Cold Storage Plant, Oklahoma City, Okla¬ 
homa. Cement and Eng. News, Jan., 1903, 
p. 1. 

Arnand Apartment House, Paris. Jean Shopfer, 
Arch. Rec., Aug., 1902. 

Hecla Portland Cement & Coal Co., Michigan. 

Eng. News, June, 1902, p. 449. 

College Fraternity Building, New Haven, Conn 
Cement, Jan., 1902, p. 334. 

Factory Building, Cambridge, Mass. Cement 
March, 1900, p. 18. 

Pacific Coast Borax Co’s Plant, Bayonne, N. J 
Eng. Rec., July, 1898, p. 188. 

Museum Building of Leland Stanford, Jr., Uni¬ 
versity, Calif. Charles D. Jameson, Port¬ 
land Cement, 1898, plates V and VI. 

Record Building of Discount Bank, Paris. Rev. 
Tech., May 10, 1898.f 

Beocsin Cement Works, Germany.t Oest. Mo- 
natschr. f. d. Oeff. Baudienst, July, 1897. 

Concrete Structures in Denmark and Russia. 
Eng. News, April, 1896, p. 253. 

A Concrete House Built in 1872. W. E. Ward. 
Trans. Am. Soc. Mech. Engs., Vol. IV, p. 388 


especially noteworthy. 



REFERENCES TO CONCRETE LITERATURE 


73 1 


Dams 


Ohio River Bear-Trap Dam. Eng. News, 
Mar., 1909, p. 235. 

Scranton, Pa. Buttressed Dam. Eng. Ree., 
Mar., 1909, p. 347. 

Connecticut River Power Company Hydro- 
Electric Plant. Eng. Rec., Mar., 1909, 
p. 340. 

Kern River Hydro-Electric Plant. Eng. 

News, Dec., 1908, p. 701. 

Chicago Drainage Canal Movable Dams and 
Lock. Eng. News, Nov., 1908, p. 5 12. 
Bellows Falls, Vt. Erection Plant. Eng. 

News, Dec., 1908, p. 745. 

Croton Falls Reservoir Dam. Eng. Rec., Dec., 
1908, p. 67S. 

Berrien Springs, Mich. Hydro-Electric Devel¬ 
opment. Eng. Rec., Dec., 1908, p. 728. 
Uncas Power Company Hydro-Electric Plant. 

Eng. Rec., Nov., 1908, p. 572. 

Roosevelt Dam, Salt River Project. Eng. 

News, Sept., 1908, p. 265. 

Horse Shoe, N. Y. Combination Dam and 
Bridge. Eng. News, Apr., 1908, p. 385. 
Westchester County, N. Y., near Croton Falls. 
Eng. Rec., Mar., 1908, p. 377. 


McCall Ferry, Pa. Eng. News, Sept., 1907, 
p. 267. 

Katonah, N. Y. Cross River Dam. Eng. 

Rec., Sept., 1907, p. 281. 

West Point, N. Y. Buttress Dam. Eng. 

Rec., Aug., 1907, p. 214. 

Bates, L. Crocker’s Reef, N. Y. Eng. Cont., 
July, 1907,0. 17. 

Utica, N. Y. Eng. Rec., July, 1907, p. 75. 
Marklissa. Dumas, A. Gen. Civ., June i 5 , 
1907. 

Ellsworth, Me. Eng. News, May, 1907, p. 
557 . 

Holland de Muralt, Dr. L. R. Beton u. 

Eisen. Heft I, 1907, p. 8. 

Warriors Ridge Qap, Pa., above Huntington. 

Eng. Rec., Dec., 1906, p. 678. 

Plattsburg, N. Y. Eng. Rec., Mar., 1906, p. 
335 . 

Columbus, 0 . Scioto River Gravity Storage 
Dam. Eng. Rec., Sept., 1905, p. 302. 
Schuylerville, N. Y. Eng. Rec., Mar., 1905, p. 
267. 

Fenelon Falls, Ont. Eng. News, Feb., 1905, 
p. 135 . 


*Lynchburg, Va. Eng. Rec., July, 1904, p. 108. 
*Ithaca, N. Y. Eng. Rec., April, 1904, p. 446. 
Danville, Ill. Eng. Rec., April, 1904, p. 396. 
South Australia. A. B. Monerieff, Eng. News, 
April, 1904, p. 321. 

*New Milford, Conn. Walter Scott Morton, Eng. 

Rec., Feb., 1904, p. 187. 

Birmingham, Eng. Eng. Rec., Jan., 1904, p. 120. 
Theresa, N. Y. Ambursen & Sayles, Eng. News, 
Nov., 1903, p. 403. 

San Diego Calif. Eng. Rec., Nov., 1903, p. 590. 
*Spier Falls, Hudson River. Geo. E. Howe, Eng. 
Rec., June, 1903, p. 688. 

*Chaudiere Falls, Province of Quebec. Eng. News, 
May, T903, p. 398. 

*Norwich, Conn. H. M. Knight, Eng. News, June, 
1902, p. 470. 

Lake Winnibigoshish. W. C. Weeks, Cement, 
March, 1901, p. 20. 

Osage River, Missouri. Rept. Chief of Engs., 
U. S. A., 1900, p. 80. 


Millinocket, Maine. Eng. Rec., Dec., 1900, p. 56®. 
Johannesburg, So. Africa. Eng. Rec., Jan , 1899, 
p. 112. 

*Mechanicsville, N. Y. Eng. News, Sept., 1898, 
p. 130. 

Muchkunki, India. Eng. Rec., May, 1898, p. 570. 
Pioneer Power Plant, Ogden, Utah. Henry Gold- 
mark, Trans. Am. Soc. Civ. Eng., Vol. 
XXXVIII, p. 246. 

Rock Island Arsenal, III. O. C. Horney, Jour. W. 

Soc. Engs., Vol. II, p. 339. 

Rio Grande River. Eng. News, July, 1897, p. 36. 
Arch Dam, Ogden, Utah. Eng. Rec., March, 1897, 
p. 291. 

Cold Spring, N. Y. Eng. Rec., July, 1896, p. 105. 
Manchester, England. Eng. Rec., Nov., 1891, 
P- 387- 

*Croton River, New York. J. R. Croes, Trans. Am. 
Soc. Civ. Eng., Vol. Ill, p. 337. 


Elasticity of Concrete and Mortar 


Heintel. Elasticity of Concrete in Shear. 

Cement, Apr., 1908, p. 461. 

Howard. J. E, Elasticity of Materials Com¬ 
pared. Eng. Rec., May, 1906., p. 658 . 


Thompson, Sanford E. Discussion Trans. 
A n. Soc. Civ. Engs. Vol. LIV, part E, 
p. 594. 

Woo'san, Ira H. [Recent Tests. Eng. News, 
June, 1905, p. 56 i. 


Watertown Arsenal. Elasticity of Mortar Prisms. 

Tests of Metals, 1902,. p. 467. 

Watertown Arsenal. Elasticity of Concrete Cubes. 

Tests of Metals, 1898 to 1903. 

Sewell, John S. Study of Stress-strain Curves. 

Int. Eng. Cong., St. Louis, 1904. 

Thompson, Sanford E- Discussion on Stress- 
strain Curves. Int. Eng. Cong., St. Louis, 
1904. 

Hatt, W. K. Experiments on Elasticity of Con¬ 
crete. Jour. Assn. Eng. Socs., June, 1904, 
p. 321. 

Van Ornum, J. L. The Fatigue of Cement Prod¬ 
ucts. Trans. Am. Soc. Civ. Eng., Vol. LI, 
p. 443 * 

Johnson, J. B. Miscellaneous Tests of Elasticity. 
Various authorities, Johnson’s Materials of 
Construction, 1903, p. 575. 

Falk, Myron S Elasticity during Flexure. Trans. 

Am. Soc. Civ. Eng., Vol. L, p. 473. 

Christophe Paul. Data from various authorities. 
Beton Arme, 1902, p. 468. 

*An asterisk precedes the references 


Thacher, Edwin. Effect of Age and Composition 
on Elasticity. Cement, May, July, and Nov., 
1902. 

Kurtz, Charles M. Austrian Society Values for 
Steel, Concrete, and Mortar. Jour. Assn. 
Eng. Socs., Feb., 1901, p. 109. 

*Henby, W. H. Relative Elasticity of Cinder and 
Broken Stone. Jour. Assn. Eng. Socs., Sept., 
1900, p. 145. 

Moliter, David. Curves from Tests of Prof. Bach. 

Jour. Assn. Engs. Socs., May, 1898, p. 349. 
Brown, W. L. Tables and Curves. Pro. Inst. 

Civ. Engs., Vol. CXXXVII. p. 402. 

Bach, C. Experiments on the Elasticity of Con¬ 
crete. Jour. W. Soc. Engs., Jan., 1896, p. 84 
Hartig, E. Formula for Variation with Age of the 
Modulus of Elasticity. Pro. Inst. Civ. Eng., 
Vol. CXX, p. 375. 

Baker, Benjamin. Effect of Sand on the Elasticity 
Pro. Inst. Civ. Eng., Vol. CXV, p. 108. 


which are especially noteworthy 




732 


A TREATISE ON CONCRETE 


Expansion and Contraction 


Gowen, C. S. Effect of Temperature Changes 
on Masonry. Trans. Am. Soc. Civ. 
Engs. Vol. LXI, p. 399. 

Heat Expansion Stresses in Chimneys. Eng. 

News, March, 1908, p. 259. 

Expansion Joints in Pressure Sewer. Eng. 

News, March, 1908, p. 335. 

Expansion Joints in Viaduct. Eng. News, 
Dec., 1907, p. 628. 

White, Linn. Expansion Joints in Concrete. 
Eng. News, June, 1907, p. 653. 


Lewerenz, A. C. Expansion and Contraction 
of Concrete Structures. Eng. News, 
May, 1907, p. 5 12. 

Expansion Joints in Sandy Hill Bridge. Eng. 
News, May, 1907, p. 503. 

Becker and Lees. Expansion Joint in Con¬ 
crete Roof in Carp and Bldg., May, 1907, 
p. 167. 

Webb, W. L. Long walls built without 
joints with 3% of steel. Munic. Eng., 
Aug., 1906, p. 112 


Fuller, Geo. W. Expansion Wells in Water Puri¬ 
fication Works, Little Falls, N. J. Trans. 
Am. Soc. Civ. Engs., Vol. L, p. 406. 

♦Johnson, A. L. Continuous Concrete Walls with¬ 
out Expansion Joints. R. R. Gaz, March 13, 
1903. 

♦Railway Superintendents. Provisions for Expan¬ 
sion and Contraction. Pro. Assn. Ry. Supts., 
1900, p. 166. 

Adams, A. L. Contraction Cracks in Reservoir 
Lining. Trans. Am. Soc. Civ. Engs., Vol. 
XXXVI, p. 30. 


Paine, C. W. Joints in Butte, Mont., Reservoir- 
Jour. Assn. Eng. Socs., Oct., 1902, p- 

151. 

♦Pence, W. D. The Coefficient of Expansion 
of Concrete. Eng. News, Nov., 1901, p. 

380. 

Gary, Max. Tests showing Shrinkage in Air and 
Expansion under Water. Trans. Am. Soc. 
Civ. Engs., Vol. XXX, p. 17. 

A. S. C. E. Committee. Expansion and Contrac¬ 
tion Experiments. Trans. Am. Soc. Civ 
Engs., Vol. XV, p. 722, and Vol. XVII, p. 214 


Fire Resistance of Concrete and Mortar 


Waite, Guy B. Cinder and Stone Concrete 
Under Fire. Trans. Am. Soc. Civ. Engs., 
Vol. LX, p. 470. 

Woolsen, Ira H. Fireproof Qualities of Con¬ 
crete Partitions. Cement Age, June, 
1908, p. 578. 

Thompson, Sanford E. Concrete in the Chel¬ 
sea Fire. Cement Age, June, 1908, p. 
5 69. 

Report on Parker Building Fire, N. Y. City. 
Eng. News, May, 1908, p. 567. 

Gilbert, J. B. Fire at Dayton Motor Car 
Works. Eng Rec., March, 1908, p. 384. 

Report on Fire and Earthquake Damage to 
Buildings at San Francisco. Trans. Am. 
Soc. Civ. Engs., Vol. LIX, p. 208. 

Woolson, Ira H. Investigation of the Ther¬ 
mal Conductivity of Different Mixtures 
and Effect of Heat upon Them. Pro. 
Am. Soc. Test Mat., Vol. VI and VII. 

Effect of Heat on the Strength and Elastic¬ 
ity of Concrete. Pro. Am. Soc. Test 
Nat., Vol. V, p. 335. 


Thompson, Sanford E. Fire Resistance of 
Reinforced Concrete Construction. Con. 
Eng. June, 1907, p. 261. 

MacFarland, H. B. Fire and Load Test of 
Beams. Eng. Rec., March, 1907, p. 380. 
Tests of the Effect of Heat on Reinforced 
Concrete Columns. Eng. News, Sept., 
1906, p. 316. 

Comparative Resistance to Fire of Stone 
apd Cinder Concrete. Eng. News, May, 
1906, p. 603. 

San Francisco Earthquake and Fire. U. S. 
Geological Survey Bulletin, No. 324 
April, 1906. 

Fire and Water Tests of Stone Concrete and 
Cinder Concrete Floors. Eng. News, 
Feb., 1906, p. 1 15 . 

Probst, E. A Model Reinforced Concrete 
Theater for Studying Theater fires. 
Cement & Eng. News, Feb., 1906, p. 34. 
Fire Resistance of Different Concretes. Eng. 
Rec., July, i 9 o 5 , p. 97. 


♦Watertown Arsenal. Tests of Cement set at Differ¬ 
ent Temperatures. Tests of Metals, U. S. A., 
1902, p. 383. 

♦Norton, Chas. L. Tests of Fire Resistance of 
Concrete. Tech. Qr., June, 1900; Dec., 1902; 
June, 1904. Ins. Eng., Dec., 1901, p. 483; 
Feb., 1902, p. 72; March, 1902, pp. 118 and 
211. 

♦Norton, Chas. L., and Gray, Jas. P. Report on the 
Baltimore Fire. Eng. News, June, 1904, 
p. 528. 

Sewell, John S. Report on the Baltimore Fire. 

. Eng. News, March, 1904, p. 276. 

Johnson, J. B. Miscellaneous Tests. Materials 
of Construction, 1903, p. 625. 

Newberry, S. B. Theory of Protection. Cement, 
May, 1902, p. 95. 


Pacific Coast Borax Co., Bayonne, N. J. Cement, 
May, 1902, p. 85. 

Norton, Charles L. Tests to find Temperature of 
Steel during a Fire. Ins. Eng., Feb., 1902. 

Test Building at Mineola, L. I. Cement, Jan., 
1902, p. 358.. 

Moore, Francis C. Extracts from Publications of 
the British Fire Prevention Committee. Can. 
Eng., Aug., 1898. 

Tests of Fireproof Floors. Eng. News, Sept., 1896, 
p. 182; Nov., 1896, pp. 296 and 314; Jan., 
1897, pp. 6 and 15; Dec., 1897, p. 367; Nov., 
1901. p. 378; May. 1902 p. 441. 

Himmelwright, A. L. A. Fireproof Construction 
and Recent Tests. New York. Eng. Mag. 
Dec., 1896, p. 460. 


Forms 


Adjustable Forms for Heavy Battered Walls. 

Eng. Rec., April, 1909, p. 540. 

Scott, C. p. Patented Steel Form for Arch, 
Culvert and Bridge. Eng. Contr., Feb., 
1909, p. i 5 o. 

Adjustable Steel Centers for Sewer. Eng. 
Contr., Jan., 1909, p. 65 . 


Caldwell, W. L. Metal Forms in Reinforced 
Concrete Construction. Nat. Asssn. Cem. 
Users, Vol. IV, p. 286. 

A Collapsible Form for Small Culvert. Eng. 
Cont. Dec., 1908, p. 408. 


*An asterisk precedes the references which are especially noteworthy. 




733 


REFERENCES TO CONCRETE LITERATURE 


Steel Forms Used in the Blue Island Avenue 
Sewer, Chicago. Eng. News, Oct., 1908, 
p. 441. 

Patented Forms Used in Bronx Valley Sewer. 

Cement Age, Oct., 1908, p. 309. 

Wooden Forms for Concrete Manhole. Eng. 

Cont. Oct., 1908, p. 270. 

Steel Centering, Harlem Creek Sewer at St. 
Louis, Mo. Eng. News, July, 1908, p. 
I 3 I * 

Adjustable and Portable Forms for Concrete 
Building Construction. Eng. News, 
March, 1908, p. 264. 

Design and Construction of Forms. Con. 

Eng., March, 1908, p. 59. 

Forms for Big Cottonwood Conduit, Salt 
Lake City. Eng. Rec., March, 1908, p. 
3S3. 

Teichman, F. Traveling Mold for Making 
Concrete Pipe. Eng. News, Feb., 1908, 
p. 184. 

Proposed Traveling Form for Construction of 
Water Pipes and Sewers. Eng. Contr., 
Jan., 1908, p. 30. 

Thompson, Sanford E. Forms for Concrete 
Construction. Trans. Nat. Assn. Cem. 
Users, Vol. Ill, p. 64. 

Centering and Forms in Selby Hill St.Tunnel, 
St. Paul, Minn. Eng. Rec., Sept., 1907, 
p. 308. 

Reinforced Concrete Syphon on an Irrigation 
Canal in Spain. Eng. News, Aug., 1907, 
p. 116. 

Forms for Jacksonville Viaduct Piers and 
Spandrels. Eng. Rec., May, 1907, p. 
6°6. 

Hotchkiss, L. J. Retaining Wall Forms. 
Eng. Rec., March, 1907, p. 339. 


Collapsible Centering for Street Railway Con¬ 
duits. Eng. News, March, 1907, p. 315. 

Centering for Piney Creek Bridge, Washing- 
ton, D C. Eng. Rec., Jan., 1907, p. 88. 

forms tor Molding Concrete Pipe Culverts 
Eng. News, Dec., 1906, p. 65 1. 

Portable Arch Centering—Hodges Pass Tun- 
nel.—Eng. New., Dec., 1906, p. 586 . 

Centering for the Concrete Arches for P. & R 
R. R. Bridge. Eng. Rec., Oct., 1906* 
P- 399 - 

Heavy Panels for Retaining Walls Handled by 
Locomotive Crane. Eng. Rec., Sept' 

. 1906, p. 273. 

Reinforced Concrete Forms for Arch Rib 
Bridge. Eng. Rec., Sept., 1906, p. 237. 

Arch Rib Bridge, Grand Rapids, Mich. Eng! 
News, Aug., 1906, p. 2 i 5 ; March, 1906, 
p. 322. 


Centering for 5 o ft. Span Segmental Arch 
Eng. News, Aug., 1906, p. 207. 

Forms for a 5 ft. 9 in. Sewer, New Orleans 
Eng. Rec., June, 1906, p. 678. 

Forms for Sewer, South Bend, Ind. Eng. 
Rec., June, 1906, p. 736. 

Forms for Connecticut Ave. Bridge, Wash¬ 
ington. Eng. Rec., June, 1906, p’. 675. 

Special Falsework for a Concrete Bridge 
Eng. Rec., April, 1906, p. 484. 

Retaining Wall Forms, N. Y. Central R R 
Eng. Rec., Jan., 1906, p. 24. 

Evans, R. R. Traveling Form for Construct¬ 
ing invert of Sewer. Eng. News, March 
1905, p. 254. 

Carver G. P. Forms for 36-in. Sewer, Bev¬ 
erly Mass. Eng. News, June, 1904 
p. 55 o. > > •+» 


Steel Centers. Eng. News, Oct., 1904, p. 350. 
♦Courtright, P. A. Center for 54-ft. Span Arch. 

Eng. News, May, 1904, p. 456. 

Clark, H. Q. Catch-basin Forms. Eng. News, 
May, 1904, p. 473. 

♦Centers for 5-ft. Egg Sewer, Washington, D. C. 

Eng. News, Feb., 1904, p. 163. 

A Tie for Concrete Forms. C. M. & St. P. Ry. 

Eng. News, Jan.. 1904, p. 96. 

♦Tunnel Forms, Central Mass. R. R. Eng. Rec., 
Jan., 1904, p. 5. 

♦Forms for Core Walls. Cedar Grove Reservoir. 
> Eng. Rec., Dec.. 1903, p. 680. 

Taylor, C. G. Methods of Building a Cellar Wall. 

Chr. & Bldg., Aug.. 1903, p. 213. 

♦Arch Center in New York Subway. Eng. News, 
June, 1903, p. 514. 

♦Kleinhans, Frank B* Centering Arch Bridge, 


C. M. & St. P. Ry. Eng. News, March, 1903, 
p. 267. 

Skew Back Forms. Long Island R. R. Eng. 

News, Dec., 1902, p. 519. 

♦Arch Centering. Zanesville, O., Bridge. Eng. 

News, March, 1902, p. 264. 

Template for Sewer Invert, New York Rapid 
Transit Railway. Eng. News, March, 1902, 
p. 200. 

Wall Forms in Nassau County Jail. Photograph. 

Cement, March, 1901, p. 37. 

Abbot, F. V. Details of Forms in Improvement of 
Mississippi River. Cement, Jan., 1901,9.229. 
♦ Hazen, Allen. Groined Arch at Albany Filtration 
Plant. Trans. Am. Soc. Civ. Engs., Vol. 
XLIII, p. 270. 

A Collapsible Center for Sewer Arches. Eng. News, 
Jan., 1899, p. 22. 


Foundations 


Colberg, Otto. Tests of Strauss System cf 
Piles, Vienna. Beton u Eisen, Heft III 
1909, p. 54. 

Howell, C. S. Straight or Tapered Concrete 
Piles. Eng. News, Feb., 1909, p. 223. 
Method of Pipe Protection on Piles. Eng. 

Rec., Jan., 1909, p. 67. 

Thompson and Eox. Cast Reinforced Concrete 
Piles. Jour. Assn. Eng. Socs., Jan., 1909. 
Cannon, M. M. Concrete Piles, Brunswick, 
Ga., and Charleston, S. C. Jour. Assn. 
Eng. Socs., Jan., 1909. P* 24. 

Mensch, L. J. Shop-made Reinforced Con¬ 
crete Piles. Eng. News, Dec., 1908, p. 
620. 

Usina, D. A. Recent Developments in Pneu¬ 
matic Foundations. Trans. Am. Soc. 
Civ. Engs., Vol. LXI, 1908, p. 211. 


Foundation Wall Supported by a Reinforced 
Concrete Girder. Eng. Rec., Feb., 1908, 
p. 175 . 

Compressol System of Concrete Founda¬ 
tions. Eng. Cont., Oct., 1907, p. 220. 

Chamber of Commerce, Vienna. Beton u. 
Eisen, Apr., 1907, p. 85 . 

Foundation of Buildings in Mountaneous 
Regions. Beton u Eisen, Mai, 1907, 
p. T13. 

Foundations of Singer Building Extension, 
New York Eng. Rec., Feb., 1907, p. 116. 

Concrete Foundation Mat for a Power Station. 
Con. Eng., Feb., 1907, p. 77. 

Caisson Foundations for The Trust Company 
of America Building. Eng. Rec., Oct., 
1906, p. 470. _ 

Footings for Transmission Poles. Eng. News, 
June, 1906, p. 648. 


*An asterisk precedes the references which are especially noteworthy. 



734 


A TREATISE ON CONCRETE 


Hollow Concrete Foundation Piers, U. S. 
Post Office at Cleveland, Ohio. Eng. 
Rec., May, 1906, p. 607. 

Machinery Foundation in Quicksand, Knick¬ 
erbocker Building, New York. Eng. 
Rec., March, 1906, p. 247. 

Unusual Foundation at the Hoboken Termi- 
ual. Eng. Rec., Nov., 1905, p. 546. 


Foundations for the Yonkers Power House 
of the N. Y. C. & H. R. R. R. Eng. Rec., 
Dec., 1904, p. 676. 

Concrete Piling at Washington Barracks, D. 

C., Eng. Rec., Oct., 1904, p. 463. 
Concrete Pile Foundation of the U. S. Ex¬ 
press Co. Bldg., New York City. Eng. 
News, Oct., 1904, p. 348. 


Anderson, W. P. Concrete Piles. Eng. Rec., 
Oct., 1904, p. 494. 

Holmes, J. Albert. Reinforced Concrete Piles with 
enlarged Footings. Eng. News, June, 1904, 
P- 567-. 

Concrete Piles. Eng. Rec., May, 1904, p. 596. 
Concrete Piles. Cement, Nov., 1903, p. 331. 
Kimball, Geo. A. Foundations for the Elevated 
Structure of the Boston Elevated Railway. 
Jour. Assn. Eng. Socs., June, 1903, p. 351. 
♦Francis, Geo B. Foundations. Jour. Assn. Eng. 

Socs., June, 1903, p. 336. 

♦Worcester, Joseph R. Boston Foundations (with 
discussion). Jour. Assn. Eng. Socs., June, 
1903, p. 285. 

Making Concrete Piles in Place. Eng. News, 
March, 1903, p. 275. 

Concrete-steel Piles. Cement, March, 1903, p. 
16. 


A Concrete-steel Pile Foundation in Germany. 

Eng. News, Feb., 1903, p. 173. 

Concrete Pile Foundations at Aurora, Ill. Eng. 

News, Dec., 1902, p. 495. 

Mensch, L. Reinforced Piles and Sheet Piling. 

Jour. Assn. Eng. Socs., Sept., 1902, p. 108. 
Concrete-steel Column Footing with Corrugated 
Bars. Eng. News, April, 1902, p. 273. 
Franklin Building Foundations, New York. Eng. 
Rec., May, 1898, p. 566. 

♦Breuchaud, J. The Underpinning of Heavy Build¬ 
ings. Trans. Am. Soc. Civ. Engs., Vol. 
XXXVII, p. 31. 

Hunt, Randall. The Design of Foundations for 
Tall Buildings. Jour. Assn. Eng. Socs., July, 
1896. p. 1. 

♦Murphy, Martin. Bridge Substructure and Foun¬ 
dations in Nova Scotia. Trans. Am. Soc. 
Civ. Engs., Vol. XXIX, p. 620. 


Marine Construction 


Sub-structure and Concrete Pier, White Shoal 
Light, Lake Michigan. Eng. Rec., June, 
1909, p. 735 . 

Sea Wall, Fort Morgan, Ala. Eng. Rec., Apr. 
I 9 ° 9 , P- 545 . 

Welcker, Rudolph. De Muralt System of 
Shore Protection. Eng. News, Dec., 
1908, p. 674. 

Judson, W. V. Reinforced Concrete Caissons 
for Breakwater at Algoma, Wis. Eng. 
News, Oct., 1908, p. 421. 

Improvement of Milwaukee Harbor. Eng. 

Rec., Oct., 1908, p. 452. 

Cameron, H. F. Sea Wall, Cebu, Philippine 
Isis. Eng. Rec., Apr., 1908, p. 544. 
Quay Walls for Dry Dock, Charleston, S. C., 
Navy Yard. Eng. Rec. Feb., 1908, 
p. 120. 


Harbor Work, Huron, Ohio. Eng. Rec., 
Oct., 1907, p. 45 o. 

Low, Emile. Breakwater at Harbor Beach, 
Mich. Eng. News, March, 1907, p. 339. 

The Racine Reef Lighthouse and Fog Signal 
in Lake Michigan. Eng. Rec., Mar., 
1907, P- 384. 

Docks, Port Chalmette, La. Eng. Rec., July, 
1906, p. 88. 

Pier, Atlantic City, N. J. Cement, July, 1906, 
p. 119. 

Connor, E. H. Wharf, Tampico, Mexico. 
Eng. News, June, 1905, p. 603. 

Pier, and Bulkhead Construction, New York 
Harbor. Eng. News, May, 1905, p. 503. 


Failure and Reconstruction of a Sea Wall. Clar¬ 
ence T. Fernald, Jour. Assn. Eng. Socs. 
June, 1903, p. 343- . , „ , „ T ' 

Hennebique System applied to Hydraulic Works. 
A. von Horn, Oest. Wochenschr. f. d. Oeff. 
Baucfienst, June 27, 1903. 

♦South Pier, Duluth, Minn Clarence Coleman. 

Cement, Sept , 1900, p. 141. 

Bruges Ship Canal, Belgium. 3,000 ton blocks. 

Eng. News, Nov., 1899, p. 300. 

Dock Wall, Clinton Ave., B-rooklyn, N. Y. Eng. 

Rec., Jan., 1897, p. 114. 

Monolithic Dock Foundations, Newcastle, Eng. 
Eng. News, April, 1895, p. 222. 


♦Breakwater Construction, Buffalo, N= Y. Emile 
Low, Trans. Am. Soc. Civ. Engs., Vol. LII, 
P- 73 - 

♦Concrete Breakwaters at various place?. Re¬ 
port Chief of Engs., U. S. A., 1900 an 
1901. 

Wharf at Portslade, Sussex, Eng. Joseph Cash, 
Pro. Inst. Civ. Engs., Vol. CXVIII, p. 392., 
Breakwater, near Middlesborough, Eng. Eng. 

News, Aug., 1893, p. 153. 

♦Colombo Harbour Works. John Kvle, Pro. Inst. 

Civ. Eng., Vol. LXXXVII, p. 76. 

♦Wicklow Harbour Improvements. W.G.Strype, 
Pro. Inst. Civ. Engs., Vol. LXXXVII, p. 114. 


Permeability and Porosity 


Davis, J. L. Tests on Water-retaining Ability 
of Stone and Concrete. Eng. News, July, 
1908, p. 130. 

Fuller and Thompson. Tests of Permeability. 
Trans. Am. Soc. Civ. Engrs., Vol. LIX, 
1907, P- 73 - ^ 

Feret, R. Tests of Permeability. Trans. 
Am. Soc. Civ. Engrs. Vol. LIX, 1907, p. 
157. 


Thompson, Sanford E. Tests of Permeability. 

Pro. Am. Soc. Test Mat. Vol. VI, p. 377. 
Method of Determining Porosity of Cement. 

Cement, May, 1905, p. 67. 

Thompson, Sanford E. Permeability Tests 
of Concrete with the Addition of Hydrated 
Lime. Am. Soc. Testing Mat., Vol. 
VIII, 1908. p. 5 oo. 


♦An asterisk precedes the references which are especially noteworthy. 





REFERENCES TO CONCRETE LITERATURE 


735 


♦Marston, A. Porosity of Sand-lime and Sand- 
cement Brick and Concrete Building Blocks. 
Eng. News, April, 1904. p. 387. 

Thompson, Sanford E. Results of French Experi¬ 
ments. Trans. Am. Soc. Civ. Engs., Vol. LI, 
p. 131. 

Am. Soc. Civ. Engs. Discussion on Impervious 
Concrete. Trans. Am. Soc. Civ. Engs., Vol. 
LI, p. 114. 

“•Thompson, Sanford E. Recommendations for 
Testing. Pro. Am. Soc. Civ. Engs., Aug., 
1903. 

Percolation Testing Machine for Cement. Cement, 
May, 1903, p. 88. 

McIntyre & True. Permeability under High Pres¬ 
sures. Eng. News, June, 1902, p. 517. 


Lang. Permeability to Air. Ann. des Trav. Pub. 
de Belgique, April, 1900. 

Hazen, Allen. Voids in Ordinary Concrete. 
Trans. Am. Soc. Civ. Eng., Vol. XLII, p. 128. 

Tetmajer. Tests. Tetmajer’s Communications, 
Vol. VI. 

Ross, H. H., Broenniman, A. E. Tests of Porosity 
of Neat Cement and Mortar. Jour. W. Soc. 
Engs., Vol. II, p. 449. 

French Commission. Standard Methods of Tests 
and Results of Tests. Commission des Me- 
thodes d’Essai des Materiaux de Construc¬ 
tion, 1893, Vol. I. 

♦Feret, R. Tests and Conclusions. Ann.desPonts 
et Chauss., 1892, II, p. 77. 


Protection of Metal 


Schaub, J. W. Silicate of Iron Formation, which 
is soluble in Water. Trans. Am. Soc. Civ. 
Engs., Vol. LI, p. 124. 

* American Society Civil Engineers. Discussion: 
The Preservation of Materials of Construction. 
Trans. Am. Soc. Civ. Engs., Vol., L, p. 293. 
Toch, Maximilian. The Permanent Protection of 
Iron and Steel. Jour. Am. Chem. Soc., 1903. 
Pabst Hotel Steel Frame, New York. Eng. News, 
Jan., 1903, p. 113. 


♦Norton, C. L. Tests to determine the Protection 
afforded to Steel by Portland Cement. Ins. 
Eng. Experiment Station, Reports No. IV 
and IX. Tech. Qr., Dec., 1902. 

♦Newberry, S. B. The Chemistry of Concrete-Steel 
Construction. Eng. News, April, 1902, p. 

. 335 - 

Action of Cinder Concrete on Steel. Eng. News, 
1897, p. 186. 


Reservoirs and Tanks 


Reservoir, Rolla, Mo. Eng. Rec., Mar., 1909, 
p. 322. 

Tufts, R. B. Water Tower, Atlanta, Ga. 

Eng. Rec., Jan., 1909, p. 9. 

Mater Tower, Grand Rapids, Mich. Eng. 

Rec., Dec., 1908, p. 662. 

Torrance, Wm. M. Reinforced Concrete 
Freezing Tanks. Eng. News, Dec., 1908, 
p. 641. 

Torresdale Preliminary Filters, Philadelphia. 

Eng. Rec., Nov., 1908, p. 577. 

Carver, George P. Coal Pocket, Charlestown, 
Mass. Eng. News, Aug., 1908, p. 229. 
Locomotive Coaling Station, Concord, Va. 

Eng. News, June, 1908, p. 690. 

Hudson, Wilbur G. Locomotive Coaling and 
Ash-Handling Plant, Elizabethport, N. J. 
Eng. News, Apr., 1908, p. 414. 

Elevated Water Tanks in Cuba. Eng. News, 
Apr., 1908, p. 471. 

Brewer, B. Storage Well, Waltham, Mass. 

Eng. Rec., Mar., 1908, p. 272. 

Septic Tank, Ithaca, New York. Eng. Rec., 
Feb., 1908, p. 136. 

Stewart, C. B. Tanks and Tubes for Experi¬ 
mental Purposes at University of Wis¬ 
consin. Eng. News, Jan., 1908, p. 3 °- 
Power Plant Reservoir, Cos Cob, Conn. Eng. 
Rec., Sept., 1907. P- 3 1 *. 


Circular Tanks, Lancaster Filtration Plant. 

Eng. Rec., feept. 1907, p. 298. 

Mater Tower, Anaheim, Cal. Eng. Rec., 
Aug., 1907, p. 203. 

Ellis, A. W. Sand Bins and Dryer. Con. 
^ Eng., Aug., 1907, p. 47. 

Coal lockets, Greensburg, Pa. Eng. Rec., 
May, 1907, p. 554. 

Collapse 9f Reservoir in Madrid, Spain. Beton 
u. Eisen, Apr., 1907, p. 106. 

Stand Pipe, Attleboro, Mass. Eng. News, 
Feb., 1907, p. 212. 

Reservoir, Waltham, Mass. Eng. Rec., Jan., 
1907, p. 32. 

Gas Holder Tank, New York City. Eng. 

Rec., Mar., 1906, p. 262. 

Water Tower, Bordentown, N. J. Eng. Rec., 
Jan., 1906, p. 39. 

Godfrey, Edward. A 75,000 Gallon Cistern, 
Allegheny, Pa. Eng. News, Sept., i 9 o5, 
P- 330 . 

Filtration Plant, Marietta, Ohio. Eng. Rec., 
Apr., 1905, p. 452. 

Doten, Leonard S. Y\ ater Tower and Stand¬ 
pipe, Fort Revere, Hull, Mass. Cement 
„ , Ag ?’ ^ e £-’ I9 ° 5 ’ p * 353 - 
Mechanical Filters, Hackensack, N. J. Eng. 

Rec., Nov., 1904, p. 590. 

Hot Well, New York Subway Power House. 
Eng. Rec., Nov., 1904, p. 611. 


Bins for Grain Elevator. Eng. News, June, 1904, 
P- 597 - 

♦Canadian Pacific Grain Elevator, Eng. Rec., 
April, 1904, p. 448. 

Tanks for Cornell University Filter Plant, Ithaca, 
N. Y. Eng. Rec., April, 1904, p. 444. 
Tanks for Acid Liquor under Pressure. A. C. 

Arend, Eng. News, April, 1904, p. 384. 
Reservoir, East Orange, N. J. Eng. Rec., March 
1904, p. 386. 

*8o-ft. Standpipe, at Milford, Ohio. Eng. News, 
Feb., 1904, p. 184. 

♦The Groined Arch Roof. Leonard Metcalf, Eng. 
News, Dec., 1903, p. 564. 


Cement Storage Tanks, Illinois Steel Company. 

Eng. News, Aug., 1902, p. 148. 

Swimming Tank for New York Apartment House. 

Eng. News, July, 1902, p. 17. 

Frankley Reservoir, Birmingham, Eng. Cement, 
March, 1902, p. 5. 

Reservoir Lining and Dome, Nyack, N. Y. J. H. 
Fuertes, Trans. Am. Soc. Civ. Eng., Vol. XLV. 
p. 492. > 

Tanks of Singer Manufacturing Co., Cairo, Ill. 

Cement, May, 1901, p. 88. 

Reservoir with Expanded Metal at Waalheim, 
Belgium. Rev. Tech., Oct. 19, 1900. 


*An asterisk precedes the references which are especially noteworthy. 




736 A TREATISE ON CONCRETE 


♦Reservoirs in the United States. Leonard Metcalf, 
Eng. News, Sept., 1903, p. 238. 

♦Filtration Works of the East Jersey Water Co. at 
Little Falls, N. J. Geo. W. Fuller, Trans. 
Am. Soc. Civ. Eng., Vol. L, p. 394. 

Works and Water Supply of the Butte Water Co. 
Chas. W. Paine, Jour. Assn. Eng. Socs., Oct.. 
ipo2, p. 143. 


Reservoir at Auvers, France. Rev. Tech., Vol. 
XXI, p. 385. 

Aussig, Bohemia Reservoir. Zeitschr. d. Oest. 

Ing. u. Arch. Ver., April 23, 1897.! 

Beton Tank in Water Tower. Monier. Calbe, 
Germanv.t Zeitschr. d. Ver. Deutscher Ing., 
March, 13, 1897. 

Sewage Tank. Paris. J. F. Flagg, Eng. Rec., 
Dec., 1896, p. 5. 


Sand and Stone, — Their Physical Characteristics 

(See also Strength of Concrete and Mortar^ 


Spackman and Lesley. Sands—Their Relation 
to Mortar and Concrete. Pro. Am. Soo. 
Test Mat., Vol. VIII, p. 429- 
Larned, E. S. The Importance of Sand in 
Concrete. Proc. Nat. Assn. Cem. Users, 
Vol. IV, p. 2o5. 

Am. Ry. Eng. & M. of W. Assn. Weight of and 
per cent, of Voids in Broken Stone. Eng. 
News, March, 1903, p. 284. 

Method of Washing Sand on Work of L. I. R. R. 

Eng. News, Dec., 1902, p. 519. 

♦Candlot, E. Nature of Sand and Yield of Mortars. 

Ciments et Chaux Hydrauliques, 1898, p 241. 
♦Wheeler, E. S. Change in Volume of Sand by 
Addition of Water. Rep. Chief of Engs., 
U. S. A., 1895, P- 2935. 

Sandeman. Voids in Different Stones. Pro. Inst. 

Civ. Engs., Vol. CXXI, p. 218. 

♦Feret, R. Experiments with Different Sands for 
French Commission. Commission des Me- 
thodes d’Essai des Materiaux de Construc¬ 
tion, Vol. IV, 1895, pp. 73 and 309. 


■’Thompson, Sanford E. Sand for Mortar and 
Concrete. Am. Port. Cem. Manf. Assn. 
Bulletin, No. 3, 1906. 

Concrete Aggregates. Nat. Assn. Cem. Users, 
1906, p. 27. 

Eckel, Edwin C. Specific Gravity of Stone and 
Cements. Eng. News, Sept., i 9 o5, p. 238. 

Hazen, Allen. Relation of Voids to Specific Grav¬ 
ity. Trans. Am. Soc. Civ. Eng., Vol. XLII. 
p. 126. 

Roper, W. H. Sand Washiug Machine. Eng. 
News, Feb., 1899, p. in. 

♦Hazen, Allen. Physical Properties of Sands and 
Gravels. Mechanical Analysis. Rep., State 
Board of Health of Mass., 1892. 

♦Feret, R. Density of Hydraulic Mortars. Granu¬ 
lometric Composition of Sand. Ann. des Ponts 
et Chauss., 1892, II. Bulletin de la Societe 
d’Encouragement pour 1 ’Industrie Nationale, 
1897, Vol. II, p. 1591. 

♦Alexandre, P. Experimental Researches on Hy¬ 
draulic Mortars. Ann. des Ponts et Chauss. 
1890, II, p. 277. 


Sea Water,—Its Effects Upon Concrete and Mortar 


Vetillart and Feret. Note on the Addition of 
Puzzolana to Mortars Setting in Sea 
Water. Ann. d. Ponts et Chaus, Vol. I, 
p. 121. 

Feret, R. A Quick Method for Comparing the 
Decomposition of Cements in Sea Water. 
Ann. d. Ponts et Chauss, Vol. I, p. 107. 


♦Le Chatelier, Rebuffat, Feret, etc. Papers in 
Congres Internationa! des Methodes d’Essai 
des Materiaux de Construction. Tome 2, 
1901, pp. 51, 79. 9i and 95. 

Schuljatschenko. The Destruction of Hydraulic 
Cement by the Action of Sea Water. Cement, 
Nov., 1901, p. 291. 

de Rochemont. Note sur la Decomposition des 
Ciments de Portland dans l’Eau de Mer. 
Ann. des Ponts et Chauss., 1900, IV, p. 281. 

Lidy, M. Alteration of Reinforced Concrete by 
Sea Water. Ann. des Ponts et Chauss., 1899, 
IV, p. 229. 

♦Feret, R. Addition of Puzzolanic Matter to Ce¬ 
ment. Chimie Appliquee, 1897, p. 490. 
Ann. des Ponts et Chauss., 1901, IV, p. 191. 

Candlot, E. The Influence of Sea Water on Mor¬ 
tars. Eng. Rec., Nov., 1897, p. 557. 

Michaelis, Wm. The Behaviour of Hydraulic 
Cements in Sea Water. Digest of Physical 
Tests, Feb., 1897, p. 198. 

*-The Action of Sea Water upon Hydraulig 

Cements. Pro. Inst. Civ. Engs., Vol. CXXIX, 
P- 325 - 


Thacher, Edw. Effect of Sea TV ater upon 
Concrete. Trans. Am. Soc. Civ. Engrs. 
Vol. LXL, p. 42. 

Examples of Tidal Injury to Concrete. Eng. 

News, Oct., 1908, p. 453. 

Effect^ of Sea TV ater at Charlestown Navy 
Yard. Eng. News, Aug., 1908, p. 238. 


♦ Ryle, John. Experience in laying Concrete in the 
Sea. Pro. Inst. Civ. Engs., Vol. CXXX, p. 183. 

Feret, R. Effect of size of Sand on Decomposition. 
Baumaterialienkunde, I, Jahrgang, 1896, 
P- 139 - 

Le Chatelier, H. Composition of Artificial Sea 
Water. Commission des Methodes d’Essai 
des Materiaux de Construction, 1895, Vol. IV, 
p. 279. 

-Methods of Testing Hydraulic Materials. 

Ann. des Mines, Sept, and Oct., 1893. 

Alexandre, P. Miscellaneous Mortar Experi¬ 
ments. Ann. des Ponts et Chauss., 1890, IJ, 
p. 277. 

♦English Authorities. Marine Construction in Eng¬ 
land. Pro. Inst. Civ. Engs., Vols. LXII 
LXVII, LXXXVII, CVII. CXI. 

Clarke, E. C. Tests. Trans. Am. Soc. Civ. Engs., 
Vol. XIV, p. 155. 

Beckwith, L. F. Action of the Sea on Beton-Coig- 
net. Trans. Am. Soc. Ciy. Engs., *VoL I, 
p. no. 


*An asterisk precedes the references which are especially noteworthy. 






REFERENCES TO CONCRETE LITERATURE 


737 


Sewers and Conduits 


Culbertson, M. S. Water Power Develop¬ 
ment at Loch Leven, Scotland. Eng. 
Rec., May, 1909, p. 56 o. 

Consaul, F. I. Concrete Block Sewer, Toledo. 

O. Eng. News, Feb., 1909, p. 123. 
Thompson, W. A. Outlet Sewer, E. St. Louis, 
Ill., Eng. News, Jan., 1909, p. ii5. 
Bronx Valley Sewer. Eng. Rec., Jan., 1909, 
P- 32. 

Smith, C. W. Reinforced Pipe for Carrying 
Water at High Pressure. Trans. Am. 
Soc.. Civ. Engs., Vol. LX, 190S, p. 124. 
Methods and Cost of Lining Ditches and 
Canals. Eng. Cont., Dec., 1908, p. 451. 
Reinforced Pipe with Reinforced Joint. Eng. 

News, Dec., 1908, p. 643. 

Details of Baltimore Sewerage System. Eng. 

Rec., Dec., 1908, p. 698. 

Triple Barrel Sewer, The Bronx, New York 
City. Eng. Rec., Apr. 1908, p. 409. 
Sewer as Flood Protection in Grand Rapids, 
Mich. Eng. Rec., Oct., 1908, p. 495. 
Big Cottonwood Waterworks Conduit, Salt 
Lake City, Utah. Eng. Cont., Aug., 
1908, p. 78. 

Pumping Station Conduits and Outfall Sewer, 
Washington, D. C. Eng. Rec., Aug., 
1908, p. 237. 

Conduits for Electric Cables, Long Island R. R. 
Eng. News, July, 1908, p. 90. 

Larned, E. S. Underground Conduits. Ce¬ 
ment Age, May, 1908, p. 496. 

Flat Top Concrete Spans for Waterways. 

Eng. Rec., Apr., 1908, p. 396. 

Details of Mold for 38-in. Concrete Pipe. 

Eng. Rec., Apr., 1908, p. 400. 

Taylor, Wm. flavin. Intercepting and Out¬ 
fall Sewer, Waterbury, Conn. Eng. 
News, Mar., 1908, p. 333. 


♦Standard Concrete Culvert, So. Mo. Ry. Chas. 

A. Sheppard, Eng. Rec., April, 1904, p. 478. 
♦Philadelphia Filtration System. Eng. Rec., Feb., 
1904, p. 191. 

♦Jersey City Water Supply Company Conduits. 

Eng. Rec., Jan., 1904, p. 72. 
Concrete-jacketed Steel Pipe under Hackensack 
River. Eng. News, April, 1903, p. 327. 
♦Concrete-Steel Culvert, Kalamazoo, Mich. Geo. 

S. Pierson, Eng. News, Feb., 1903, p. 163. 
Penstock at Grenoble, France. Eng. News, Jan., 
1903, p. 74. 

Harrisburg Intercepting Sewer. Cement, Nov., 
1902, p. 374. Eng. Rec., Oct., 1904, p. 444. 


Sewer Pipe Trestle across Los Angeles River 
Eng. Rec., Mar., 1908, p. 299. 

Concrete Pipe Drain and Outfall Sewers, 
Baltimore, Md. Eng. Rec., Feb., 1908, 
p. 163. 

Intercepting Sewer, Salt Lake City. Eng. 

• ^ eC- ’ Feb., 1908, p. 2x6. 

Main Conduit, Los Angeles Water System. 
Eng. Rec., Peb., 1908, p. 231. 

Conduit of Special Design, Ogden, Utah 
Eng. Rec., Jan., 1908, p. 65 . 

Harlem Creek Sewer, St. Louis, Mo. Eng. 
Rec., Dec., 1907, p. 664. 

Circular Trunk Sewer in Borough of Queens, 
N. \ . Eng. Rec., Nov., 1907, pp. 5i8 
and 599. 

Reinforced Sewers in Staten Island. Eng. 
Rec., Nov., 1907, p. 486. 

Siphon on an Irrigation Canal in Spain. Eng. 
News, Aug.,. 1907. p. 116. 

Sewer Construction under Brooklyn Subway. 
Eng. Rec., Aug., 1907, p. 228/ 

Catskill Aqueduct. Eng. Cont., Dec., 1906, 
P. 193- 

Buchartz, H. Method of Testing Clay and 
Concrete Pipes. Eng. Rec., Aug., 1906, 
p. 190. 

Hardesty, W. P. Conduit Ruilt of Block Sec¬ 
tions, Los Angeles, Cal. Eng. News, 
May, 1906, p. 596. 

Reinforced Pipe Sewers in St. Joseph, Mo. 
Eng. Rec., Apr., 1906, p. 543; May, 1906, 
p. 555 . 

Holmes, A. E. Reinforced Sewers at Des 
Moines, la. Eng. Rec., Apr., T906, p. 537. 

Ferguson, J. N. Charles River Standard 
Manholes and Crossings of Existing Over¬ 
flows. Eng. Rec., Mar., 1906, p. 301. 

Bursting Strength of Reinforced Concrete 
Pipes. Eng. Rec., Dec., 1905, p. 656 . 


Chicago Transfer and Clearing Co. Sewers. E. 

J. McCdustland, Cement, Sept., 1902, p. 265. 
New York Rapid Transit Sewers. Eng. News, 
March, 1902, p. 199. 

Paris Sewerage Disposal Works. Eng. News, 
March, 1898, p. 170. 

Paris Sewer under Pressure. A. Dumas, Gen. 

Civ., Vol. XXVIII, p. 277. 

Paris Sewers, their Dimensions and Cost. L. F. 
Beckwith, Trans. Am. Soc. Civ. Engs., Voi. I, 
p. 107. 


Specifications for Cement and Concrete 


Report of Joint Committee on Concrete and 
Reinforced Concrete. Proc. Am. Soc. 
Civ. Engs., Aug., 1909. 

Report of Committee on Reinforced Concrete. 
Proc. Nat. Assn. Cem. Users, Vol. V, 
1909. 

Lesley and Lazell. New, German Cement 
Specifications. Eng. News, Dec., 1908, 

Austrian Government Regulations for Con¬ 
crete and Reinforced Concrete Construc¬ 
tion. Cement, Feb., 1908, p. 377 . and 
Mar., 1908, p. 430. 

French Rules on Reinforced Concrete. Ce- 
ment Ag6, Nov., 1906, P« 4 IO > Sept., 
1907, p. 169. . . 

Report of British Joint Committee on Rein¬ 
forced Concrete. Eng. Rec., July, 1907, 
p. 103. 


C. B. & Q. R. R. Specifications for Culverts. 

Eng. Cont., Oct. 3, 1906, p. 86. 
Specifications for Reinforced Concrete, Na¬ 
tional Fire Protective Association. Eng. 
Rec., June, 1906, p. 716. 

Miller, R. P. Proper Legal Requirements for 
Use of Cement Construction. Eng. 
Rec., Apr., 1906, p. 538. 

Moisseiff, Leon S. German Specifications for 
Concrete Structures. Eng. News, Nov., 
1905, p. 478. 

Lesley, R. W. British Standard Specifica¬ 
tions for Cement. Proc. Am. Soc. Test. 
Mat. Vol. V, p. 363. 

Prussian Regulations for Reinforced Concrete 
in Building Construction. Eng. Rec., 
July, 1904, p. 25 . 


*An asterisk precedes the references which are especially noteworthy. 





73 8 


A TREATISE ON CONCRETE 


♦Thompson, Sanford E. Recommendations for 
Testing Compression, Bending, Adhesion, 
Porosity, and Permeability. Pro. Am. Soc. 
Civ. Engs., Aug., 1903, p. 645. 

Can. Soc. C. E. Canadian Standard Specifica¬ 
tions for Portland Cement. Cement, May, 
1903, p. 98. 

♦Am. Soc. C. E. Committee, Standard Specifica¬ 
tions. Pro. Am. Soc. Civ. Engs., Jan., 1903. 

Swiss Societies. The new Swiss Standards com¬ 
pared with the old. Schw. Bau., April 19, 
1902, p. 173. 

♦Am. Ry. Eng. & M. W. Assn. Specifications for 
Portland Cement Concrete and for Portland 
and Natural Cements. Eng. News, March, 
1902, p. 246, and March, 1903, p. 284. 

Newberry, S. B. Report of Assn, of German Port¬ 
land Cement Manufacturers. Cement, Jan., 
1902, p. 350. 

Jameson, C. D. German Specifications for stand¬ 
ard Portland Cement Tests. Portland Ce¬ 
ment, 1898, p. 80. 

♦Feret, R. Studies on the Intimate Composition of 
Hydraulic Mortars. Bulletin de la Societe 
d’Encouragement pour l’Industrie Nationale, 
1897, Series 5, Vol. II, p. 1591. 

Le Chatelier, H. Methods of testing Hydraulic 
Materials. Ann. des Mines, Sept, and Oct., 
1893. 

Strength in Compression of 

Howard, J. E. Compressive Strength of 
Concrete Prisms and Columns. Tests of 
Metals, 1904, 1905, 1906, 1907, 1908. 

Fuller, W. B., and Thompson, Sanford E. Law 
of Proportioning Concrete. Trans. Am. 
Soc. Civ. Engrs., Vol. LIX, p. 67. 


Johnson, J. B. Quotations from various authori¬ 
ties. Materials of Construction, 1903, p. 603. 

McCaustland, E. J. Strength and Elasticity of 
6-inch cubes and 10-inch Columns. Trans. 
Am. Soc. Civ. Eng., Vol. L, p. 482. 

Clark, T. S. Effect of Mica in the Stone. Eng. 
News, July, 1902, p. 68. 

Costigan, J. S. Tests of Concrete Cubes. Eng. 
Rec., 1902, p. 393. 

Carson, H. A. Prisms of Pebbles vs. Gravel vs. 
Trap Concrete. Tests of Metals, U. S. A., 
1901, p. 617. 

Clarke & Son, William Wirt. Cubes of Stone and 
Gravel Concrete, with Natural Cement. Tests 
of Metals, U. S. A., 1901, p. 609. 

♦Watertown Arsenal. Miscellaneous Tests, includ¬ 
ing the effect of Retarded Set and the effect 
of Plaster Adulteration. Tests of Metals, 

U. S. A., 1901, p. 471. 

Kingsley, M. W. Slag vs. Limestone. Tests of 
Metals, U. S. A., 1900, p. 1099. 

♦Henby, W. H. Tables of Tests and Curves for 
Stone and Cinder Concrete. Jour. Assn. Eng. 
Socs., Sept., 1900, p. 152. 

Hawley & Krahl. 6-inch Cubes with different per¬ 
centages of Voids. Eng. News, June, 1900, 

P- 375 - 

Boston Transit Com. 1:2:4 Prisms at different 
ages. Tests of Metals, U. S. A., 1899, p. 839. 

U. S. Engineer Corps, Fla. Concrete of Brick, 
Sand, and Gravel. Tests of Metals, U. S. A., 
1899, p. 835. 

♦Watertown Arsenal. 12-inch Cubes of Mortar and 
Concrete with different sizes of Stone and 
Gravel and Brick. Tests of Metals, U. S. A., 
1898, p. 575; 1899, p. 783;i9oi, p. 600; 1902, 

P- 51 . 3 - 

*An asterisk precedes the references 


*U. S A. Engineers. Testing Hydraulic Cements. 
Prof. Papers No. 28, U. S. A., 1901. 

♦Humphrey, R. L. The Inspection and Testing of 
Cements. Jour. Fr. Inst., Dec., 1901, Jan. 
and Feb., 1902. 

Assn. Ry. Supts. of B. & B. Specifications of 
Various Railroads. Pro. Assn. Ry. Supts., 
1900. 

Butler, D. B. German and French Specifications 
for Standard Portland Cement Tests. Port¬ 
land Cement, pp. 330 and 340. 

♦Thacher, Edwin. Specifications for Concrete and 
Concrete-steel. Eng. News, Sept., 1899, 
P- 179 - . 

Candlot, E. Cement Specifications for French and 
German Public Works. Ciments et Chaux 
Hydrauliques, 1898, p. 375. 

-Tests of Hydraulic Products. Ciments et 

Chaux Hydrauliques, 1898, p. 184. 

♦French Commission. Recommendations for Tests 
of Cement. Commission des Methodes d’Essai 
des Materiaux de Construction, Vol. I, 1893. 

Faija, H. The Manufacture and Testing of Port¬ 
land Cement. Trans. Am. Soc. Civ. Eng., 
Vol. XXX, p. 43. 

♦A. S. C. E. Committee. Uniform tests of Cement. 
Trans. Am. Soc. Civ. Eng., Vol. XIII, p. 53. 
Trans. Am. Soc. Civ. Eng., Vol. XIV, p. 475. 
Pro. Am. Soc. Civ. Eng., Jan., 1903, p. 2. 

Plain Concrete and Mortar 

Woolsen, Ira H. Tests of Concrete at Col¬ 
umbia University. Eng. News, June, 
1905, p. 56 i. 

Thompson, Sanford E. Strength of Concrete. 
Jour. Assn. Eng. Socs., Apr., 1905, p. 171. 


Black, W. M. Gravel and Stone Concrete, Natural 
and Portland Cement. Rep. Eng. Dep., D. G. 
1898. 

Aberthaw Construction Co. Columns of varying 
heights and proportions, Hand and Machine 
Mixed. Tests of Metals, U. S. A., 1897, 
P- 35 i- 

♦Talbot, A. N. Stone Screenings vs. Sand in Con¬ 
crete. Jour. W. Soc. Engs., Aug., 1897, 
P- 39 i- 

Gary, Max. Roman Cement, and Portland Ce¬ 
ment Mortar Cubes, and mixed Roman and 
Portland. Also Lime 1:2. Baumaterialen- 
kunde, Vol. V, Heft 14, p. 217. 

Magens. Safe strength with different proportions. 
Kleinen Cement Buchs. Deutsche Bau., Vol. 
XXXI, p. 636. 

Dyckerhoff, R. Cubes of different proportions. 
Portland Zement, Berlin, pp. 90, 94 and 112. 

♦Bruce, A. Fairlie. Experiments on the Strength 
of Portland Cement Concrete. Pro. Inst. 
Civ. Eng., Vol. CXIII, p. 220. 

Worcester Polytechnic Institute. Prisms of differ¬ 
ent proportions. Eng. News, Nov., 1896, 
p. 302.. 

Patton. 6-inch and 12-inch Cubes, compressed 
and not compressed. Civ. Eng., 1895, p. 306. 

Simeon, P. Studies of Form for Compression 
Specimens. Commission des Methodes d’Es¬ 
sai des Materiaux de Construction, 1895, Vol. 
IV, p. 187. 

♦Feret, R. Tests of Mortars under various condi¬ 
tions. Complete Tables and Curves. Ann. 
des Pontset Chauss., 1892. II, p 117. Societe 
d’Encouragement pour l’lndustrie Nationale, 
1897, Series 5, Vol. II, p. 1591. Chimie Ap- 
pliquee. 1897. 

which are especially noteworthy. 




REFERENCES TO CONCRETE LITERATURE 


739 


♦KimDau, George A. 12-inch Cubes of different 
proportions. Tests of Metals, U. S. A., 1899, 
p. 717. 

Rogers, W. A. Gravel vs. Hard Stone vs. Soft 
Stone Concrete. Eng. News, Dec., 1899, p. 
386. 

Mass. Institute of Technology. 2-inch Cubes of 
Cement and Mortar, and tests of same Mate¬ 
rials in Tension. Tech. Qr., 1899, Vol. XII, 
pp. 239-244. 

Rogers, VV. A. 12-inch Cubes of different propor¬ 
tions, Portland and Natural Cement. Ry. & 
Eng. Rev., Feb., 1899, p. 88. 

♦Candlot, F.. Tests of Mortar and Concrete of 
various proportions, aggregates and condi¬ 
tions. Ciments et Chaux Hydrauliques, 1898. 

*Watertown Arsenal. 12-inch Cubes of Cinder 
Concrete. Tests of Metals, U. S. A., 1898, 
p. 561. 

♦Rafter, George W. Tests with different percent¬ 
ages of Mortar, varying consistency and differ¬ 
ent Stones. Tests of Metals, U. S. A., 1898, 
P- 4 i 5 - 


♦Alexandre, P. Experimental Researches on Hy¬ 
draulic Mortars. Ann. des Ponts et Chauss., 
1890, II, p 277. 

Grant, John. Concrete with various aggregates. 

Pro. Inst. Civ. Engs., Vol. XXXII, p. 299. 
Am. Soc. C. E. Committee. Tests of Cubes and 
Prisms of different heights. Trans. Am. Soc. 
Civ. Engs., Vol. XVIII, p. 266. 

Von Mauk. 8-inch Cubes of different proportions. 

Portland Zement, Berlin, p. 92. 

Kyle, John. Concrete and Mortar Cubes. Pro. 

Inst. Civ. Eng., Vol. LXXXVII, p. 88. 
Unwin, W. C. Formula for rate of hardening of 
Cement. Pro. Inst. Civ. Engs., Vol. LXXXIV, 
p. 400. 

Hamilton, Schuyler. Tests comparing Concrete of 
Cement and of Hydraulic Lime. Trans Am. 
Soc. Civ. Engs., Vol. IV, p. 98. 

Cubes of different proportions. Otto Lueger’s 
Lexikon der Gesamter Technik, Vol. II, 
P- 295. 


Strength in Tension of Plain Concrete and Mortar 


Johnson, J, B. Tests from various authorities 
illustrating different Mixtures and Conditions 
Materials of Construction, 1903, p. 568. 

Taylor and Thompson. Variation in Strength of 
Mortars. Cement, July, 1903, p. 165. 

Duryec, Edw. Tests of Sand Cement. Eng. 
News, May, 1903, p. 487. 

♦Griesenauer, G. J. Comparative Tests of Lime¬ 
stone and Gravel Screenings and Torpedo 
Sand. Eng. News, April, 1903, p. 342. 

Clark, T. S. Stone Dust versus Sand in Mortar. 
Eng. News, July, 1902, p. 68. 

Taylor, Harry. Tests of various Sands. Rep. 
Chief of Eng., U. S. A., 1902, p. 2455. 

Carson, H. A. Tests on Concrete Briquettes. 
Eighth Rep. Boston Transit Com., 1902, p. 62. 

Humphrey, R. L. The Inspection and Testing of 
Cements. Jour. Fr. Inst., Dec., 1901, Jan. 
and Feb., 1902. 

Hatt, W. K, Tests of 4 brands of Slag Cements 
and Diagram. Pro. Ind. Eng. Soc., 1901, 
p. 45 - 

♦Henby, W. H. Tables and Curves for various 
Concrete Mixtures. Jour. Assn. Eng. Socs., 
Sept., 1900, p. 145. 

Ana. Soc. C. E. Committee. Answers to questions 
propounded to various authorities. Pro. Am. 
Soc. Civ. Eng., April, 1900, p. 99. 

U. S. A. Engineers. Tests of Puzzolan Cement. 
Rep. on Steel Portland Cement, 1900. 

♦Humphrey, R. L. Tests of Natural and Portland 
Cement. Pro. Engs., Club of Phila., May, 
1899, p. 178. 

♦Candlot, E. Tests of Strength of Hydraulic Limes, 
Cements, and Mortars. Ciments et Chaux 
Hydrauliques, 1898, pp. 399 and 410. 

♦Dow, A, W. Tests from one day to 4 years Neat 
and with Sand. Rep. Eng. Dept., D. C., 
1898, p. 120. 

Joly, M. de. Experiments on Strength and Elas¬ 
ticity. Ann. des Ponts et Chauss., 1898, III, 
p. 198. 


Gary, M. Comparative Tests of Standard Sands 
from different countries. Baumaterialen- 
kunde, 1898. 

Lundteigen, Andreas. Notes on Portland Cement. 
Trans. Am. Soc. Civ. Eng., Vol. XXXVII, 
p. 501. 

Thompson, Sanford E. Tests of Mortar from Neat 
to 1: 9 at Holyoke Dam. Eng. News, May, 
1897, p. 294. 

♦Feret, R. Mortars of Fine Sand. Baumaterialien- 
kunde, I Jahrgang, 1896, p. 139. 

Baker, I. O. Mortars affected by different qualities 
of Sand. Jour. W. Soc. Engs., Jan., 1896, 
P- 73 - 

Wheeler, E. S- Experiments with different Sands 
at different Ages. Rep. Chief of Engs., U. S. 
A., 1895, pp. 2953 and 3013; 1896, pp. 2829 
and 2862. 

Cooper, A. S. Experiments with different Sands. 
Jour. Fr. Inst., Vol. CXL, p. 326. 

♦Feret, R. Miscellaneous Tests of Strength. Ann. 
des Ponts et Chauss., 1892, II, p. 117. 

Russell, S. B. Neat Tests vs. Sand Tests for Port¬ 
land Cement. Trans. Am. Soc. Civ. Eng., 
Vol. XXV, p. 295. 

♦Alexandre, P. Experimental Researches on Hy¬ 
draulic Mortars. Ann. des Ponts et Chauss., 
1890, II, P- 277. 

Faija, H. Portland Cement Testing. Trans. Am. 
Soc. Civ. Eng., Vol. XVII, P- 218. 

Whittemore, D. J. Tensile Tests of Cement. 
Trans. Am. Soc. Civ. Eng., Vol. IX, p. 329. 

Maclay, W. W. Notes and Experiments on the 
Use and Testing of Portland Cement. Trans. 
Am. Soc. Civ. Eng., Vol. VI, p. 311. 

Beckwith, L. F. Strength of Beton-Coignet. 
Trans. Am. Soc. Civ. Eng., Vol. I, p. 100. 

♦Grant, John. Time Tests of Lime, Cement, and 
Mortars. Pro. Inst. Civ. Eng., Vol. XXV. 
p. 88, XXXII, p. 280, LXII, p. 165. 


Strength of Beams and Arches of Plain Concrete and Mortar 

Carson, Howard A. Tests of Reinforced Beams. Carson, H. A. Screenings vs. Sand in Concrete 
Report Boston Transit Commission. 1904. Beams. Eighth Rep., Boston Transit Com. 

Falk, Myron S. Stress in Concrete and Mortar 1902, pp. 61 and 63. _ 

Beams. Tables and Curves. Trans. Am. —-- Clean vs. Dirty Gravel in Beams. Seventh 

Soc. Civ. Eng., Vol. L, p. 473. ReDt. Boston Transit Com., 1901, p. 39. 

Clark, T. S. Tests of Neat Portland Cement Moore, Robert. Tests 1: 3: 6 Limestone Concrete. 
Beams, and relation between Tensile and Eng. Rec., Feb., 1900, p. 187. 

Transverse Strength. Eng. News, July, 1902, Contractors Plant Co. Table of Transverse Tests. 
6g'_ Tests of Metals, U. S. A., 1900, p. mo. 


♦An asterisk precedes the references which are especially noteworthy. 



740 


A TREATISE ON CONCRETE 


von Schon, H. Tests with various Mixtures. 

Trans. Am. Soc. Civ. Eng., Vol. XLII, p. 139. 
MoIIer, M. Testing a Concrete Girder. Pro. 

Inst. Civ. Eng., Vol. CXXXIX, p. 435. 
♦Talbot, A. N. Concrete with Screenings vs. Sand. 

Jour. W. Soc. Engs., Aug., 1897, p. 394. 
♦Wheeler, E. S. Tests of Beams at St. Mary’s Falls. 

Rept. Chief of Engs., U. S. A., 1895, p. 2924. 
Durand-Claye. Relation of Tension to Flexion. 
Commission des Methodes d’Essai des Ma- 
teriaux de Construction, 1895, Vol. IV, p. 211. 
♦Abbott & Morrison. Comparison of Flexure and 
Tension. Eng. News, Dec.. 1893, p. 466. 


♦Bruce, A. F. Experiments at Glasgow, with for¬ 
mula for growth in Strength. Pro. Inst. Civ. 
Eng., Vol. CXIII, p. 217, and Vol. CXVIII, 
p. 389. 

Kyle, John. Stone and Gravel Concrete of differ¬ 
ent proportions. Pro. Inst. Civ. Eng., Vol. 
• LXXXVII, p. 88. 

Hutton, D. Shingle Concrete of different propor¬ 
tions. Pro. Inst. Civ. Eng., Vol. LXII, p. 196. 
Lowcock, Richard. Tests and Formulas. Pro. 
Inst. Civ. Eng., Vol. Ill, p. 356. 


Strength of Reinforced Concrete 


Withey, M. O. Tests of Plain and Reinforced 
Concrete Columns. Eng. Rec., July, 
1909, p. 41. 

Talbot, A. N. Tests of Reinforced Concrete 
Beams: Resistance to Web Stresses. 
Univ. of Illinois Bulletin No. 29, 1909. 
Talbot, A. N. Tests of 3 Large Reinforced 
Concrete Beams. Univ. of Illinois Bul¬ 
letin No. 28, 1908. 

Thompson, Sanford E. Discussion on Con¬ 
crete Columns. Trans. Am. Soc. Civ. 
Engs., 1908, Vol. LXI, p. 46. 

Lindau, A. E. Analysis of Semicircular Arch. 
Trans. Am. Soc. Civ. Engs., 1908, Vol. 
LXI, p. 387. _ 

Cantilever Girders, Philadelphia, Pa. Eng. 

News, Apr., 1908, p. 447. 

Van Ornum, J. L. The Fatigue of Concrete 
Beams. Trans Am. Soc. Civ. Engs., 
Vol. LVIII, p. 294. 

Tirrell, C. E. Concrete Girders, 75-foot Span. 

Eng. News, Dec., 1907, P- 633. 

Moisseiff, L. S. Compression Tests of French 
Government, Cement, Sept., 1907, P. 

175. 

Diagrams for Design of Beams. Eng. News, 
July, 1907, p. 28. 

Talbot, A. N. Tests of Reinforced Concrete 
T-Beams. Univ. of Illinois Bulletin No. 
12, 1907. 

Hatt, W. K. Effect of Time Element in 
Loading. Proc. Am. Soc. Test. Mat., 
1907, p. 421. 

McKibben, F. P. Loads, Bending Moments 
and Shears for Bridges. Eng. News, 
Apr., 1907, p. 372. 

Talbot, A. N. Tests of Concrete Columns. 
Univ. of Illinois Bulletin No. 10, 1906, and 
No. 20, 1907. 


Thullie, Dr. M. R. V. Column Tests. Beton 

u. Eisen, Heft II, 1907, p. 43. 

Sewell, J. S. Economical Design of Rein¬ 
forced Concrete Floor Systems. Trans. 
Am. Soc. Civ. Engs., Vol. LVT, 1906, p. 
2 52 

Withey, M. O. Tests of Plain and Rein¬ 
forced Concrete. Univ. of Wisconsin 
Bulletin No. 197, 1907, and No. 175, 
1906. 

Jonson, E. F. Theory of Continuous Col¬ 
umns. Trans. Am. Soc. Civ. Engs., Vol. 
LVI, p. 92. 

French, A. W. Reinforced Concrete Beams 
and Floor Systems. Trans. Am. Soc. 
Civ. Engs., Vol. LVI, 1906, p. 360. 

Dana, R. T. A Rapid Method of Calculation 
of Reinforced Concrete Sections. Eng. 
Rec., Sept., 1906, p. 249. 

Thompson, Sanford E. Discussion on Plain 
and Reinforced Columns. Proc. Boston 
Soc. Civ. Engs., Sept., 1906. 

♦Howard. J. E. Tests of Columns. Eng. 
News, July, 1906, p. 20. Tests of Metals, 
1905, 1906, 1907, 1908. 

Goldmark, H. Discussion of Formulas for 
Beams. Eng. Rec., Mar., 1906, p. 420. 
Talbot, A. N. Tests of Reinforced Concrete 
Beams. Univ. of Illinois Bulletin No. 
1, 1904; No. 4, 1906. 

Harding, J. J. Tests of Reinforced Concrete 
Beams. Eng. News, Feb., 1906, p. 168. 
Condron, T. L. Strength of Reinforced Con¬ 
crete Munic. Eng., Sept., 1905, p. 167. 
Tests of Efficiency of Vertical Stirrups, Bush 
Terminal. Eng. News, July, 1905, p. 5. 
Elwitz, E. Economic Beam Designs. Beton 
u. Eisen, Heft II, 1905, p. 38. 


♦Talbot, A. N. Tests of Reinforced Beams. Pro. 

Am. Soc. Test. Mat., 1904. 

♦Turneaure, F. E. Tests of Reinforced Beams. 

Pro. Am. Soc. Test. Mat., 1904 
♦Marburg, Edgar. Tests of Reinforced Beams. 

Pro. Am. Soc. Test. Mat., 1904. 

♦Howe, M. A. Tests of Reinforced Beams. Jour. 
W. Soc. Engs., 1904. 

♦Prussian Regulations for Reinforced Concrete in 
Building Construction. Eng. Rec., July, 
1904, p. 25. 

Johnson, L. J. Tests of Reinforced Beams. Jour. 

Assn. Eng. Socs., June, 1904, p. 308. 

Am. Ry. Eng. & M. of W. Assn. Rept. Com. on 
Steel-concrete, 1904. 

French, Gov. Com. Preliminary Conclusion on 
Reinforced Concrete. Cement, Jan., 1904, 

p. 414- 

♦Considere, A. Test of a 65-ft. Truss Bridge. 

Ann. des Ponts et Chauss., 1903, III, p. 5. 
♦Considere, A. Concrete-Steel and Hooped Con¬ 
crete. Reinforced Concrete. 1003, p. 119. 


♦ Burr, Wm. H. Theories of Steel Reinforcement. 
Elasticity and Resistance of the Materials of 
Engineering, 1903, p. 619. 

New York Bureau of Buildings. Regulations in 
regard to the Use of Concrete-Steel. Eng. 
Rec., Oct., 1903, p. 429. 

Bortsch, Robert. A Graphostatical Investigation 
of Compound Bodies of Concrete and Iron. 
Oest. Wochenschr. f. d. Oeff. Baudienst, July 
4, 1903. 

♦Schaub, J. W. Diagram and Formula for deter¬ 
mining Percentage of Steel in Beams. Eng. 
News, April, 1903, pp. 348 and 392. 

Johnson, A. L. Steel-Concrete Construction. 

R. R. Gazette, March 13, 1903, p. 183. 
♦Thacher, Edwin. Tests, Formulas, and Tables for 
Beams and Slabs. Cement, July, 1902, p. 
179. 

Sewell, J. S. Tests of Concrete Steel Slabs. Eng. 
News, Jan., 1903, p. 112. 


*An asterisk precedes the references which are especially noteworthy. 



REFERENCES TO CONCRETE LITERATURE 


74i 


Ramisch, O. Influence Lines. Beton & Eisen, 
II Heft, 1903, p. 122. 

Thullie, Max R. v. Shearing Stresses in Rein¬ 
forced Concrete Beams. Beton & Eisen, II, 
Heft, 1903, p. 117. 

♦Sanders, L. A. Comparative Tests upon Rein¬ 
forced Concrete. Beton & Eisen, I Heft, 
1903, p. 27, and II Heft, 1903, p. 94. 

*von Emperger, Fritz. Tests of Beams and Slabs 
of Steel-Concrete. Beton & Eisen, 1903, 
Heft I, p 23; Heft II, p. 94; Heft III, pp. 181 
and 195. 

Rabut, M. Rupture Tests upon Hennebique 
Floors. Beton & Eisen. I Heft, 1903, p. 17. 

Ribera, At. J. Eugenio. Details of Computation of 
a Reinforced Arch of 35 metres Span. Beton 
& Eisen, I Heft, 1903, p. 1. 

Tests of Hennebique Arch Bridge, Chattelerault, 
France. Cement, July, 1902, p. 169. 

♦Hatt, W. K. Theory of Reinforced Beams. Eng. 
News, Feb., 1902, p. 170. 

Spitzer, J. A. Development of Reinforced Con¬ 
crete Construction. Zeitchr. d. Ing. u. Arch. 
Ver. Oest., Jan., 1902, p. 73, 

Carson, H. A. Tests of Reinforced Concrete 
Beams. Eighth Rept., Boston Transit Com., 
1902, appendix V. 

Tests of Concrete Floors of various systems. Jour. 
Assn. Eng. Socs., Feb., 1901, pp. 73 to 148. 

Molitor, David. Theories of Masonry and Con¬ 
crete-steel Arches. Jour. Assn. Eng. Socs., 
Jan., 1900, p. 46. . 

Rosshander, Josef. Theory and Applications of 
Concrete-Iron Construction. Schw. Bauz., 
Sept. 8, ipoo.f 

Barberis, C. Hennebique Slabs Tested. Rivista 
di Artiglieria e Genio, 1900, Vol. Ill, p. 122. 

Hoch, A. Testing a Concrete Bridge Arch. Pro. 
Inst. Civ. Engs., Vol. CXXXIX, p. 436. 

♦Noe, Harel de la. Theory and Recent Applications 
of Reinforced Concrete. Ann. des Fonts et 
Chauss., 1899. 1 " 


Considere, M. Variations in Volume. Influence 
of Reinforcement. C imptes Rendus, Sept. 
18, 1899 + 

♦Tedesco, N. de. Construction in Reinforced Ce¬ 
ment. Ing. Civ. de France, Jan., 1899T 
Hill, George. Steel-Concrete Construction; Tests 
of Slabs, Tables and Formulas. Discussion. 
Trans. Am. Soc. Civ. Eng., Vol. XXXIX, 
p. 617. 

Lavergne, Gerard. Reinforced Cement Construc¬ 
tions. Genie Civ., Nov. 12, 1898, p. 22. 
Thullie, M. R. v. The Computation of Stresses in. 
Monier Arches. Zeitschr. Oest. Ing. u. Arch. 
Ver., Sept., 1898,! P- 549- 
Osaenfeld, A. Calculations for the Monier System 
of Construction. Zeitschr. d. Oest. Ing. u. 
Arch. Ver., Jan., 1898.+ 

Hermanek, J. The Influence of Temperature 
Changes on Concrete-Steel Construction. 
Zeitschr. d. Oest. Ing. u. Arch. Ver., Dec., 
1897,f p. 694. 

Aberthaw Construction Co. Tests of Columns 
Plain and Reinforced. Tests of Metals, U. S. 
A., 1897, p. 355. 

Johnson, J. B. Calculation of Ultimate Strength 
of Concrete-Steel Beams. Eng. News, Oct., 
1897, p. 261. 

von Emperger, F. The Theory of Reinforced 
Beton Beams. Zeitschr. d. Oest. Ing. u. Arch. 
Ver., May, p. 351, and June, 1897,+ p. 364. 
Spitzer, Josef Anton. The Theory of Concrete- 
Steel Construction. The Monier Arch. Zeit¬ 
schr. d. Oest. Ing. u. Arch. Ver., Jan., 1897,f 
p. 26. 

Marstrand, O. J. Strength of Monier Plates. 

Eng. News, July, 1896, p. 32. 

Melan, J. Concerning the Computations for Con¬ 
crete-Iron Construction. Oest. Monatschr. 
f. d. Oeff. Bau., Dec., 1896.! 
von Emperger, F. Tests on Brick, Concrete, and 
Steel-Concrete Arches. Eng. News, Aug., 
1893. P- I 57 * 


Strength of Cement Affected by Admixtures 


alcohol 

Tetmaicr, L. Curves showing Effect of Addi¬ 
tion. Tetmajer, Vol. VII, p. 24. 

CLAY AND LOAM 

Effect of Clay in Cement Mortar. Eng. Rec. 
June, 1907, p. 70 3 - 

Thompson, Sanford E. Impurities in Sand 
for Concrete. Trans. Am. Soc. Civ. 
Engs., 1909. 

Hain, J. C. Tests of Impure Sand for Con¬ 
crete. Eng. News, Peb., 1906, p. 127. 

The Effect of Loam on Concrete. Eng. Rec., 
July, 1904. P- 89- 

♦Griesenauer, G. J. Tests of Loam and C lay 
in Sand. Eng. News, April, 1904, p. 
4i3- 

♦Sherman, C. E. Experiments and Dia¬ 
grams. Eng. News, Nov., 19° 3 » P- 443 - 
Richey, and Prater. Table of Tests. Tech¬ 
nograph, 1902-3, p. 36. 

Wheeler, E. S. Tests. Rept. Chief of Engs. 
U. S. A., i 8 9 5 , p. 3002; 1896, pp. 2826 

and 2830. . , _ , „ 

Grant, W. H. Test of Mortar with Sand Con¬ 
taining Clay. Trans. Am. Soc. Civ. Engs. 
Vol. XXV, p. 269. 


Clarke. E. C. Tests of Rosendale Mortar Con¬ 
taining Loam. Trans. Am. Soc. Civ. 
Engs., Vol. XIV, pp. 163 and 164. 

GLYCERINE 

Tetmajer, L. Curves showing Effect of 
Addition of Glycerine. Tetmajer, Vol. 
VII, p. 24. 

LIME 

Lazell, E. W. Hydrated Lime and Cement 
Mortars. Proc. Am. Soc. Test. Mat., 
Vol. VIII, 1908, p. 418. 

Alexandre, P. Tests of Strength. Ann. des. 

Ponts et Chauss., 1890, II, p. 306. 

Candlot, E. Table of Tests of various Mixtures 
of Cement, Lime, and Sand. Ciments et 
Chaux Hydrauliques, 1898, p. 293 
♦Feret, R. Tests. Chimie Appliquee, p. 480. 


PEAT 

irant, John. Experiments with Lime and Cement 
Mortar. Pro. Inst. Civ. Engs., Vol. LXII, 
p. 160. 

Jeven, O. Experiments. Pro. Inst. Civ. Engs., 
Vol. LXXXVIII, p. 463- 


*An asterisk precedes the references which are especially noteworthy. 


742 


A TREATISE ON CONCRETE 


PLASTER 

♦Watertown Arsenal. Curves and Tables. Tests 
of Metals, U. S. A., 1901, p. 507. 

♦Candlot, E. Influence of Chloride of Calcium and 
of Sulphate of Lime on the Setting and Hard¬ 
ening of Mortars. Ciments et Chaux Hy- 
drauliques, 1898, p. 318. 

Wheeler, E. S. Tests. Rept. Chief of Engs., U. 
S. A., 1896, p. 2854. 

Tetmajer. Tests. Tetmajer, Vol. VII, p. 39. 


PUZZOLAN CEMENT 

♦Feret, R. Chimie Appliquee, 1897, p. 490. 


SALT 


Johnson, J. B. Tests quoted from various author¬ 
ities. Materials of Construction, 1903, p. 615. 
♦Wheeler, E. S. Tests. Rept. Chief of Engs., 
U. S. A., 1895, pp. 2955, 2968; 1896, p. 2829. 
Hill, W. F. Tests at Cornell University. Eng. 


News, May, 1895, p. 282. 

Carey, A. E. Tests. Pro. Inst. Civ. Engs., Vol. 
CVII, p. 40. 


SAWDUST 

Wheeler, E. S. The Use of Sawdust in Portland 
Cement Mortar. Rept. Chief of Engs., 
U. S. A., 1896, p. 2866. 


SODA 


Hatt, W. K. Strength Affected by Soda, Alum 
Soap, etc. Trans. Am. Soc. Civ. Engs., Vol 
LI, p. 128. 

Carey, A. E. Tests. Pro. Inst. Civ. Engs., Vol. 
CVII. 


SUGAR 


Carey, A. E. Tests. Pro. Inst. Civ. Engs., Vol. 
CVII, p. 71. 


TALLOW 

Clarke, E. C. Experiments with Briquettes of Ce¬ 
ment and Tallow. Trans. Am. Soc. Civ. 
Engs., Vol. XIV, p. 165. 


Strength of Concrete and Mortar Affected by Frost and Heat 


Aberthaw Construction Co. Tests of Effect 
of Low Temperature on Setting. Eng. 
News, March, 1909, p. 257. 

Goodrich, E. P. Use of Concrete in Freezing 
Weather. Cement and Eng. News, Dec., 
1907, p. 279. 

Gow, C. R. Tests of Concrete Piles Frozen 
and Thawed. Jour. Assn. Eng. Socs., 
Oct., 1907, p. 263. 


♦Gowen, C. S. Tests of Portland Cement Mortar 
exposed to cold. Pro. Am. Soc. for Test. 
Mat., 1903. 

Johnson, J. B. Notes from various authorities. 

Materials of Construction, 1903, p. 613. 
Costigan, J. S. Frost Tests at Chaudiere Falls, 
P. Q. Eng. News, Oct., 1902, p. 262. 
♦Watertown Arsenal. Specimens exposed to differ¬ 
ent temperatures. Tests of Metals, U. S. A., 
1901, p. 530. 

Railway Superintendents. Notes from Practical 
Experience. Eng. News, Oct., 1900, p. 271. 
Pro. Assn. Ry. Supts., 1900, pp. 168, 170, 177. 
Hobart, A. C. Tests of Frozen Mortar. Techno- 
graph, 1897-98, p. 72. 

Barker & Symonds. Thesis Experiments on Freez¬ 
ing. Eng. News, Vol. XXXIII, p. 262. 


Concrete Work at 2 5 ° to 30° below Zero. 

Eng. News, July, 1907, p. 49. 

Howard, J. E. Tests of Effect of Low Tem¬ 
perature. Eng. Rec., May, 1905, p. 521 
Safeguards for Concrete Work in Frosty 
Weather. Eng. Rec., March, 1905, p. 
249. 


Rogers, W. A. Experiments on Freezing. Jour. 

W. Soc. Engs., Vol. Ill, p. 264. 

♦Wheeler, E. S. Experiments on Mortar at various 
temperatures and under various conditions. 
Rept. Chief of Engs., U. S. A., 1894, pp. 2335, 
2353. 2349, 2360; 1895, p. 2955; 1896, pp. 
2829, 2863. 

♦Noble, A. The Effect of Freezing on Cement 
Mortars. Trans. Am. Soc. Civ. Engs., Vol. 
XVI. p. 79. 

Godfrey, C. H. The Effects of Frost on the Strength 
of Portland Cement. Pro. Inst. Civ. Engs., 
Vol. CXXXIV, p. 378. 

Maclay, W. W. Effect of Temperature in Testing 
Cement. Trans. Am. Soc. Civ. Engs., Vol. 

vi, p. 329- 


Strength of Concrete and Mortar Affected by Retarded Set 


Johnson, J. B* Tests from various authorities. 

Materials of Construction, 1903, p. 593. 
Richardson, T. F. Mortar Experiments. Rept. 
Met. W. & S. Board, 1902, p. 93; 1903, 
p. 120. 

Skeels, G. Y. Regaging from 20 minutes to 9 
hours. Eng. News, Nov., 1902, p. 382. 
♦Clark, T. S. Retempering Portland and Rosendale 
Mortars. Eng. News, July, 1902, p. 68. 
♦Watertown Arsenal. Experiments on Retarded 
Set of Cement Mortar. Tests of Metals, 
U. S. A., 1899, p. 799; 190X, p. 497. 

♦Candlot, E. Discussion and Tables on Cohesion 


and Adhesion. Ciments et Chaux Hydrau- 
liques, 1898, pp. 355 and 365. 

Wheeler, E. S. Regaging Cement Mortar. Co¬ 
hesion and Adhesion. Rept. Chief of Engs., 
U. S. A., 1895, p. 2979; 1896, pp. 2814 and 
2868. 

Faija, H. Experiments on Regaged Mortar. Soc. 
of Engs., London, 1888. 

Kinipole, W. R. Plastic Concrete. Pro. Inst. 
Civ. Engs., Vol. LXXXVII, p. 66. 

Clarke, E. C. Briquettes Rotempered after Pulver¬ 
izing. Trans. Am. Soc. Civ. Engs., Vol. XIV, 
p. 169. 


*An asterisk precedes the references which are especially noteworthy. 



743 


REFERENCES TO CONCRETE LITERATURE 

Tunnels 


Shaft and Gate Chamber, Blue Island Avenue 
Tunnel, Chicago. Eng. News, Oct., 1908, 
p. 440. 

Buffalo Water Works Tunnel. Eng. Rec., 
Oct., 1908, p. 396. 

Rotherhithe Tunnel under the Thames, Lon¬ 
don. Gen. Civ., Sept., 1908. 

Plant and Methods, Detroit River Tunnel. 

Eng. Rec., Sept., 1908, p. 312. 

Machinery and Methods for Placing Tunnel 
Linings. Eng. Cont., July, 1908, p. 3. 
Shelby Hill Tunnel, St. Paul. Eng. Rec., 
Sept., 1907, p. 306. 

Penn. R. R. Tunnel, North River, N. Y. Eng. 

News Oct., 1903, p. 331. 

Standard Tunnel Section, P. C- & W. R. R. Eng. 

News, May, 1903, p. 447. 

New York Subway. Eng. News, 1902 and 1903. 
East Boston Tunnel. H. A. Carson, Jour. Assn. 
Eng. Sees., Dec., 1902, p. 205. 


Construction of Penn. R. R. Tunnels at New 
Y'ork. Eng. News, Dec., 1906, p. 603. 
Reinforced Concrete Tunnel Caisson, Sub¬ 
way System, New York. Eng. Rec., 
Sept., 1906, p. 340, Oct., 1906, p. 377. 

Tunnel Roof of Concrete Blocks. Eng. News, 
July, 1906, p. 1 o 1. 

The Simplon Tunnel. Gen. Civ., June 23, 
30, 1906. 

Penn. R. R # Tunnel, Washington, D. C. Eng. 
News, Sept., 1905, p. 267. 

Sudbury Aqueduct, Mass. D. FitzGerald, Trans 
Am. Soc. Civ. Eng., Vol. XXXI, p. 294. 
Clifton Culvert, N. J. O. Chanute, Trans. Am. 
Soc. Civ. Engs., Vol. X, p. 291. 


Volumes oi Materials for Concrete and Mortar 


*Thacher, Edwin. Table of Materials for Mortar 
and Concrete. Cement, July, 1902, p. 194. 

Metropolitan Water & Sewerage Board, Mass. 
Cement per cubic yard of Concrete. Rept. 
for 1903, p. 112. 

Gillette, H. P. Formulas for computing Cement 
Required. Eng. News, Dec., 1901, p. 422, 
and June, 1902, p. 482. 

Parkhurst, H. W. Materials in Wet versus Dry 
Concrete Specimens. Jour. W. Soc. Engs., 
April, 1902. 

*Saville, C. M. Materials used at Forbes Hill Reser¬ 
voir, Quincy, Mass. Eng. News, March, 
1902, p. 220. 

Sherman, L. K. Experiments for Chicago Drain¬ 
age Canal. Eng. News, Jan., 1902, p. 31. 

Railway Superintendents. Materials for one cubic 
yard of Concrete. Pro. Assn. Ry. Supts., 
1900, pp. 170-1. 

Coleman, Clarence. Materials used at Duluth 
Harbor, Minn. Eng. News, July, 1900, p. 56. 

Baker, Ira O. Tables of Materials for one cubic 
yard of Mortar and Concrete. Masonry Con¬ 
struction, p. 88. 

*Rafter, George W. Volume of Mortar from differ¬ 
ent proportions. Trans. Am. Soc. Civ. Engs., 
Vol. XLII, p. 154, and XLVIII, p. 96. - 

*Hazen, Allen. Method of Computing Quantities 
by Weight. Trans. Am. Soc. Civ. Engs., 
Vol. XLII, p. 129. 


Fowler, C. E. Table of Materials for one cubic 
yard of Concrete. Trans. Am. Soc. Civ. 
Engs., Vol. XLII, p. 117. 

*Sabin, L. C. Table of Materials for one cubic 
yard of Mortar. Munic Engng., Feb., 1899, 
p. 69. 

Jameson, Chas. D Concrete made with different 
proportions of Materials. Portland Cement, 

1898, p. 139. 

Watertown Arsenal. Weights and Volumes of 
Materials in Specimens of Mortar and Con¬ 
crete. Tests of Metals, U. S. A., 1898, p. 655; 

1899, p. 736. 

*WheeIer, E. S. Materials for Beams at St. Mary’s 
Falls Canal, Mich. Rept. Chief of Engs. 
U. S. A., 1895, p. 2924. 

Feret, R. Production and Density of Mortars. 
Commission des Methodes d’Essai des Me 
teriaux de Construction, 1895, Vol. IV, p. 243. 
Cement per Cubic Meter with different propor¬ 
tions. Zeit. f. Bau., 1894, p. 542. 

Mortar from different proportions. Portland Ze- 
ment, Berlin, p. 127. 

Grim, F. Tests of Mortar and Stone for one cubic 
yard of Concrete. Technograph, Vol. XIII, 
P- 53 - 

Grant, John. Tests of Cement and Sand per cubic 
yard of Mortar. Pro. Inst. Civ. Engs., Vol. 
XXII, p. 102. 


Water in Concrete and Mortar 


Taylor and Thompson. Quantity of Water to Use 
in Gaging Mortars. Cement & Eng. News, 
Nov., 1903, p. 112. 

*Larned, E. S. Effect of Water on the Setting and 
Strength of Cement. Pro. Am. Soc. Test 
Mat., 1903, p. 40. 

Doyle & Justice. The Strength of Concrete as 
affected by different percentages of Water. 
Eng. News. July, 1903, p. 97 - 


Sussex, James W. The Relative Strength of Wet 
and Dry Concrete. Eng. News, July, 1903, 
P 67. 

*Parknurst, H.W. Wet, Dry, or Medium Concrete. 
Jour. W. Soc. Engs., 1902. 

*Hitz, Irving. Experiment with Wet and Dry 
Concrete. Jour. W. Soc. Engs., Dec., 1900, 
p. 488. 


*An asterisk precedes the references which are especially noteworthy. 



744 


A TREATISE ON CONCRETE 


Mlenby, W. H. Cinder Concrete Wet and Dry. 

Jour. Assn. Eng. Socs., Sept., iqoo, p. 157. 
Hazen, Allen. Quantity in Actual Work. Trans. 

Am. Soc. Civ. Engs., Vol. XLII, p. 128. 
Rafter, Q. W. Tests of Concrete of different con¬ 
sistency. (Discussion.) Tests of Metals. 
U. S. A., 1898, p. 553. 


Candlot, E. Influence of the Degree of Humid¬ 
ity of the Sand on the Setting and Hard¬ 
ening of Mortars. Ciments et Chaux 
Hydrauliques, 1898, p. 349. 

*Feret, R. Quantity of Water for Gaging Mor¬ 
tars. Ann. des Ponts et Chauss., II, 1892, 
P 3 - 


*An asterisk precedes the references which are especially noteworthy. 





APPENDIX I 


745 


APPENDIX 1 

METHOD SUGGESTED FOR THE ANALYSIS OF LIMESTONES, 
RAW MIXTURES, AND PORTLAND CEMENTS BY THE COM¬ 
MITTEE ON UNIFORMITY IN TECHNICAL ANALYSIS OF THE 
AMERICAN CHEMICAL SOCIETY, WITH THE ADVICE OF 
W. F. HILLEBRAND. 

Solution: One-half gram of the finely powdered substance is to be 
weighed out and, if a limestone or unburned mixture, strongly ignited in 
a covered platinum crucible over a strong blast for 15 minutes, or longer 
if the blast is not powerful enough to effect complete conversion to a cement 
in this time. It is then transferred to an evaporating dish, preferably of 
platinum for the sake of celerity in evaporation, moistened with enough 
water to prevent lumping, and 5 to 10 c. c. of strong HC 1 added and digested, 
with the aid of gentle heat and agitation, until solution is completed. 
Solution may be aided by light pressure with the flattened end of a glass 
rod.* The solution is then evaporated to dryness, as far as this may be 
possible on the steam bath. 

Silica: The residue, without further heating, is treated at first with 5 to 
10 c. c. of strong HC 1 which is then diluted to half strength or less, or upon 
the residue may be poured at once a larger volume of acid of half strength. 
The dish is then covered and digestion allowed to go on for 10 minutes 
on the bath, after which the solution is filtered and the separated silica 
washed thoroughly with water. The filtrate is again evaporated to dry¬ 
ness, the residue, without further heating,' taken up with acid and water 
and the small amount of silica it contains separated on another filter 
paper. The papers containing the residue are transferred wet to a 
weighed platinum crucible, dried, ignited, first over a Bunsen burner 
until the carbon of the filter is completely consumed, and finally over 
the blast for 1 minute and checked by a further blasting for 10 minutes 
or to constant weight. The silica, if great accuracy is desired, is treated 
in the crucible with about 10 c. c. of HF 1 and four drops of H 2 S 0 4 and 
evaporated over a low flame to complete dryness. The small residue is 
finally blasted, for a minute or two, cooled and weighed. The difference 


*If anything remains undecomposed it should be separated, fused with a little Na 2 C 03 » dissolved 
and added to the original solution. Of course a small amount of separated non-gelatinous silica 
is not to be mistaken for undecomposed matter. 


746 A TREATISE ON CONCRETE 

between this weight and the weight previously obtained gives the amount 
of silica.* 

A 1 2 0 3 and Fe 2 O s : The filtrate, about 250 c.c., from the second evapo¬ 
ration for Si 0 2 , is made alkaline with NH 4 OH after adding HC 1 , if need 
be, to insure a total of 10 to 15 c.c. strong acid, and boiled to expel excess 
of NH 3 , or until there is but a faint odor of it, and the precipitated iron and 
aluminum hydrates, after settling, are washed once by decantation and 
slightly on the filter. Setting aside the filtrate, the precipitate is dissolved 
in hot dilute HC 1 , the solution passing into the beaker in which the precipi¬ 
tation was made. The aluminum and iron are then re-precipitated by 
NH 4 OH boiled, and the second precipitate collected and washed on the 
same filter used in the first instance. The filter paper, with the precipitate, 
is then placed in a weighed platinum crucible, the paper burned off and 
the precipitate ignited and finally blasted 5 minutes, with care to prevent 
reduction, cooled and weighed as A 1 2 0 3 + Fe 2 0 3 .f 

Fe 2 0 3 : The combined iron and aluminum oxides are fused in a platinum 
crucible at a very low temperature with about 3 to 4 grams of KHS 0 4 , or, 
better, NaHS 0 4 , the melt taken up with so much dilute H 2 S 0 4 that there 
shall be no less than 5 grams absolute acid and enough water to effect 
solution on heating. The solution is then evaporated and eventually 
heated till acid fumes come off copiously. After cooling and redissolving 
in water the small amount of silica is filtered out, weighed, and corrected 
by FIF1 and H 2 S 0 4 4 The filtrate is reduced by zinc, or preferably by 
hydrogen sulphide, boiling out the excess of the latter afterwards while 
passing C 0 2 through the flask, and titrated with permanganate.§ The 
strength of the permanganate solution should not be greater than .0040 gr. 
Fe 2 0 3 per c.c. 

CaO: To the combined filtrate from the A 1 2 0 3 + Fe 2 0 3 precipitate a few 
drops of NH 4 OH are added, and the solution brought to boiling. To the 
boiling solution 20 c.c. of a saturated solution of ammonium oxalate is 
added, and the boiling continued until the precipitated CaC 2 0 4 assumes 
a well-defined granular form. It is then allowed to stand for 20 minutes, 


*For ordinary control work in the plant laboratory this correction may, perhaps, be neglected, 
the double evaporation never. 

•j-This precipitate contains TiOo, P2O5, Mn 3 C>4. 

fThis correction of AI2O3 Fe 2 0 3 for silica should not be made when the HFl correction of the 
main silica has been omitted, unless that silica was obtained by only one evaporation and filtra¬ 
tion. After two evaporations and filtrations 1 to 2 mg. of SiG 2 are still to be found with the AI2O3 
Fe 2 0 3 . 

§In this way only is the influence of titanium to be avoided and a correct result obtained for 
iron. 


APPENDIX / 


747 


or until the precipitate has settled, and then filtered and washed. The 
precipitate and filter are placed wet in a platinum crucible, and the paper 
burned off over a small flame of a Bunsen burner. It is then ignited, 
redissolved in HC 1 , and the solution made up to ioo c.c. with water. 
Ammonia is added in slight excess, and the liquid is boiled. If a small 
amount of A 1 2 0 3 separates, this is filtered out, weighed, and the amount 
added to that found in the first determination, when greater accuracy is 
desired. The lime is then re-precipitated by ammonium oxalate, allowed 
to stand until settled, filtered, and washed,* weighed as oxide bv ignition 
and blasting in a covered crucible to constant weight, or determined with 
dilute standard permanganate.f 

MgO: The combined filtrates from the calcium precipitates are acidified 
with HC 1 , and concentrated on the steam bath to about 150 c.c., 10 c.c. 
of saturated solution of Na (NH 4 )HP 0 4 are added, and the solution boiled 
for several minutes. It is then removed from the flame and cooled by 
placing the beaker in ice water. After cooling, NH 4 OH is added drop by 
drop with constant stirring until the crystalline ammonium-magnesium 
ortho-phosphate begins to form, and then in moderate excess, the stirring 
being continued for several minutes. It is then set aside for several hours 
in a cool atmosphere and filtered. The precipitate is redissolved in hot 
dilute HC 1 , the solution made up to about 100 c.c., 1 c.c. of a saturated 
solution of Na(NH 4 )HP 0 4 added, and ammonia drop by drop, with con¬ 
stant stirring until the precipitate is again formed as described and the 
ammonia is in moderate excess. It is then allowed to stand for about 
2 hours when it is filtered on a paper or a Gooch crucible, ignited, cooW 
and weighed as Mg 2 P 2 0 7 . 

K 2 0 and Na 2 0 : For the determination of the alkalies, the well-known 
method of Prof. J. Lawrence Smith is to be followed, either with or without 
the addition of CaC 0 3 with NH 4 C 1 . 

S 0 3 : One gram of the substance is dissolved in 15 c.c. of HC 1 , filtered 
and residue washed thoroughly .% 

The solution is made up to 250 c.c. in a beaker and boiled. To the 
boiling solution 10 c.c. of a saturated solution of BaCl 2 is added slowly 
drop by drop from a pipette and the boiling continued until the precipitate 
is well formed, or digestion on the steam bath may be substituted for the 

*The volume of wash water should not be too large. Vide Hillebrand. 

•j-The accuracy of this method admits of criticism, but its convenience and rapidity demand its 
insertion. 

^Evaporation to dryness is unnecessary, unless gelatinous silica should have separated and 
should never be performed on a bath heated by gas. Vide Hillebrand. 


748 


A TREATISE ON CONCRETE 


boiling. It is then set aside over night, or for a few hours, filtered, ignited, 
and weighed as BaS 0 4 . 

Total Sulphur: One gram of the material is weighed out in a large 
platinum crucible and fused with Na 2 C 0 3 and a little KN 0 3 , being careful 
to avoid contamination from sulphur in the gases from source of heat. 
This may be done by fitting the crucible in a hole in an asbestos board. 
The melt is treated in the crucible with boiling water and the liquid poured 
into a tall, narrow beaker and more hot water added until the mass is 
disintegrated. The solution is then filtered. The filtrate contained in a 
No. 4 beaker is to be acidulated with HC 1 and made up to 250 c.c. with 
distilled water, boiled, the sulphur precipitated as BaS 0 4 and allowed to 
stand over night or for a few hours. 

Loss on Ignition: Half a gram of cement is to be weighed out in a plati¬ 
num crucible, placed in a hole in an asbestos board so that about f of the 
crucible projects below, and blasted 15 minutes, preferably with an inclined 
flame. The loss by weight, which is checked by a second blasting of 
5 minutes, is the loss on ignition. 

May, 1903: 

Recent investigations have shown that large errors 
due to the use of impure distilled water and reagents, 
therefore, test his distilled water by evaporation and 
appropriate tests before proceeding with his work. 


in results are often 
The analyst should, 
his reagents by ap- 


APPENDIX II 


749 


APPENDIX II 

FORMULAS FOR REINFORCED CONCRETE BEAMS* 

Direct working formulas suited to all ordinary cases of reinforced concrete 
design are presented in Chapter XXI. The analytical methods of deduc¬ 
tion, however, are omitted there in order to make the book handier for 
every day use and are presented in this Appendix. 

These formulas cover all the usual conditions occurring in practice 
and in theoretical treatment of beam design, as follows: 

(1) Rectangular beams with steel in bottom, assuming that concrete 
bears no tensile stress. (See page 751.) 

(2) T-shaped section of the beam, for use in combined beam and 
slab construction. (See p. 754.) 

(3) Beam with steel in both top and bottom, for use in connection with 
the design of a continuous beam at the supports and other special cases. 
(See p. 757.) 

(4) Beam with steel in bottom and concrete assumed to bear tensile 
stress, for theoretical use in determining accurate stresses at early stages 
of loading. (See p. 760.) 

(5) Beam with compressive stress varying as a parabola, to illustrate 
a method of computation occasionally used. (See p. 762) 

The first three of* these analyses are for common use and follow the 
recommendations of the Joint Committee on Concrete and Reinforced 
Concrete. This fact has necessitated no changes in the analyses in the 
first edition of this treatise except in the adoption of the new standard of 
notation. 

As stated in Chapter XXI, the straight line theory,—that is, the theory 
in which the modulus of elasticity of concrete in compression is assumed 
to be constant within usual working limits,—is adopted as the standard 
and the concrete is assumed to bear no tension. 

The various other rational formulasf which have been advanced by 


*The authors are indebted to Prof. Frank P. McKibben for the formulas in this Appendix 
which have been especially prepared by him for this Treatise. 

-j-See Christophe’s Beton Arme and Morel’s Ciments Arme, 1902. 


75o 


A TREATISE ON CONCRETE 


different mathematicians are based upon the same analytical methods of 
treatment, but on different assumptions of stress. Many have complicated 
their equations by taking moments about the neutral axis instead of about 
the centers of tension or compression, but the general principles of the 
deduction are the same and in accordance with the analyses given below. 

It is possible to evolve by calculus a general formula which satisfies all 
of the various hypotheses,* but the treatment is omitted here and only 
the more practical demonstrations are given 

NOTATION 

The same notation is adopted in this Appendix as in Chapter XIV. 
h = height of beam. 

t = thickness of slab, i. e ., thickness of T-flange. 
b = breadth of rectangular beam or breadth of flange of T-beam. 
b' = breadth of web of T-beam. 

p = ratio of cross-section of steel in tension to cross-section of beam 
above this steel. 

p' — ratio of cross-section of steel in compression to cross-section of beam 
above the steel in tension. 

f c = unit compressive stress in outside fiber of concrete. 
f c ' = unit tensile stress, or pull, in outside fiber of concrete. 
f s = unit tensile stress, or pull, in steel. 

// = unit compressive stress in steel. 

E c = modulus of elasticity of concrete in compression. 

E c f = modulus of elasticity of concrete in tension. 

E s = modulus of elasticity of steel. 

K 

n = — 

d = distance from outside compressive fiber to center of gravity of steel. 
k = ratio of depth of neutral axis to depth of steel in tension. 
kd = distance from outside compressive surface to neutral axis in beam 
in which the depth to steel in tension is d. 
z = depth of resultant compression below top. 
j = ratio of lever arm of resisting couple to depth d. 
jd = d — z = arm of resisting couple. 
e = extra thickness of concrete below steel in tension. 
d! = depth to center of compressive steel. 

M = moment of resistance or bending moment in general. 


*See Burr’s Materials of Engineering, 1903, p. 633. 


APPENDIX II 


75i 


ANALYSIS OF RECTANGULAR BEAM 

We may represent the stresses in the beam by the diagram shown in Fig. 
238, page 751. At any vertical section through the beam the concrete in 
the upper portion resists the forces which tend to compress it, and the 
steel in the lower part of the beam resists the forces which tend to stretch 
and break it in tension. The compressive resistance acts in one direction 
and the tensile resistance in another direction, as designated by the large 
arrows in the diagram. The center of tension in the steel is at the center 
of the bar, or, if there is more than one tier of bars, at the center of 
gravity of the set of bars. The center of pressure of the concrete passes 
through the center of gravity of the triangle which represents the com¬ 
pressive stresses. 




Fig. 238.—Resisting Forces in a Reinforced Concrete Beam. {Seep. 751.) 

The internal resisting forces may be replaced by two forces: the total 
compression acting in the center of gravity of the triangle, having for its 
base f c and its height kd , and the total pull acting in the center of gravity 
of steel. For equilibrium the sum of all forces must equal zero or the 
total compression must equal the total pull, so that the forces form a couple. 
If either tension or compression exceeds its maximum strength, the beam 
fails. These conditions are assumed to be true only after the point of 
loading is reached at which the tension is transferred to the steel, as other¬ 
wise the tension would be made up of two forces, the tension in the steel 
and the tension in the concrete, as discussed on page 760 in this Appendix. 

The moment of resistance of the couple must be equal to or greater 
than the bending moment produced by the live and dead loads. 























752 


A TREATISE ON CONCRETE 


Since it is assumed that a plane section before bending remains a plane 
section after bending, we have the proportion 


deformation in steel _ d (i — k) 

deformation in outside compressive concrete fibers kd 

. . . . - . stress per square inch . 

And since deformation = ————-—-— . . — we have 

modulus of elasticity 

f*_ 

= TNI or A = lA 

fc_ kd nf c k 

E c 

From which 



k = 


i + 


Solving formula (i) for f c 


fc fa 


Is 

»/« 

k 


(i - k) 


n 




Now, as stated above, for equilibrium the total tension in the steel must 
be equal and opposite to the total compression in the concrete. The total 
tension in the steel is its unit tension,/ s , multiplied by the area of the steel, 
pdb, and the total compression in the concrete is represented by the area 
of the pressure triangle, \fjzd times the breadth of the beam, b. Equat¬ 
ing these two stresses and cancelling out the db which occurs in both, 

f c k 

Pf>= 2 W 

If the value of k in formula (2) be substituted for the k in formula (4), 
we have 



1 





For any given percentage of steel the values of f s and f c cannot be assumed 
independently , as they bear a constant ratio to each other. 

Substituting the value of f c in formula (3) for f c in formula (4), we have 

k k 

p = - 

2 (1 — k)n 

Solving this quadratic equation and adopting the positive sign before the 
square root, 


k — — np + 1 / 2 np -f- (np) 2 


(6) 


















APPENDIX II 


753 


We thus have k in terms of n and p, and from formula (6) the location 
of the neutral axis may be calculated with any percentage of steel for con¬ 
crete and steel having known moduli of elasticity. 

The moment of resistance is obtained from the couple by taking moments 
about the center of compression in the concrete, using for the force the 
total tension in the steel, which, as above, is pfjbd times the arm (see 
Fig. 238, p. 751), jd 

or M 

M = pfjbd? and /, = (7) 

The moment of resistance may also be expressed in terms of compression 
in the concrete by combining equations (4) and (7), or, more directly, by 
taking moments about the center of the tension in the steel, thus 

Lkjbd 2 2 M 

M = 2 and = .kjbd 2 ® 


Values for k with various percentages of steel and moduli of elasticity 
are given in table 12 on page 521. 

The value of the moment of resistance, M, may also be expressed without 
using k by substituting in formulas (7) and (8) the value of p from formula 
(5) and the value of k from (2), thus giving 




(10) 


Formula (10) is apparently more complex than (7) and (8), but as the 
latter require the determination of k , formula (10) is more readily solved 
unless the table on page 521 is employed. 

In the use of formula (10), f s and f c must be corresponding values and 
cannot be assumed independently of each other, since for any given per¬ 
centage of steel the ratio of f s to f c is a constant. (See formula (5), p. 752). 
For a given quality of concrete and steel the values of / a , and f c and n 

1 

are constant, so that the term in brackets may be replaced by a constant — 2 
















754 


A TREATISE ON CONCRETE 


We may thus write in place of formulas (9) and (10) the formula 


M = 


bd 2 

C r 


(11) 


where C is a constant for any given concrete and steel. Values of C under 
different conditions are tabulated on pp. 519 and 520. 

Following directly from formula (11) 

\M 

d = C\j (12) 

In the above formula M represents the bending moment which must 

be equal to or smaller than the moment of resistance. Also, since in fig. 

238, p. 751, d = li — e, the formula may be written 

I M 

h = CyJ j + e (13) 

from which the required height of the rectangular beam or slab may be 
directly obtained. 


T-SHAPED SECTION OF BEAM 

When a reinforced concrete floor slab and beam are built as one piece 
the slab adds to the strength of the beam by increasing the area which is in 
compression. 

The working formulas for this shape of beam termed a T-beam are given 
in Chapter XXI, page 423, in sufficient detail for the ordinary design where 



Fig. 239. — Resisting Forces in T-shaped Section of Beam. (See p. 755.) 

the beam and the slab are assumed to act as a unit. The method of analysis 
and the formulas deduced are presented below. 

These are based upon the assumption that the intensity of the compres¬ 
sion in the concrete does not diminish from the web outward towards the 














































APPENDIX II 


755 


edges of the flange. For a section having a narrow flange, this is practi¬ 
cally correct, but with a wide flange, it is probable that the intensity of 
the compression in the flange diminishes from the web outward so that 
the breadth of slab should be limited, as indicated on page 424. If this 
pressure is assumed to decrease either uniformly or otherwise, the formulas 
may be modified accordingly. 

Assuming the compression to be distributed as shown in the diagram, 
and the steel to take all the tension, the formulas given below may be 
deduced as in the preceding cases. 

Case I. Neutral Axis Below Flange, kd > t. 


Neglect the slight amount of compression in the web below the intersec¬ 
tion of the web and flange. 

As in the previous case using notation on page 750 and referring to 
Fig. 239. 


1 + 


h 

n fc 


By equating the forces acting on the section 


^ sJs Jc 


2 kd 


2 kd 


t . 
bt 


Solving the two above equations for kd and eliminating f c and f s 

2 n d A -f b t 2 

kd = — ri — rr 

2n A s + 2 b t 


(14) 


The position of the resultant compression lies in the center of gravity of 

* kd — t 


the trapezoid, the parallel sides of which are equal to f c and f c 


kd 


and 


the height to t. 

The distance of this center of compression from upper surface of beam is 


z = 


7 ,kd — 2 1 t 
2kd —t 3 


(i 5 ) 


The arm of resisting couple 
hence 


jd = d—z 

2 kd — t 

M= ^kT ht ^ 


M = A , jd f s (16) and 


(i 7 ) 









756 


A TREATISE ON CONCRETE 


or 



M MU 

A Jd ( ' l8) and • /c “ bt(kd-\t)jd 


(19) 


From the figure, taking similar triangles, the relation between f 8 and f c is 
found to be 


fs J_ 
n i — k 


(20) 


The approximate moment arm of resisting couple may be taken as 

t 

jd = d- — (21) 

2 

which changes formula (19) to 

M 

(22) 

This formula gives for ordinary cases correct and safe results, but should 
not be used when the flange is small as compared with the stem. 

In the above formulas the compression in the stem is neglected. In 
large beams, where the stem forms the larger part of the compressive area 
the following formulas derived by the same principles used in derivation 
of formulas in the previous analysis should be used, 

I 2 nd A s +(b — b ')( 2 In A + (b — b') A 2 nA + (b — b')i 

kd = yj + \ b , ) - y r ' ( 2 3 ) 


fs 


d-~ 
2 > 


(approximate) 


(kdt 2 - § / 3 ) b + 


2 = 


C U -ty[t + \ (u - t) 


b r 


Arm of resisting couple 
Moment of resistance 


t ( 2 kd — t) b + (kd — t ) 2 b' 
jd = d—z 


fc r 

M = A ,Ws (26) M= —[(2 kd - t)bt + (kd-t) 2 b']jd 

Fiber stresses 


M 


2 Mkd 


Ajd^ and f° [( 2kd _ ^ ht + ( kd _ t y b ,y d 


(24) 


(25) 


(27) 


(29) 


Case II. Neutral Axis in Flange or at Underside of Flange, kd < t 

In this case use the rectangular beam formula, considering the T-beam 
as a rectangular beam of the same depth, the breadth of which is the 
breadth of the flange. The percentage is then based on the total area bd. 


















APPENDIX II 


757 


STEEL IN TOP AND BOTTOM OF BEAM, NO TENSION IN 

CONCRETE 

Although the use of steel in the compressive portion of the beam is gen¬ 
erally uneconomical, its introduction there is sometimes a necessity for 
practical reasons. In the ends of a continuous beam the steel in the bottom 
is usually carried through into the supports, and if the length is enough to 
provide bond its value in compression may be taken as assisting to resist 
the negative bending moment. 

It is possible to reduce the working formulas to extremely simple form 
by introducing constants which vary with different conditions, as outlined 
on page 427, the values for the constants being given in table 8, page 516. 

The treatment of a beam subjected to bending and direct stress with 
the steel in compression is presented in connection with the design of arches 
on page 563, and these formulas may also be used in other cases of eccentric 
thrusts. 




Fig. 240. —Resisting Forces with Steel in Top and Bottom of Beam. 

(Seep. 757.) 

The analytical treatment of the design of an ordinary beam adopting as 
usual the assumption of a constant modulus of elasticity and no tension 
in the concrete, but assuming that the compressive stresses are partially 
borne by the steel in the compression portion of the beam, is as follows: 


FORMULAS. 

Deformations, as usual, are assumed to vary directly as distance from 
neutral axis, hence from Fig. 240, using notation on page 750. 


k 

k 

fc 


d (1 — k) 



Whence k = 


1 + 


(30) 


E 


dk 


1 


*fe 


































75» 


A TREATISE ON CONCRETE 


Also, 


kd - d' 




d — kd 
i — k 


(31) and f s ’=nf c 


kd - d’ 
kd 


fs = n fc ~-J- (33) and /„- f l ~ 


(3 2 ) 


( 34 ) 


Equating the horizontal forces acting on the cross-section of the beam 
we have: 


bd 


’fJ* 


+ P'fs I = bd Pfs 


Whence p = 7 (' ' + p'f/ 


Jo \ 2 


i //, k 2 kd — d r 

f s \2 n i — k P^ s d — kd 


Hence 


k 2 


d' 

k —d 


t- 


2 n (1 — &) ^ 1 — k 


Solving equation (35) for k, 


M = bd 2 


f c k l k\ ( d r 


or by eliminating// by means of equation (32), 


M = f c bd 2 


k\ n P'{ k ~j 
2 \ 1 3/ + k 


d r 

d 


( 35 ) 


1 / d' \ 

k =: y 2 n (p + p' — ) + n 2 (p + p'Y — n (p + p') (36) 

Taking moments about the center of pull in the steel, we have 

bf c kd( kd\ 

M = (d - y ) + // p'bd {d - d') 


( 37 ) 


Taking moments about the center of compresssive stress in the steel, we 
have 


fa P\ 1 “ 


d 


f c k (k _ d' 

2 V3 d 


M = bd 2 
















APPENDIX II 


759 


or by eliminating f c , 
M =/, bd 2 


P i ~ 


d'\ k 2 / k d' 

2n (i — k ) V 3 d 


( 38 ) 


Then taking moments about center of compression in concrete: 

/ k\ / k d' 

M -bp\f,p (1 - -j +/,?/-- d 


or by eliminating f s , 


M = 


1 — k 

k —— 
d 


k\ Ik d' 
1 --) + />' 


( 39 ) 


The values in the square brackets in formulas (37), (38) and (39) are 

d' 

constant for any combination of n, p , p' and —. 


Substituting 


C ‘ “iV" j) + 


n p' ( k ~ 


d' 

d 


1 — 


a 


C s = P [ 1 


d' 

d 


k 2 


d' 


2n (1 — &) \ 3 d 


1 — k ( k \ ( k d' 

c '° = f A 1 -~ 3 ) + p \i~d 

k -- d 


(40) 


(41) 


(42) 


M 


= bd 2 f c C c (43) and f e = ^r 


M 


M = W 2 /* C. ( 45 ) and/, = 


(44) 


(4b) 


and 


M 


M= bd 2 /,' C,' ^y) and /,' = ^77 


and 


(48) 


d' 


Values of C c , C s , and C/ for different combinations of n, p } p' and ^ 
are given in table 8, page 516. 













760 A TREATISE ON CONCRETE 


STEEL IN BOTTOM OF BEAM, CONCRETE BEARING TENSION 

In the earlier stages of loading of reinforced concrete beams, the defor¬ 
mation curves (see fig. 130, p. 409) indicate that the concrete actually 
bears a portion of the pull. Although it is not good practice to consider 
this pull in the design of beams, but, instead, it is customary to take the 
working strength as a factor of the ultimate, or nearly the ultimate strength 
of the beam, the following formulas are useful for determining the actual 
stresses and for calculating deflections at the earliest stages of loading. 

Formulas. Since elongation of steel and concrete at the same point 



N 



Fig. 241. —Resisting Forces with Concrete Bearing Tension. 


(,See p. 760.) 


must be equal, and since cross-sectional planes are assumed to remain plane 
during bending, we have from Fig. 241, the following equations: 

fa_ 

E a 


E c 


kd 


fc h ~ kd 


hence /, = - - // 


d — kd 
li — kd 


Ec' 


E. 


kd 


Jc E c ' Jc h - kd 


E t 


1 — k 


E' h - kd 


fs Ec fc k 


(51) also f: = -^ f e — 


Equating horizontal forces on the section we have 

bf kd f ' b (h — kd) 

-- - Pfs bd + •- 

2 2 

The elimination of f a and// from (53) gives 

kd E s 1 — k E c ' (h — kd) : 

~ = pd E c k + E c ' 2 k,l 


( 49 ) 


( 5 °) 

(52) 


( 53 ) 


( 54 ) 


2 












































APPENDIX II 


76.1 


From wmch 


P = 


E. 


2 (1 - k) L E f 
Solving equation (55) for k , 


kr 


E c ' I h - kd X2 
E~ 


( 55 ) 


2 £ + 


EE h 2 


£ = 


£ s ^ 2 




+ 






£ + 


E. 


E' c h 
E S J 
EE 


P + 


EE h 


E s d 


E. 


( 56 ) 


E c 


Taking moments about the center of the pull in the concrete, the center 
of compression in the concrete and the center of pull in the steel respec¬ 
tively, we have the three following equations for the moment of resistance: 


kd 2J1 \ f bkd 2h 
M = fs p bd [ d — — ) + 

3 3 / 23 


= JM 


kd 2I1 \ E c lik 2 

p[d -J-j) + ENrN 


(57) 


or 


^ s J kd \ , fc'b (h - kd) 2J1 

M — j s p bd [ d ) + 

3 / 2 3 


= fc' b 


E s i - k 


fd3 ^--3/ E'.h--kd 


h 

+ ~ (h 
3 


or 


M = 


fc bkd 


d - 


kd' 

3 


fc b 


kd 2 


If b (h - kd) 


E' c (h - kd) : 


d 


1 — — 
3 


E c kd 


— kd) 

kd 
3 

kd 
3 


C58) 


2 h 

3 

2I1 

3 


( 59 ) 


If now E c f = E c , that is, if the modulus of elasticity of concrete is the 
same in tension as in compression, the line MN becomes straight. 


Equation (55) then becomes, letting — = n 

h 2kd — h 


P-i 


n<P 


( 60) 



































762 


A TREATISE ON CONCRETE 


From which 


li 2 + 2 pnd 2 

k = --- 

2 dli + 2 pnd 2 

Equation (57) is hot changed 

Equation (58) simply has E c instead of E c ' 

Equation (59) becomes 


or 



k \ (h — kd) 2 / ‘kd 



h 2 h 2 

2 d — 7 — h + , , 

k $kd J 



(61) 


(62) 


COMPRESSIVE STRESS AS A PARABOLA, STEEL IN BOTTOM 
OF BEAM, NO TENSION IN CONCRETE. 

Many experiments upon the compression of concrete show a gradually 
decreasing modulus of elasticity as the load increases. From the form of 
the stress deformation curve of these specimens, the stress on the com¬ 
pression side of a beam is sometimes assumed to vary as a parabola instead 
of as a straight line. This method was first suggested in the United States 
by Prof. W. Kendrick Hatt.* The formulas which follow present this 
method of analysis, and permit the comparison^ of results by this assump- 




242.—Resisting Forces with Pressure Varying as a Parabola. {Seep. 762.) 


tion, with results of the straight line theory adopted by the authors in chap¬ 
ter XXL 


* Proceedings American Society for Testing Materials, 1902. 
| See p. 407 for comparative values by the two theories. 







































APPENDIX II 


763 


Formulas. As in preceding cases, from Fig. 242, 
we have 

fs 

E s d (i — k) 1 — k 
kd k 


hence 


fc 

& 


k = 


1 + 


A 

n fc 


from which 




/. 


n 1 — k 

Equating horizontal forces on the section of the beam we have 

2 bf c kd . 2 f c k 

pbdf s = - , or more simply, pf 8 =- 

3 3 

Substitute the value of k from (63) and we have: 

2 

P = 


n f8 ( , Js 

fc V 1 n fc 


(63) 


(64) 


(65) 


( 66 ) 


which gives the ratio of steel required for any consistent values of f s , f 
E s , E c . The position of the neutral axis is dependent upon the per cent 
of steel and the moduli of elasticity of steel and concrete, and the value of 
k may be found by substituting in (65) the value of J s from equation (64). 
Thus 


2 fc k 


= tfc n 


I — k 


l? 


or, p = 


_2 


(1 — k) n 


Solving this quadratic equation and using the positive sign after taking 
the square root, 


k = V\ np + (%np) 2 — f np 


or in another form, 


k = } np 


\ J 


8 


3 n P 


+ 1 - 1 


(67) 
















764 


A TREATISE ON CONCRETE 


The moment of resistance may be found by taking moments about the 
center of compression in the concrete, thus, 

M = f s pbd 2 (1 — | k) (68) 

or by taking moments about the center of pull in the steel, 

M = lf c kbd 2 { 1 - ffc) (69) 

Eliminating k from these equations by substituting its value from equa¬ 
tion (63), and also substituting the value of p from equation (66), we have 


M = §/ s bd 2 


fc 


SI fs 

I + — 


I — 


8(1 + 


n 


VC/ 


nfe 


( 7 °) 


or 


M = if c bd 2 


1 + 


A 

nfc 


1 — 


81 + 


A 

nf c 


(7O 


VERTICAL AND INCLINED REINFORCEMENT IN BEAMS. 


In any beam the horizontal shear is the same as the vertical shear pro¬ 
duced by the loads (see p. 448). Concrete, however, is so strong to 
resist direct shear (see p. 382) that, in ordinary rectangular or T-beams, 
no appreciable direct shear comes upon the vertical or inclined bars, 
the concrete alone being capable of resisting it. The shear stress is there, 
however, and tends to resolve itself into components of tension and com¬ 
pression, one of which acts in the line of least resistance. Since concrete 
is weak in resistance to pull, the tension component tends to pull apart 
and crack the concrete in the typical diagonal lines (see p. 443). This 
may be resisted by inclined steel bars at right angles to the cracks, or 
by vertical stirrups, or both, as illustrated on page 445. 

The action of stirrups in resisting this pull may be illustrated by con¬ 
sidering the beam acting like a truss in which the horizontal steel is the 
lower chord, the concrete in the top of the beam the upper chord, the 
stirrups the vertical tension bars, and the concrete web between the stir¬ 
rups the compression diagonals. (See Fig. 242a, p. 764 a.) Tests of 
deformation in reinforced concrete beams show that compression and 
tensile stresses of this character are all actually taking place when a beam 
is loaded. 














APPENDIX II 


764 a 

This is the ordinary Howe truss action. If the stirrups are inclined, 
as bent bars, the action is similar but corresponds to* the Pratt truss, 
the steel diagonals being in tension and the vertical members, i.e., the 
concrete section, being in compression. 

To show how the stress in any stirrup is measured by the shear, verti¬ 
cal stirrups in a reinforced concrete beam may be considered as spaced a 
distance apart equivalent to the effective depth of the beam, jd, thus 
giving the diagonal compressive concrete between 2 adjacent stirrups 
an angle of 45 0 , so that the horizontal and vertical components of this 
diagonal are equal. 

Considering the joint a , in Fig. 242a, from simple mechanics the ten¬ 
sion, or pull, in the vertical at this point must be equal in magnitude to 


CENTER OF COMPRESSION' 


VL 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


a 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


/ 


<— 


/ 




jd- 


/ 


/ 


• / 
/ 


rd 




/ 


/ 


/ 


/ 


k 


7J/W77777 


T TT 


STEEL IN TENSION 

Fig. 242a. Illustration of Truss Action. (See page 764a) 


the vertical component of the compression diagonal in panel ab and, 
since the horizontal and vertical components of stress in a 45 0 diagonal 
are equal, the tension, or pull, in the stirrup at a is equal in magnitude 
to the horizontal component of the compressive stress in the diagonal. 
This horizontal component of the compressive stress in the diagonal, which, 
as just stated, is the equivalent in magnitude of the tension or pull in the 
vertical stirrup, is equal, in a Howe truss, to the difference between the tensile 
stress, or pull, in the horizontal chord just to the left of a and the tensile 
stress or pull in the horizontal chord just to the left of b. 

In a given beam under load, the stress or pull in the horizontal chord 
at any point is directly proportional to the bending moment. This is illus¬ 
trated in formula (7), page 420. From this formula it is seen that, the 
actual stress in the horizontal steel equals the bending moment divided 

M 

by the- effective depth of the beam, or —. 













A TREATISE ON CONCRETE 


7646 


Considering now any two points on the horizontal chord that are an 
infinitesimal distance apart, the difference between the bending moments 
at these two points is equal to the external vertical shear at this place 
in the beam times the infinitesimal distance.* Hence, if the two points 
are a definite distance apart, as a and b in Fig. 242a, and the shear is 
assumed to be constant between these two points, then the diference 
between the bending moment at a and the bending moment at b is equal to 
the external shear, V, at this place in the beam multiplied by the length ab. 

It follows from the second preceding paragraph that the diference 
between the tensile stress, or pull , in the chord at point a and the pull at 
point b, as in any simple truss, is equal to the diference between the mo¬ 
ments at these two points divided by the effective depth, jd. 

Since, now, this difference in chord stress has been shown to be equal 
to the tensile stress or pull in the vertical stirrup, A s f s , and the difference 
in bending moment has been shown to be equal to the external shear 
times the length ab, it follows directly that the stress in the vertical 
stirrup, A s f s , is equal to the external shear times the length ab divided 

Vab 


by the effective depth jd, or 


jd- 


That is, when the stirrups are spaced 


jd apart, so that ab = jd, the tensile stress or pull, A s f a , in the vertical 
stirrup equals the external shear, V. 

For any stirrup spacing, s, the action is that of a multiple truss and 
the stress in the stirrup, AJ S , equals, without appreciable error, V times 

the ratio —. In practice stirrups always should be spaced closer together 
Jd 

thank'd (seep. 450). 

In this demonstration, for simplicity, the stirrup is assumed to take 
all of the vertical tensile stress. If the concrete is assumed to take part 
of this, the formulas given on page 449 result. 


*This follows from the fundamental principle in mechanics that the first differential coefficient 
of the bending moment, which is of course the rate of change of that moment, is equal to the 
shear. 


APPENDIX 111 


765 


APPENDIX III 


FORMULAS FOR REINFORCED CONCRETE CHIMNEY AND 

HOLLOW CIRCULAR BEAM DESIGN 

The analysis which follows is based upon the several fundamental 
assumptions adopted in reinforced concrete beam design with the additional 
assumption that, since the concrete is usually thin as compared to the 
diameter of the chimney, no appreciable error is involved in assuming all 
material as concentrated on the mean circumference of the shell. An 
analysis for shear is also given together with an example of chimney design 
and review. 

The principles involved in the demonstration of the thickness of steel and 
concrete are taken by permission from the analysis by Messrs. C. Percy 
Taylor, Charles Glenday, and Oscar Faber.* 

The principal formulas given below are quoted in the text, where 
the general subject of concrete chimneys is discussed, and tables are 
presented there with the values of constants for use in design. 


NOTATION 


W = weight in pounds of the chimney above the section under considera¬ 
tion. 

M = moment in inch pounds of the wind about that section. 

P = total compression in concrete. 

T = total tension in steel. 


n 


fc 


f. 

D 

r 

t 

h 


= —? = ratio of modulus of elasticity of steel to that of concrete 

E c 

= maximum compression in concrete in pounds per square inch (me:. 

ured at the mean circumference). 

= maximum tension in the steel in pounds per square inch. 

= mean diameter of shell in inches. 

= mean radius of shell in inches. 

= total thickness of shell in inches. 

= thickness in inches of concrete only. 


♦ Engineering (London), Mar. 13, 1908. 


766 


A TREATISE ON CONCRETE 


t s = thickness in inches of an imaginary steel shell of mean radius r. 
and having a cross-sectional area equivalent to the total area of rein¬ 
forcing bars. 

A s = total cross-sectional area, in square inches, of reinforcing bars in the 
section under consideration. 

k = ratio of distance of neutral axis, from mean circumference on com¬ 
pression side, to diameter D. 

j,z, C P and C T = constants for any given value of k. (Tables 1 and 2, 
pp. 635 and 636.) 

jD = distance between center of compression and centre of tension. 
zD = distance from center of compression to center of force due to weight. 

Referring to Fig. 243, if f c is the maximum intensity of stress in the con¬ 
crete at the mean circumference on the 
compression side, then the intensity 
of compression in the steel at that 
point is nf c . Since f s is the maximum 
intensity of stress in the steel at the 
mean circumference on the tension 
side, then the variation of the stress 
in the steel, across the section cd, is 
represented by the straight line ab 
which cuts the linecd at e, thus locat¬ 
ing the neutral axis or the line of 
zero stress. Having assumed a con¬ 
stant value for the modulus of elas¬ 
ticity of the concrete in compression, 
it therefore follows that, at any point 
of a given section, the stress in either the concrete or the steel is directly 
proportional to the distance of that point from the neutral axis. 

Calling kD the distance of the neutral axis from the mean circumference 
on compression side as shown in Fig. 243, we have by similar triangles 



Fig. 243.—Resisting Forces in a Re¬ 
inforced Chimney. (See p. 766.) 


kD = n fc 
D fs+ n fc 


whence 























APPENDIX III 767 

By this formula the position of the neutral axis may be determined for any 
combinations of f c , / g , and n. 

If now, as shown in Fig. 244, a represents half the angle subtended at the 
center by the portion in compression, we have 

cos a = (1 — 2 k) 


from which, for any given value 
and sin a. Thus having located 
the neutral axis for any given com¬ 
binations of f c , f 8 and n and bear- 
ingin mind that the stress at any 
point of the shell is proportional 
to the distance of that point from 
the neutral axis, it is now possible 
to determine the total force on the 
compression side, the total force 
on the tension side, and also the 
location of the center of compres¬ 
sion and the center of tension. 

Considering a small radial ele¬ 
ment subtending an angle dO , as 


of z, cos a becomes known as well as a 



Fig. 244.— Distribution of Stresses in the 
Steel of a Reinforced Chimney. (See 
p. 767.) 


shown in Fig. 244, we have in this 

element, since the length of an arc is its radius times the angle, 

area of concrete = t c rdO 
area of steel = t 8 rdd 


The distance of the element from the neutral axis is r(cos 6 — cos a), 
while the distance from the neutral axis to the point of extreme stress f c is 
_ cos a'). Therefore the intensity of stress on this elemental area is 


fc 


r (cos 0 — cos a) 
r (1 — cos a) 


in the concrete 


and 


fc 


n 


r (cos 6 — cos a) 


in the steel. 


r (1 — cos a) 




























768 


A TREATISE ON CONCRETE 


Assuming these intensities at the mean circumference to represent the 
average for the entire element, we have the total force on the elemental area 
(concrete and steel) 


d P = (t c + nt s ) r d 


6 


f c r (cos d — cos a) 
r (1 — cos a) 


The total force P on the compression side of the section is therefore 

f c r (cos 0 — cos «) ^ 

(1 — cos a) 

Integrating this expression, gives 



2 

P — f r r (t c + n L ) ;- 1 -- (sin a — a cos a) 

Jc c 8 (1 — cos a) 


Since any given position of the neutral axis determines a, as shown above, 
this equation may take the form 

p = Cpfc r Qc+ nt„) (2) 


in which C P is a constant for a given position of the neutral axis. (See 
Table 1, page 635.) 

Having determined the magnitude of P, its location, with respect to the 
neutral axis, may best be found by taking its moment about that axis and 
dividing by P, thus giving the distance from the neutral axis to the center 
of compression l lt as shown in Fig. 244. 

As before, the compressive force on an elemental area is 


d P — (t, + nt 8 ) r d 0 


f c r (cos 6 — cos a') 
r (1 — cos a) 


The distance of this force from the neutral axis being cos 6 
have as its moment about that axis 


cos a), we 


d M c = (t c + nt 8 )rd 0 


f c r 2 (cns 0 — COS O ') 2 
r (1 — cos a) 


while the moment of the total compressive force P is 


M c = (*c + n 0 2 


r*a 

fj 0 


f r r (cos 6 — cos a) 2 

r --- . -. . 7 - dd 

(1 — cos a) 









APPENDIX 111 


769 


2 Sc ^ 

*(<. + *0 7~z 


a 


— 2 cos a 

Integrating, we have 
M c - (t c + nt a )/ c r 2 — 


£ 


cos a) 
cos 6 d 0 + cos 2 a 


cos 2 Odd 


a 


dO 


(1 — cos a 


y [(a cos 2 a. — | sin cj cos a + f a)] 


Dividing df c by P we have 

M c (a cos 2 a — f sin a cos a + f a) 
1 P (sin a — « cos a') 



Following a similar method of procedure it is possible to determine the 
total tension and the location of the center of tension. 

In accordance with our assumption that the concrete is to take no tensile 
stress it is evident that in considering the forces on the tension side of the 
section we are concerned merely with the steel. On the tension side a small 
element therefore has an area = t, s r d 6 

The intensity of stress on this element, being proportional to its distance 
from the neutral axis, is 


r (cos 6 + cos o') 

J s ; ; ^ 

r (1 + cos n) 


while the total tension on the small element is 


d T = t s r d Of, 


(cos 0 + cos «) 
(1 + cos a ) 


The total force T on the tension side of the section is therefore 




(7T —a) ( C os 0 + cos a') 

t s r f -;-r— 

o s (! -f cos a) 


d 0 


Integrating, we have 

2 

T = f.r L - -:-; (sin a + (x — a) cos a) 

Js s (l + cos a) 


Since, as before, any given position of the neutral axis determines a, this 
equation may take the form 

T = C T f s r t s (4) 

in which C T is a constant for a given position of the neutral axis (see Table 
1, page 635). By a method similar to that used in considering the force on 










770 


A TREATISE ON CONCRETE 


the compression side we may write the moment, about the neutral axis, of 
the force on a small element on the tension side as 


d M t — t a r d 6f 8 


r (cos 0 + cos a-) 


A 2 


(i + cos a) 

while the moment of the total tensile force T about this axis is 

— a) r ( CO s 0 + cos a') 2 


M t = 2 )t s r/ s 


(i + cos a) 


dd 


Integrating, we have 


Mr — t 8 r 2 f t 


2 / ___ 


(i -f- cos a) 


[(n — a) cos 2 a + f sin a cos a' + i (n — a)] 


Dividing M T by T we have as the distance of the center of tension from 
tne neutral axis 

( (tt — a) cos 2 a + 4 sin 7T cos a + \ (tt — a) ) 

L =-7-7- — -r-7- r t5) 

(sin a + (7Z — a) cos a) 

From formulas (3) and (5) it is evident that the distance between the total 

force in compression and the total force 
in tension (i. e., h + h) may, for any 
given position of the neutral axis, be 
expressed as a constant times the 
diameter D. Thus h + l 2 = jD as 
shown in Fig. 245. Likewise, as shown 
in Fig. 245, zD may represent the dis¬ 
tance of the center of compression 
from the center of the chimney, z also 
being a constant for any given position 
of the neutral axis. 

In a chimney the tensile and compres¬ 
sive stresses which we have been con¬ 
sidering are produced by a combina¬ 
tion of wind pressure and the weight of the chimney. Thus, on any 
horizontal section cd, as shown in Fig. 245, the forces external to that sec¬ 
tion are: the horizontal pressure of the wind, causing a moment M about 
the section, and a central vertical load IT representing the weight of that 
portion of the chimney above the section under consideration. These 
forces are resisted, and held in equilibrium, by the forces P and T which 
represent the compressive and tensile stresses in the concrete and steel. 



Fig. 245. —External and Internal 
Forces Acting upon a Chimney. 
(See p. 770.) 




















APPENDIX III 

The system of forces as shown in Fig. 245 must be in equilibrium, 
taking moments about the force P, we may write 

TjD = M - WzD 

But 

T = C T f s rt s 


771 

Hence, 


Therefore 

Whence 


C T fs r hi D = M ~WzD 
M - WzD 


rt s = 


C T f s jD 

The total area of steel A„ = 2izrt a 

o O 

Therefore 

27 z(M — WzD) 


a, = 


C T f s jD 


(6) 


From Table I, page 635, it may be seen that the constant 
slightly for a considerable variation in the position of the 


j changes but 
neutral axis. 


27T 

Taking^- 

i 


= 8 for all cases, equation (6) may be 
_ 8 (M — WzD) 

■ “ • c T /p 



While this formula is not exact, the error involved is inappreciable for almost 
any case so that formula (7) may always be used instead of formula (6). 

Applying now the condition that the summation of all vertical forces must 
be zero, we have 

p _ T = W 


Substituting values of P and T as previously found, the equation becomes 

C P U (t c + nt 8 ) - C T f s rt s = W 

Transposing and solving for t c we obtain 


h = 


W + (C T / S - C P f c n) rt s 


C P f c r 


The total thickness of the shell is 


t — t. A- t. 


W + (C T f s - C P f c n) rt s 

c P U 




whence 









77 2 


A TREATISE ON CONCRETE 


For convenience in use, after having determined A s by the formula given 

D A 

above, by substituting r = — and t s — this formula for t may best 

z 7 tU 

be written 


2W + (C T f s - C P f c n) 


t = 


7 T 


^ pJc^ 


+ 


7 zD 


( 8 ) 


In view of the fact that formulas (6), (7) and (8) contain the constants z,j, 
C T and C F , which, as has been shown, are dependent for their value solely 
upon the location of the neutral axis, it is evident that, for any specific 
values of f c , f s , and n , which in turn will determine the position of the 
neutral axis, the expressions for^ 4 s and t will admit of a further simplification. 
For given values of f c ,f s and n , the necessary thickness of shell and area of 
reinforcement may be expressed merely in terms of the moment of the wind 
M, the weight W, and the mean diameter D. The expressions, as given, 
however, seem best adapted to general use, and when supplemented by 
the tables given on pages 635, 636, are rendered quite simple of solution 
for specific values. 

In Table 2, page 636, is given values of k , the location of the neutral axis, 
for various combinations of f c , f s and n ; while Table 1, page 635, gives the 
corresponding values of the constants C P ,C T ,z and j for various positions 
of the neutral axis. 

Shear or Diagonal Tension. Having determined the necessary thickness 
of shell and vertical reinforcement, the size and spacing of the circular steel 
hoops must be considered. The external forces produce shear ana diagonal 
tension which may be analyzed similarly to like stresses in rectangular beams, 
and the reinforcement necessary to resist the diagonal tension, which is a 
function of the vertical tension, may be determined. Usually this reinforce¬ 
ment is not so great as that which it is advisable to insert for the proper dis¬ 
tribution of temperature stresses, but nevertheless it should be determined 
to be sure that it is sufficient in quantity. 

The concrete should never be relied upon to carry any tension or vertical 
shear because the expansion from the heat may cause vertical cracks in the 
concrete. These need not be considered dangerous if sufficient horizontal 
reinforcement is provided any more than the vertical cracks in a brick or 
tile chimney. Considering the stresses due to vertical shear, it may be 
easily shown that at any horizontal section of a chimney the vertical shear 
per inch of height is the total horizontal shear on that section divided by the 
distance between centers of tension and compression, jD. With this as a 







APPENDIX III 


773 


basis there may be developed a formula for practical use in determining the 
necessary area and spacing of horizontal steel hoops at any given section. 

Thus let 

hi = height, in feet, of chimney above section under consideration. 

F — effective wind pressure against chimney in pounds per square foot. 
f s = allowable tensile stress in pounds per square inch in steel hoops. 

D = mean diameter of shell in inches. 

P 0 = ratio of area of steel hoop to area of concrete. 

At any horizontal section of a chimney the total shear on that section is 
equal to 


while the maximum shear per inch of height is therefore 

DJhF 

12 jD 

Having seen that for all positions of the neutral axis j remains practically 
constant, and giving j an average value of, say, 0.783, the expression for 
the maximum vertical shear per inch of height becomes 

0.106 hF 

while the shear or diagonal tension in one foot of height is 12 X 0.106 Ji t F. 

The area of steel in one foot of height of chimney will be 12 bp 0 and the 
stress the hoops in this height are capable of sustaining on their two sec¬ 
tions is 

2X12 tpj s 

Equating these we have 

12 X -106 hjF = 2 X 1 2 Apofs 

whence 

h t F 

p0 = TsIJj 

This ratio of steel is for shear or diagonal tension only. To provide for 
temperature stresses or rather to distribute the strains so as to prevent the 
localization of cracks an additional amount of horizontal steel is needed. 
This may be provided for arbitrarily by assuming 0.25% steel or rather 




774 


A TREATISE ON CONCRETE 


0.0025 f° r temperature stress in addition to the steel for shear. Express¬ 
ing this as a formula for ratio of steel gives 

hiF v 

p ° = *&£ + °-°° 25 (9) 

Small rods spaced 6 to 10 inches apart except in the upper part of the stack 
where the spacing may be greater are advised. 

The spacing of hoops in many of the chimneys already built has been 18 
inches to 36 inches, but as such chimneys have frequently cracked quite 
seriously, more recent designs have called for 8 or 9 inch spacing through 
the entire stack. 

Design of Hollow Circular Beams. The analysis of a hollow circular 
reinforced concrete beam whose thickness, compared relatively with its 
diameter, is small, is similar in principle to that of a chimney. In this case 
the weight of the member acts in the same direction as the external forces, 
so that in formulas (7) and (8) W the weight in the axial direction, is zero. 
The forces of compression, P, and tension, T , are equal. The area of steel 
and the thickness of shell are therefore obtained from formulas (7) and (8), 
pages 771 and 772, by making W — O. 

Note on Slim Chimneys. Since, in designing a chimney the selection 
of certain allowable working stresses in the concrete and in the steel will 
fix the position of the neutral axis, it is evident that the ratio of these 
working stresses limits the compressive area of the section. Hence, for 
a very high chimney in which there is a large compression in the lower 
sections, it is possible that the selection of an ordinary working stress in the 
steel of 14000 or 16000 pounds per square inch together with the custom¬ 
ary working stress in the concrete of, say, 500 pounds per square inch, 
would locate the neutral axis so near the compression side of the section 
as to make it impossible to obtain sufficient compression area to with¬ 
stand the compressive forces without exceeding the allowable unit stress 
in the concrete. 

If, therefore, the thickness of shell as computed from formula (2), 
page 634, should work out materially larger than the assumed thickness, 
recomputation should be made on the basis of a smaller working stress 
in the steel, thus changing the position of the neutral axis so as to allow 
a larger proportion of the section to carry compression. In such a case 
it may be necessary to make a series of trials with different working 
stresses in the steel until the computed thickness checks with the assumed 
thickness. In high chimneys of small diameter it may be impossible to 
utilize a working stress in the steel greater even than 7000 or 8000 pounds 
per square inch. 



APPENDIX IV 


775 


i 

APPENDIX IV 

METHOD OF COMBINING MECHANICAL ANALYSIS CURVES 

In Chapter XI the method of forming mechanical analysis curves is dis¬ 
cussed, and approximate rules are given for combining individual curves 
to form the curve of the mixture. More exact methods, which also illus¬ 
trate the principles, are given in the following pages, taking up first simple 
cases and then the more complicated ones. 

Case I. Curves which meet , but do not overlap. In Fig. 246 are shown 
three curves, No. 1, No. 2, and No. 3, representing ideal grades of sand and 
stone, which may be combined in such proportions that the curve of the mix¬ 
ture will be of the ideal form required. The problem requires the deter¬ 
mination of the percentages of each of the three materials which when com¬ 
bined will form a mixture whose curve is nearly the ideal. In order to 
prove that the percentages found will produce the resultant curve, and also 
to illustrate the theory of the mixture, the resultant curve will be first plotted 
and described in a very elementary manner, and afterwards by the method 
of ratios which would be employed in practice. 

Curve No. 3 represents a material all of whose particles will pass through 
a sieve having holes 2.00 inches diameter and all of whose particles will be 
retained on a sieve having holes 0.75 inch diameter. Stone represented 
by curve No. 2 lies between diameters 0.75 and 0.25 inch, while the 
material of curve No. 1 is all finer than 0.25 inch, that is, is all under \ 
inch. Curves No. 31 and No. 32 are referred to later. 

The curve OebA is first plotted* as a parabola. Although the latest tests 
indicate that the best curve is a combination of an ellipse and a straight line,t 
the parabola will illustrate the principle of combination as well as any other, 
and so for this problem we may assume now that the required theoretical 
mix of materials lies in this parabolic curve. This is equivalent to saying 
that the desired theoretical mixture of materials is such, that at any ordinate 

♦ Construction of the Parabola. 

D = largest diameter of stone 

d = any given diameter 

P = per cent, of mixture smaller than any given diameter 
The equation of the parabola is 

= JCP 

10000 

The parabola can be constructed in any of the numerous ways given in text-books, the writer 
finding it easiest to use a slide rule. Set D on the B scale of the rule opposite ioo on D scale, 
read any value of d on the B scale opposite any corresponding value of P on the D scale. 

-j-“Laws of Proportioning Concrete,” by William B. Fuller and Sanford E. Thompson, Trans¬ 
actions American Society of Civil Engineers. 











































































































































APPENDIX IV 


111 


or vertical line cutting the parabola, the proportion or percentage of the 
ordinate below the intersection represents the percentage by weight of the 
mixed materials which passes a sieve the diameter of whose openings cor¬ 
responds to the given ordinate, and the percentage above the curve represents 
that percentage which is too large to pass through this sieve. The parabola 
shows, for example, that 87% of the mixture of materials should pass a 
1.50-inch sieve, 71% should pass a i-inch sieve, 49% a ^-inch sieve, and so 
on. 

We may now take up the stone curves in succession to determine what 
percentage by weight of each should be used, so that when they are'com¬ 
bined, the mixture will be as nearly as possible like that called for in the 
parabola. 

The chief difficulty in the method of determining the percentages of each 
material lies in combining the individual curves so as to form a single curve 
which represents the mixture. This involves drawing on the same piece 
of paper two different lines, each of which exactly represents the composi¬ 
tion of the same lot of stone, that is, the exact per cent, of each size of 
stone in the lot. For example, as is explained below, on Fig. 246, lines 
BKA and bkA , each accurately represents the percentage composition of 
the same batch of stone, namely, No. 3, and the full meaning and value of 
these diagrams cannot be understood until it is clear how the same values 
can be accurately represented on the same diagram by two such totally 
different curves. 

In the first place it is seen that the ordinates, that is, the vertical lines in 
the diagram, are divided into 100 parts representing percentages. It is 
clear, therefore, as the divisions are relative, that the diagram would accom¬ 
plish the same results and curves could be drawn accurately representing 
the percentages passed and retained by the different sieves, whether the 
distance from o to 100 on the ordinates were, say, three times as large as 
it is, or whether it were only \ or ^ of the present length. All that is needed 
is to divide these vertical lines, whether they are long or short, into 100 parts 
and let each division represent 1%. 

Referring now to Fig. 246, the percentage composition of the No. 3 lot of 
stone is represented by line BKA. This lot of stone contains no stone 
smaller in diameter than 0.75 inch and none larger than 2.00 inches. 
Running vertically upward from B on the 0.75-inch line to b where it 
crosses the parabola, we see that the parabola from b to A also represents 
a lot of stone none of which is smaller than 0.75 inch and none larger 
than 2.00 inches, and we can look upon this lot of stone for the moment as 
entirely separated from the rest of the mixture which the whole parabola 
represents. If we wish to find the exact percentages of the various sizes 


A TREATISE ON CONCRETE 


778 

of stone which are in the portion or lot represented by the portion of the 
parabola from b to A , all that is necessary is to draw the horizontal line rq 
through the point b, then divide the vertical distance from A to rq into 100 
parts, so as to obtain a new set of horizontal lines or abscissas representing 
percentages. Now if we start at the base line rq and follow up any one of 
the vertical lines or ordinates until it meets the parabola, and then follow 
horizontally to the right along the line which intersects the parabola at the 
same vertical line or ordinate point, the reading on the new smaller percen¬ 
tage scale will give us the per cent, of stone in the lot bA which is larger 
than the diameter represented by this ordinate, etc. For example, taking 
intersection of 1.00 ordinate with the parabola and running across we find 
that 75% of the lot is coarser than 1 inch diameter. 

It is desirable to see how nearly the stone in lot No. 3 agrees with the 
theoretical lot of stone called for by section bA of the parabola. In prac¬ 
tice, the comparison may be made most readily by ratios with the aid of the 
slide rule, as is described more fully below, but the reasoning will be more 
clearly understood if the plan described in the last paragraph is followed. 

Taking first curve No. 3 we may redraw it on the same smaller scale as 
the portion of the parabola bA is drawn, that is, it may be constructed on 
rbq as a base line instead of on the zero coordinate BF. Since the vertical 
per cent, line between q and A has been divided into 100 parts, this section 
of the diagram may be used instead of the original per cent, divisions ex¬ 
tending from A to F. A piece of paper the length of Aq may be divided 
into 100 parts and placed with its upper or o end in line with the upper 
line CA of the diagram. The vertical distance from the line CA to the 
various points G, H, J, K, etc., may be read by the eye and replotted, — 
with the assistance of the small scale,— as g, h, j, k, etc. 

It is evident then that the broken line bghjk A represents (referring 
to the small percentage scale Aq) lot No. 3 of stone as accurately as 
line BGH JKA represents the same lot of stone referring to the larger 
percentage scale A F. 

Stone curve No. 3, however, would never, in actual practice, be an 
absolutely straight line from A to B. It would be in all practical cases 
an irregularly curved line, similar, for instance, to some of the actual stone 
curves shown in Fig. 71, p. 199, or it might be either convex like the curve 
No. 3 2 , Fig. 246, or concave like No. 3,. These curves may be redrawn in 
exactly the same way as curve No. 3, and if the lower end of each is 
assumed to start at point b where the new base line or bq crosses the 
parabola, we should have for No. 3 2 the new curve bg^h^jii etc., and for 
No* 3 i the curve whose beginning is shown by bh^j^ etc. Thus again 


APPENDIX IV 


779 


it is seen that the stone curves No. 3 2 and No. 3 X on the original 
full-size diagram are accurately represented also by the curves bg 2 h 2 j 2 , etc., 
bh 1 j v e tc*> drawn to the smaller scale on the same piece of paper. 

Thus far only the principles involved in understanding the curves and 
replotting them have been considered. The. result at which we are aiming 
is the determination of the percentage of each material which will be 
required in the final mixture of the aggregates. Let us first take for this 
curve No. 3. The curve of stone No. 3 ends at B, which indicates that all 
of this stone is larger in diameter than 0.75 inches (although about 4% of 
it, for instance, is smaller than 0.80 inches in diameter). Now following 
up from B on the vertical line which represents 0.75 inches in diameter 
until we come to the parabola at point b , we see that the parabola demands 
bB 61 

that —— or - or 61% of all the stone and sand in the entire mixture of 

C B 100 

stone and sand shall be smaller than 0.75 inches in diameter, and conversely 
bC 

that —— or or 39% of the mixture shall be larger than 6.75 in diameter. 

CB 100 

tyo. 3 stone is the only one of the three lots of stone which is larger in 
diameter than 0.75 inches, and therefore 39% of this grade of stone should 
be used in making up the mixture. 

These ratios give us a clue to the method of plotting the curves to the 
smaller scale with the aid of the slide rule, instead of employing the longer 
method of actually dividing the spaces into 100 equal parts. The principle 
in each case is exactly the same. By the method of ratios the curve bkA 

Cb Tg Sh 

would be plotted from the knowledge that —q- = —— = —— =, etc. The 

C B 1 G 0I1 


distances Tg, Sh, etc., may be read directly from the slide rule or from the 

TG X Cb 

equation which follows from the preceding, viz., that Tg = ——-= 

y c , an q so on 

100 

This actual plotting of the curves may be unnecessary, in fact, it is 
usually unnecessary for an experienced calculator, as the percentages can 
be obtained and the general direction of the curve estimated by inspection.* 


*It is evident that neither of the two batches or lots of materials shown by curves No. 3 2 
and No. 3, are so well adapted to form a parabola as curve No. 3 Curve No. 3 2 would more 
nearly fit the parabola than it now does if its new curve were plotted slightly lower so that it would 
cross the parabola at a different point and a larger percentage of it would be required for the 
mixture. If it crossed the parabola at V, the percentage of it to use could be found by plot¬ 
ting it in this new location and taking for the percentage the vertical distance from C to the 

end of the curve, or what is the same thing, taking the percentage as -— — — _ 51%. 

SH 2 6 $ 












780 


A TREATISE ON CONCRETE 


The next curve in order is No. 2. We note that this lot of stone is the 
only one of the three whose particles lie between 0.25 inches diameter 
and 0.75 inches, and that therefore all of the stone called for by the para¬ 
bola between these two sizes must be supplied from No. 2 lot. Following 
down from the upper end, C, of No. 2 to the parabola at b and up from the 
lower end E to the parabola at e and drawing horizontal line ex, we see 
that the proportion of No. 2 stone which is called for by the parabola is 
represented by the distance between the lines rq and ex or by line re, 

re 26 

and we have the ratio =- — = 26%, as the percentage of the weight of 

JJE 100 

the No. 2 material to the total weight of the mixture. 

Plotting curve No. 2 in its new location as a part of the mixture we have 
the dotted line eb as representing the No. 2 material after it becomes a 
part, that is, 26%, of the mixture. The upper end must join the line bA 
because we are now plotting a curve which represents a mixture of the 
two materials, No. 3 and No. 2, and the mixture must be represented by 
one single, continuous curve. We may consider rb and ex as two base 
lines, divide the vertical distance between them into 100 parts, and then 
plot the percentages downward from rb, equivalent on the small scale to 
the percentages downward from DC to the original No. 2 curve CE, as 
described on page 198, or we may take ratios, as described on page 200, 
and using the slide rule set DE (100) on De (65) and on any vertical dis¬ 
tance from DC to the line CE, we may read the distance from rb to the 
resultant curve eb. In practice, the line rb need not be plotted, but each 
ratio as it is obtained may be added to the per cent, already found for the 
No. 3 material to obtain the distance down on the ordinate for the final 
curve of the mixture, as shown on page 787. 

The required percentage of material No. 1 may be obtained by deducting 
the sum of the percentages of No. 2 plus No. 3 from 100, or by inspection 
of the parabola and the curve of the portion of the final mixture already 
plotted, ebkA. From the location of the point e it is evident that 35% of 
the total mixture of the material must pass a 0.25-inch sieve. Since No. 1 
is the only material whose particles are finer than this, it is evident that 
this percentage of the total mixture must be entirely formed by No. 1. 
In other words, the percentage of No. 1 to the total mixture of 100 parts 
is 35 %* To P lot the curve OD as a part of the mixture, we may divide 
the distance eE into 100 parts, and plot the percentages, or we may take 
the slide rule and set Ee on DE, that is, 35 on 100, and read the correspond- 





CO 

UJ 

X 

o 

z 


CO 

LL) 

j 

o 

f— 

cc 

< 

Q. 


CO 

q: 

uj 


< 

a 


781 


Fig. 247. — Diagram Illustrating Method of Combining Curves which Overlap. (See pp. 782 to 784.) 








































































































A TREATISE ON CONCRETE 



ing ratios for the other ordinates. Thus, at ordinate o.io, DE: eE — 
ZW\: zW v or ioo: 35= 71: z\V v hence zW x = 25. 

The final curve of the mixture of materials No. 3, No. 2, and No. 1 in 
proportions represented by the percentages obtained is represented by the 
dotted line AkbezO. 

To illustrate how simply such a diagram as Fig. 246 is solved in practice 
without really going through the processes described, we may determine 
the percentage by weight of each material to the weight of the final mixture 
as follows: 

Cb 39 

For material No. 3, = — = 39% 

Cn 100 

re De — 39 26 

For material No. 2, 7— or —=—— = -= 26% 

DE DE 100 


For material No. 1, 


Ee 


35 


= 35 % 


c 


ED 100 

We have thus the percentages of each aggregate material which must be 
contained in the total mixture of aggregate. The actual proportions of 
the concrete expressed in parts are obtained in the same manner as is 
described for example 2 on page 788. 

Case II. Curves which overlap. Fig. 247 shows a more complicated 
combination of materials than Case I. Curves of four materials are 
drawn. 

From the foregoing it is clear that the percentage for material No. 4 is 
represented by Cb or 14%. Since curves No. 2 and No. 3 overlap each 
other, their values are less easily determined, and we may leave them 
and first take No. 1. Curve No. 1 is determined and may be plotted in 
the same way as curve No. 1 in diagram, Fig. 246, p. 776, giving the 


curve Osg, and the percentage 


g F _ 33 

GF 100 


= 33% the percentage by weight 


of No. 1 in the final mixture. 

Having found the per cent, of No. 1 sand to use and also of No. 4 stone, 
namely, 33% for No. 1 and 14% for No. 4, we have left 53% of the total 
mixture which must be made up from No. 2 and No. 3 lots. 

On curve FE the portion from E to / is overlapped by that part of the 
DC curve extending from D to K. We note first that about 20% of the 
material in the parabola (that portion extending from g to L) must be 
supplied with scone from the No. 2 lot, while about 10% of the material 
of the parabola (the portion extending from b to M) must come from the 
No. 3, or DC curve. There is left then 53% — (20% + 10%) = about 











APPENDIX IV 


7 8 3 

2 3 % the parabola which must be supplied from the overlapping 
portions of the two curves. Judging from the general appearance of the 
two curves it would appear that No. 2 curve contained stone more nearly 
corresponding to the needs of the parabola than DC. 

For a trial, therefore, we will give a larger proportion to No. 2 than to 
No. 3 stone, say, 14% of the remaining 23% to No. 2 and 9% to No. 3. 
No. 2 stone must then furnish 20 + 14 = 34% of the final mixture and 
No. 3 must furnish 10 + 9 = I 9% of the final mixture. Through g draw 
a base line gN on which to construct the new curve for FE. 34% higher 
up draw line PQ which forms the upper limit for new curve to represent 
FE and the lower limit for new curve to represent DC. Then 19% higher 
up draw line VI , which forms the upper base line for new curve to repre¬ 
sent DC. 

Now, by dividing the vertical distance between the lines gN and PQ 
into 100 equal parts, — or else by ratios, taking the slide rule and setting 
Pg on GF and reading from the ordinates of FE, the distances from the 
base line gN to the points which locate the curve ge, — we can readily 
transfer curve FE into the new curve indicated by the dotted line ge which 
is assumed to supply 34% of the stone still needed by the parabola, and 
in the same way by dividing the vertical distance between the lines PQ 
and Tb into 100 equal parts, — or else by taking ratios, — the new db 
curve can be laid down. 

The curve from g to j and from b to k remains as it is. 

With a pair of dividers transfer the distance at each ordinate from base 
line PQ up to curve db down to curve ge, and add it to the curve. These 
new points will give the dotted curve jk as the exact location of the two 
batches of stone No. 2 and No. 3 combined, 34% of the one being used 
and 19% of the other. 

The resultant curve, jk, may be found in another manner after selecting 
the percentages of the different materials by adding on any ordinate the 
percentages of each material in the final mixture. For example, on 1.00 
diameter, 26% of No. 3 stone passes a i-inch sieve, but since No. 3 actually 
occupies only 19% of the mixture, the percentage of No. 3 stone passing 
the i-inch sieve in terms of the weight of the total mixture (which is 100%) 
would be 19% of 26% = 5%. Similarly, the percentage of the portion of 
the No. 2 stone in the final mixture which passes a i-inch sieve is 34% of 
88% or 30%. All of the No. 1 material (33%) passes the i-inch sieve, 
so this too must be added to the others, and we have 5% + 30% + 33% = 
68% as the percentage of the final mixture which will pass a i-inch sieve. 

An inspection of this dotted line jk resulting from combining these 


7 8 4 


A TREATISE ON CONCRETE 


curves leads us to the conclusion that we should have done rather better to 
have taken more of No. 2 stone, say, 38% instead of 34%, and 15% of 
No. 3 instead of 19%, in which case the combined curve would have more 
nearly corresponded with the parabola. We would have, therefore, as a 
result of our study the required percentages of material as 14% of No. 4, 
15% of No. 3, 38% of No. 2, and 33% of No. 1. 

Practical Examples of Proportioning. Having taken up in a very 
elementary fashion the principles by which curves are drawn and com¬ 
bined, we may take two examples of other combinations of materials 
liable to be met with in practise. 

Example I. —- Curves oj two materials. Suppose we have for concrete 



Fig. 248.— Method of Proportioning Two Aggregates. (See p. 784.) 


the fine sand of Fig. 200, p. 198, to use with the crushed stone of Fig. 
7°, p. 192, what proportions of each should be employed and how could 
the mixture be improved? 

Solution. —The curves of the two materials are plotted to the same scale 
in Fig. 248 as OF and DBLA, and then the theoretical curve OCA drawn 
for convenience as a parabola by the method previously described. 

Fhe curve indicates that for a theoretical mix of sizes of aggregate up 
to if inches, 93% of the mixture should pass a ij-inch sieve, 76% should 
pass a 1-inch sieve, 53% a £-inch sieve and so on. 

Where, as in this case, the materials to be mixed are represented by cnly 
two curves, no combination of which will make a curve as close to the theo¬ 
retical as is desirable, there is another limiting condition which was brought 



















































































































APPENDIX IV 


785 


out by the experiments, viz., that for the best results the combined curve 
shall intersect the theoretical on the 40% line, at C, and that the finer mate¬ 
rial shall be assumed to include the cement. 

In this case, therefore, where the stone and sand curves do not overlap 
each other, to determine the best proportions of stone and sand, we have 
merely to take such proportions of each that the resultant curve will pass 
through the ideal curve at the point C where it crosses the 40% abscissa. 

EC 60 

This percentage is obtained by taking the ratio y— = •— = 61%. The 

EB 98 

percentage by weight of sand plus cement to total aggregate will be 100% 

— 61% = 39%. The curve of the mixture may now be drawn by re¬ 
plotting the curve DBLA in its new location JCGA and the curve OF in 
its new location OJ, thus making the combined curve OJCGA. 

Now decide upon the amount of cement to use in the mix to give the 
required strength of concrete, say, one cement to eight aggregate (the pro¬ 
portion of aggregate being based on measurement before mixing together 
the sand and stone), which will make the cement one-ninth or 11% of the 
total materials. Deducting this from the sand plus cement, we have 
39% — II % = 28% sand, and our best proportions for a 1:8 mixture 
will be. 11 parts cement: 28 parts sand: 61 parts stone, which is equivalent 
to 1: 2.5: 5.5. If the proportions are required by volume and the relative 
weights of the sand and stone differ from the relative volumes, the pro¬ 
portions should be corrected accordingly. 

Plotting the analysis curves of the two materials, as described above, 
shows immediately how to improve the mix. If, for instance, the crushed 
stone had been better proportioned so as to contain more particles of 0.5 
and 1.o inch diameter, — see curve DHA, — a curve much nearer the 
parabola could have been constructed. In this case the ratio would have 
EC 60 

been-= —= 66% of stone, and the proportions of cement, sand, 

ER 91 

and stone for a 1: 8 mixture, 11: 23: 66 or 1: 2:6, a stronger and a more 
impermeable mix. A still better mixture would have resulted with the 
use of coarser sand having a curve similar to the broken line OMN, which 
with the first material, DBLA, would have brought the continuous line 

MC 

of the mixture very much nearer the ideal curve, by using the ratio = 

— = e 4 % of curve DBLA and 46% of curve OMN. This method thus 
83 

shows not only the best proportions for given materials, but also the de¬ 
fects in the materials and how to remedy them. 







786 


A TREATISE ON CONCRETE 


The most valuable use of the method of proportioning by mechanical 
analysis is in cases where the character of the work warrants employing 
several grades, that is, several sizes, of stone and sand. Such mixtures 
are being increasingly employed as engineers and contractors more fully 
appreciate the necessity of so economically proportioning the materials as 
to produce a mixed aggregate of the greatest possible density, — that is, 
with the fewest possible voids, — thereby reducing the quantity of cement 
and at the same time improving the quality of the concrete, in other words, 
making both a better and a cheaper concrete. 

The process of determining the percentages of each material is more 
complicated than where only two aggregates, sand and stone, are used, 
but it is not very difficult in practice, especially if one is familiar with the 
slide rule, and, as illustrated in Example 2, the method is more exact than 



Fig. 249. —Method of Proportioning a Graded Mixture. (See p. 786.) 


with two materials, for the reason that the resulting curve can be made to 
more nearly approach the parabola. 

Example 2. — Graded Materials. Given the medium sand, represented 
by curve in Fig. 72, page 200 and the three sizes of crushed stone repre¬ 
sented by the curves in Fig. 71, page 198, find what percentage of each 
will best combine to make the strongest and densest concrete. 

Solution. Since mechanical, analysis of each material has already been 
made, we will immediately replot the four curves on the same scale in Fig. 
249 and draw parabola passing through point O and the point at which 
curve No. 4 reaches 100%. We see at once that percentage of No. 4 

Kk 36 

stone required is — = — = 36%. (To be sure, about 8% of No. 4 is 
overlapped by No. 3, but this is so slight it need not here be considered.) 






























































































APPENDIX IV 


787 

Let us determine sand curve No. 1 at 0.10 diameter ordinate, since it 
can be seen by inspection that the portion oh of curve No. 1 very nearly 
fits the parabola and grains smaller than 0.10 diameter must be supplied 
wholly from this curve, while the larger grains represented by portion hG 
are found also in No. 2 curve. Accordingly, we have the percentage 
Fj 20 

Fk = 88 = 23 ‘ /c '' 

A part of No. 3 curve, that portion extending from D to /, is overlapped 
by nearly the whole of No. 2 curve. We can see, however, that No. 3 
curve alone must supply 14% of the material in the parabola (that portion 
extending from e to k). This leaves 100—(36 + 23 + 14) = 27% of 
the mixture to be furnished by the overlapping portions of No. 3 and No. 2 
in such ratio as best fits the parabola. 

From a study of the two curves, we find by inspection and trial plottings 
that most of the material required would be better supplied by No. 2 curve, 
since it contains stone corresponding very well to the needs of that part of 
the parabola extending from / to e. Let us consider 23% as the proper 
amount of the final mixture to be furnished by No. 2 curve, which would 
leave 14 + 4 = 18% as the total portion which must be supplied by No. 3 
curve. 

Now, on any of the ordinates, we can locate points through which a 
curve may be drawn which represents a mixture of the given sand and 
stone in the proportions just found, for example: 


Ordinate. % Retained. 

i-75 40x36%'. = 14 

1 - 5 ° 57x36%. = 20 

1.10 92 X 36%. = 26 

1.00 (100x36%) + (8x 18%) = 36 + 1. = 37 

0.80 36 + (31 x 18%) = 36 + 6. = 42 

0.60 36 + (66 x 18%) = 36 + 12. = 4 & 

0.40 36 + (88 x 18%) + (21 x 23%) = 36 + 16 + 5. = 57 

0.30 36 + (93 x 18%) + (40 x 23%) = 36 + 17 + 9. = 62 

0.15 36 + 18 4- (92 x 23%) 4- (6x23%) = 36 + 18 + 21 + 1 = 76 

0.05 36 +18 + 23 + (3° x 23%) = 36+18+23+7. = 84 


These percentages are plotted on the diagram as small circles. The 
same points would have been obtained if we had begun at the left of the 
diagram and calculated the percentages passing the sieve. 

We find that a curve drawn through these points satisfies the parabola 
sufficiently well to assume that 23% of sand, 23% of finest stone, No. 2, 
18% of medium stone, No. 3, and 36% of the largest stone, No. 4, would 
make the best concrete mixture out of the given materials. 













788 A TREATISE ON CONCRETE 

If i: 7 concrete is wanted there would be * =14.3 parts cement, and 

the proportions would be 14: 23: 23: 18: 36 or 1:1.6:1.6: 1.3: 2.5 by weight. 
This would give very nearly an ideal mix, and the resultant concrete would 
be impermeable and very strong. 




INDEX 


Abrasion tests of mortar, 125 
Absolute volumes of sand, 145 
in mortar, 135, 146 
Abutments, design of, 583 
Accelerated tests of cements, 106 
See also Soundness 
Acids, effect upon concrete, 392 
Adath Israel Temple dome, 626 
Adhesion of cement, affected by regag¬ 
ing, 159 

mold for testing, 122 
tests of cement and mortar, 121 
Adhesion of concrete to steel, 456 
References, 728 

Adhesion of old and new concrete, 284 
Aggregate, definition, 20 
Aggregates. See also Broken stone 
See also Gravel 
See also Sand 
coarse, 34 
essentials, 2 
fine, 33 

laws of volumes and voids, 160 
properties of, 5 
selection, 12 
specification,33, 34 
voids and density, 168 
Akron cement, definition, 2c 
Alcohol, effect of. References, 741 
Alum and lye, waterproof wash, 342 
Alum and soap, waterproof mixture, 
344 

Am. Soc. C. E., standard cement tests, 

63 

Analysis chemical. See Chemical 
analysis 

mechanical. See Mechanical 
analysis 

Angle of internal friction, 662 
Annealing, test for first-class steel, 40 
Apparatus for cement testing, 80 
Aqueducts. See Conduits 
Arches, 533 

References, 728 
abutments, design of, 583 
bridges. See Bridges 
centering, 587 
classification, 536 


Arches, concrete vs. steel, 534 
construction, method of, 586 
dead loads, 544 
earth pressure, 544 
erection, 586 
example of design, 574 
fixed or continuous, 548 
formulas, general 549 
formulas, moment, thrust and 
shear at crown, 553 
groined, 696, 698 
history of concrete arches, 536 
loading to use in design, 580 
Melan system, 537 
moment at the crown, 551 
Monier system, 537 
notation, 545 

relation outer loads and reac¬ 
tions at supports, 545 
rib shortening, 558 
shape of ring, 540 
shear at the crown, 551 
steel reinforcements, 535 
strength. References, 739 
stress, allowable unit, 583 
temperature, effect of, 555 
thickness of ring at crown, 540 
three-hinged, 546 
thrust at the crown, 551 
two-hinged, 547 
Wunsch system, 537 

Ash pits, 703 

Asphalt for waterproofing, 344, 346 
Automatic concrete elevator, 268 
Automatic measurers for materials, 
264 

Bag of Natural cement, weight, 31 
Portland cement, weight, 29 
Bags for depositing concrete, 306 
Ball mill, 715 
Baltimore fire, 332 
Banded columns, 492 
Barrel of natural cement, weight, 31 
of Portland cement, weight, 29 
Barrel, volume of, 3, 218 
weight of, 2d 


789 




7QO 


INDEX 


Barrow. See Wheelbarrow 
Bars, concrete splitting at, 459 

deformed, use, 2, 463, 500, 645, 
670 

depth of concrete below, 460 
length to imbed in concrete, 464 
table of areas and weights, 507 
types of, 505. 

Basement walls, 619 
Batch mixers, 256 
Beams, plain. References, 739 
Fuller’s tests, 376, 378 
strength, 378 
tests of cement, 120 
Beams reinforced, 416. See also T- 
beams 

References, 740 
analyses, 749 

bending moments to use, 439 
circular, 774 

concrete bearing tension, analy¬ 
sis, 760 

continuous at the support, 428, 
475 l6 

cracks and corrosion, 336 
deformation and deflection 
curves, 409 

depths for different bending 
moments, 419 
diagonal tension, 443 
end reinforcement, 428 
examples of design, 419, 469, 476 
experiments, 477 
formulas for concrete bearing 
tension, 760 

formulas for parabola distribu¬ 
tion, 762 

formulas for rectangular, 418, 
7Si 

formulas for review, 420 
formulas for steel in top and 
bottom, 427, 757 
formulas for T-beams, 423, 754 
foundation, 649 
general principles, 400 
Hatt’s method of stress distribu¬ 
tion, 762 
haunch, 429 
horizontal shear, 443 
loads for different bending mo¬ 
ments, 419 

modulus of elasticity, 406 
neutral axis, location of, 416 
plane section before and after 
bending, 402 
rectangular, 416 
repetitive loading tests, 481 
shearing forces, 441 


Beams, reinforced, slab load, distri¬ 
bution of to supporting beams, 

4 3 1 

spacing of tension bars, 459 
steel in top and bottom, 427, 

5 i 6 , 757 

steel in top and bottom, example, 
47°, 471 

straight line theory, 415 
tables of constants, 519, 520 
tables of constants, beam with 
steel in top and bottom, 516 
table of depth of neutral axis, 
521 

tables of safe loads, 509—51 • 
Talbot’s tests, 477 
T-beam design. See T-Beams 
tensile resistance, 412 
vertical shear, 442 
weight of, 612 
working stress, 528 
Bellows Falls Canal Company wash¬ 
ing plant, 250 

Belt conveyor for concrete machinery, 

_ . 2 73 

Bending moment. See Moment 
Bending moment diagrams, 436, 522, 

524 

Bending moments and shears, 433 
Bending tests for steel, 39, 415 
Bent bars, points to bend, 458 
Berry’s repetitive loading tests of 
reinforced beams, 481 
Bertini system, 504 
Beton-coignet, definition, 2c 
Beton, definition, 2c 
Bin gates for sand and stone, 247 
Bins, for stone crushing plant, 245 
Blackwell’s Is. bridge, mixing plant. 

274 

Blocks, concrete building, 629 
in sidewalks, 599 
molded, 307 
Boiler settings, 703 
Boiling tests, 106. See also Sound¬ 
ness 

Bolts, foundation, 650 
Bonna system, 504 
Bond of concrete and steel, 456 
hooked bars, value of, 466 
working stress, 528 
to resist direct pull, 461 
Bonding old and new concrete, 284 
Boonton. N. J., dam, 300, 676 
Bottle kiln, 721 

Boulogne method of testing consist¬ 
ency of cement, 70 
Brand of cement, selection, 45 



INDEX 


79 1 


Breakwater, building, 307 
Brick, as a substitute for sand, 156 
Brick vs. concrete columns, 373 
Brick vs. concrete conduits, 680 
Bridge piers. See Piers 
Bridges. References, 728 
arch. See Arches. 

Granite Branch Bridge, 590 
Mystic River Bridge, 590 
Ross Drive Bridge, 590 
Walnut Lane Bridge, 532, 592 
Briquettes, for tensile tests, 72 

effect of eccentricity in placing, 93 
German standard, 92 
Broken stone, classification of, 161 

characteristics. References, 736 
compacting of, 179 
concrete vs. gravel concrete, 385 
cost of, 25 

cost of crushing, 246 
crushing, 241 
hauling, 249 
plant for, 245 

quality affecting concrete, 390 
screened vs. unscreened, 188 
screenings vs. sand, 153 
selection of, 12 
size affecting strength, 389 
size and shape, .effect upon per¬ 
meability, 35I.35 2 
specifications, 34 
tables of quantities for concrete, 
23 1 

typical mechanical analyses, 198 
uniform vs. graded sizes, 15 
voids vs. gravel voids, 174 
weight, 249 

Buckets for depositing concrete, 305 

Building construction, 607 
References, 729 
advantages of concrete, 607 
cost, 607 

curtain walls, 627 
Ingalls building, 607, 611, 621 
mixing concrete, 267 
Pacific Coast Borax Co., 621 
typical illustration, 613 
walls, 621 

Burning Portland cement, 713 

over-burning and under-burning, 
62 

Calcining Portland cement materials, 
713 

Calcium choride, 326 

Cambridge bridge, concrete machin¬ 
ery, 27 r 

Candlot’s tests of concrete, 367 


Car for conveying concrete, 279 
Castings, concrete, 628 
Cast piles, concrete, 651 
Cellar walls, 619 
forms, 620 

Cement. See also Cement testing 
affected by sea water, 309 
affected by sulphate water, 310 
approximate quantity formula, 
16 

barrel, volume, 3, 218 
barrel, weight, 2d 
chemical analyses, 47 
choice, 41 

classification, 47, 54 
cost, 24 

determination of proportion in 
concrete, 186 
effect of freezing, 319 
effect of percentage upon strength 
of mortar, 392 
essentials, 2a 
fatigue, 381 
fineness, 82 
flash set, 2a 
manufacture, 705 
materials for manufacture, 55, 
708 

method of analyzing, 745 
mixture with Puzzolan and slag, 
3i7 

paint, 330 

percentages in concrete, 298 
percu.yd.of concrete, curves, 228 
per cu. yd. of concrete, tables, 
230 

production, 706 
proportion in concrete, 213 
Puzzolan. See Puzzolan ce¬ 
ment 

quantity for concrete sidewalks, 
59 6 

selection of, 12 

specifications, 28 

specific gravity, 81 

storage, 239 

to resist sea water, 312 

water for chemical combination, 

85 

weight of, 114. 219 
Cement rock, 55, 709 

chemical analysis, 710 
Cement testing, abrasion, 125 
accelerated tests, iq6 
adhesion, 121 

Am. Soc. C. E. standard methods, 








79 2 


INDEX 


Cement testing, American vs. Euro¬ 
pean sieves, 84 
apparatus for laboratory, 80 
cautions, 2 a 
chimney test, 112 
color, 113 

compression machines, 116 
compression tests, 116, 136 
consistency, normal, 68 
effect of shape of specimen, 134 
elementary directions for testing 
soundness, 79 
fineness, 67 

fineness below No. 200 sieve, 85 
for small purchasers, 3 
mixing, 73 
moist closet, 75 
permeability, 128 
porosity, 125 
purity test, 4, 65 
rate of applying strain, 94 
rate of setting, 90 
relation of different tests, 134 
setting, 70 
shearing, 125, 136 
soundness, 77, 101 
specifications, 28 
specific gravity, 65 
standard sand, 71 
standard tests, 63 
steaming apparatus, 78 
tanks for briquettes, 76 
tensile briquette, 72 
tensile machines, 93 
tensile strength, 76 
tensile tests of cement and mor¬ 
tar, 97 

transverse tests, 120, 136 
water for normal consistency, 85 
weight, 114 
yield tests, 129 

Centigrade, to convert to Fahrenheit, 
10 

Centimeter, English equivalents, 10 
Centers, arch, 587 

Chalmette docks at New Orleans, 
2 75 

Chalk, chemical analysis, 710 
Charlestown bridge piers, 269 303 
Chaudy and Degon system, 504 
Chemical analysis, cement testing, 64 
clay, 710 
lime, 47 

method for cement, 745 
method for raw materials, 745 
Natural cements, 47 
Portland cements, 47 
Puzzolan cement, 47, 724 


Chemical analysis, raw materials for 
cement, 710 
sand 159b 
slag, 724 

Chemistry of hydraulic cements, 54 
Chimney expansion test, 112 
Chimneys, reinforced concrete, 630 
analysis of stresses, 765 
construction, 630 
design, 632, 765 
Edison Electric Illuminating Co., 
631 

example of design, 636 
formulas, 634, 765 
house, 704 

shear and diagonal tension, 772 
tables, 635, 636 

Chutes for depositing under water, 
3°3 

Cinder, concrete, rust protection, 329 
slabs, table, 515 
strength and elasticity, 394 
vs. stone concrete in fires, 2 x ? 
weight, 3, 611 
Cinder pits, 703 
Cinders, selection, 615 
specific gravity, 163 
Circular beams, 774 
reservoir, 701 

Classification of broken stone, 161 
of cements, 47, 54 
Clay, bearing power, 640 
chemical analyses, 710 
effect upon mortar, 154 
effect upon mortar. Refer¬ 
ences, 741 

for Portland cement manufac¬ 
ture, 56 

water-tightness, effect upon, 343 
Clinker, microscopical tests, 115 
Clip, form for tensile briquette, 77 
Coal pockets, 703 
Coatings, 318 

Coatings for waterproofing, 342 
Coefficient of expansion, 287 
Coignet system, 504 
Cold. See Freezing 
Coloring concrete, 595 
Color of cement, 113 
Columbian system, 504 
Columns, 488, 623 

concrete vs. brick, 373 
deformation of plain and hooped, 
494 

eccentric loading, 372, 558 
flexure, formulas, 558 
footings. See Footings, rein¬ 
forced 



INDEX 


793 


Columns, formulas for, 491 

hooped columns, formulas, 496 
hooped or banded, 492 
illustration of reinforcement, 613 
modulus of elasticity, 406 
molds at Harvard Stadium, 625 
plain concrete, strength of, 371 
reinforced, 488, 527, 624 
rich proportions of concrete, 489 
strength, 371, 488, 527 
structural steel reinforcement, 
497 

table of working loads, 492 
vertical bar reinforcement, 489 
working stress, 527 
Combined footing, 647 
Compacting of broken stone and 
gravel, 179 

Composition, of cement mortars, 132 
chemical. See Chemical analy¬ 
sis 

Portland cement, 58 
various mortars, 136 
Compressive strength. References, 7 38 
Compressive strength of concrete, 
355 

average table, 360, 361 
brief table for safe strength, 27 
cinder concrete, safe strength, 
394 

columns, 371, 
concentrated loading, 367 
formula, 356 
growth, 374 

safe strength, 27, 373, 527 
short prisms, 369 
tests, 362 

various authorities, 363 
vs. transverse strength, 381 
working, in extreme fiber, 528 
Compressive strength of mortar, 136 
Feret’s formula, 140 
Feret’s tests, 136, 146 
form of specimens, 117 
prisms, 406 
various, 136 
vs. tensile strength, 119 
Compressive strength of stone, 392 
Compressive tests of cement, 116 
Concentrated loading, effect of, 367 
diagram for moments and shears 
in continuous beams, 436 
Concentrated vs. distributed loading, 
368 

Concrete blocks, 629 
Concrete tile, 629 

Concrete, contract and specifications, 

32 


Concrete, definition, 2c 

gravel vs. broken stone, 385 
mixers, 256 

mixing. See Mixing concrete 
plants, 266 

proportioning. See Proportion¬ 
ing 

rubble, 296 
rubble, definition, 2c 
strength. See Strength 
stretch, 408 

tables of quantities of materials, 
230 

tables of volumes, 234 
theory of mixture, 186, 220 
uses, 11 

vs. brick columns, 373 
vs. brick conduits, 680 
vs. terra-cotta, 333 
weight, 3 

working stresses, 527 
Concreting, elementary outline of 
process, 11 

Conductivity of concrete, 335 
Conduits, 679 

References, 737 
arch top, 694 
brick vs. concrete, 680 
construction, 685 
design, 682 

earth pressure on, 693 
forms, 688 

formulas for rectangular, 694 
in tunnel, 688 

Jersey City Water Supply Co., 
683, 689 
rectangular, 694 
thickness of, 684 
water-tightness, 681 
Weston aqueduct, 682 
Conglomerate concrete, weight, 3 
Conglomerate, specific gravity, 163 
Consistency, Boulogne method, 70 
Consistency of concrete, 279 

depositing through trough, 278 
effect on modulus of elasticity, 
406 

effect on strength, 383 

effect on water-tightness, 338 

specifications, 36 

Consistency of mortar, effect upon 
strength, 152 

Consistency of paste and mortar, 
normal, 68, 85 

Constancy of volume. See Sound¬ 
ness 

Continuous beams, bending moments 
to use, 439 






794 


INDEX 


Continuous beams, design, 428, 471 
diagrams shear and bending 
moment, 435 

moment of inertia, effect upon 
bending moment, 430 
shear and bending moment dia¬ 
grams, 435 
span, 431 

stirrups, method of placing, 450 
Continuous mixers, 256 
Contract, form for concrete, 32 
Contraction joints, 285 
Contraction. References, 732 
Conveyor belt. See Belt conveyor 
Copings, 674 * 

Core walls, 678 

rubble concrete, 678 
thickness, 678 
Corrosion of steel, 327 
Corrosion of steel in beams, tests, 336 
Cost, building construction, 607, 624 
cautions, 2b 
concrete, 24 

essentials in estimating, 2b 
facing concrete, 289 » 

labor laying concrete, 25 
materials for concrete, 24 
Portland vs. Natural cement 
mortar, 43 

ramming concrete, 283 
rubble concrete, 675 
screening sand and gravel, 239 
sidewalk construction, 604 
stone crushing, 246 
Cottacin system, 504 
Counterfort retaining walls, 67 1 
Cracks in reinforced beams, 413 
corrosion of steel, 336 
Cross reinforcement of slabs, 422 
Crushed stone. See Broken stone 
Crusher, gyratory, 244 
Crusher, jaw, 242 

Cubes vs. cylinders vs. columns, 370 
Culvert, Kalamazoo, Mich., 684 
Cummings system, 504 
Cup bar, 504 

Curbing, concrete sidewalk, 602 
Curves of cement per cubic yard, 228 

Dams, 659, 674 

References, 731 

arched, 677 

Boonton, N. J., 676 

building of rubble concrete, 300 

C audiere Falls, P. Q., 264 

Chicopee River, building, 269 

gravity design, 675 

Ogden, Utah, 678 


Dams, reinforced design, 677 
Schuylerville, N. Y., 677 
Dead loads, arches, 544 
Definitions, 2c 

See material in question 
Deformation and deflection curves 
of a reinforced beam, 409 
Deformation of hooped and plain 
columns, 494 

Deformed bars, use, 2, 463, 500, 645, 
670 

Density, definition, 2c 

method of determining, 135 
Density of concrete, 354 

curves of maximum, 200 
relation to strength, 204 
studies of, 200 
table of tests, 376 
Density of mixed aggregates, 168 
Density of mortar, application of 
laws, 149 

relation to strength, 134 
tests of mortar, 138 
tests of mortars of coarse vs. 
fine sand, 149 
De Man rods, 506 
Depositing concrete, 276 
cautions, 2a 
specifications, 36 

Depositing concrete underwater, 301 
Depth, concrete below rods, 460 
Depth of T-beam, diagram, 525 
economical, 425 
example, 470, 471 
minimum, 424 

Derrick for laying concrete, 305 
Design. See article in question 
cautions, 2b 
Destructive agencies, 392 
Diagonal tension. See Tension, dia¬ 
gonal 

Diagrams, for arch design, 569, 572 
bending moments, 436, 522-524 
mechanical analysis, 197 
T-beam design, 525 
Diamond bar system, 506 
Dietzsch kiln, 721 
Dikes. See also Cor6 walls 

Metropolitan Water Works, 678 
Parsippany, laying, 273 
Distribution of beam and slab loads 
to girders, 432 

Distribution of slab load to support¬ 
ing beams, 431 

Distribution of stress, diagrams, 569, 

57 2 ’ 573 

plain concrete, 562 
reinforced concrete, 565 





INDEX 


795 


Domes, 626 

Temple Adath Israel, 626 
Yale University, 626 
Dome kiln, 721 

Donath system of reinforcement, 506 
Driveways, 606 
Dry concrete, 280 

rammers for. 281 
Dry concrete under water, 308 
Dry dock, building of rubble con¬ 
crete, 301 

Duplex paddle mixer, 258 • 
Durability, concrete inverts, 681 
concrete piers, 654 
Dwelling houses, 704 

Earth, bearing power, 639 
weight of, 662 
Earth pressure, 663 
arches, 544 
conduits, 693 
formulas, 664, 666 
inclined back of wall, 665, 666 
tables for, 663, 665 
vertical back of wall, 664 
wall with surcharge, 666 
East Boston Tunnel, 690 
mixing plant, 271 
Eccentric loading, 372 
Eccentric loads, diagrams, 569, 572 
distribution of stresses, plain 
concrete, 560 

distribution of stresses, rein¬ 
forced concrete, 563 
Economical depth of T-beam, 425 
diagram for, 525 
example of, 470, 471 
Edison Electric Illuminating Co., 
chimney, 631 

Elastic limit See also Yield point 
Elastic limit required in mild steel, 34 
Elasticity. See Modulus 
Electrolytic action, effect upon con¬ 
crete, 393 

Elementary volumes, 135 
Elevator, automatic concrete, 268 
Elevat rs, grain, 703 
Elongation in concrete, 408 
Elongation required in first-class j 
steel, 38 

Elongation required in mild steel, 34 
Estimating, essentials, 2b 
Erection of arches, 586, 

Expanded metal, 506 
Expansion joints. See Contraction 
joints 

Expansion of cement. See also 
Soundness 1 


Expansion of cement, measurement, 
111 

Expansion of concrete, while harden¬ 
ing, 287 

coefficient for temperature, 287 
Experiments upon reinforced beams, 
477 

Face cutter, 289 
Facing concrete walls, 288 

photographs of surfaces, 290 
specifications, 37a 
Factory construction, cost, 608 
Factory, Pacific Coast Borax Co., 621 
Fahrenheit, to convert to centigrade, 

1 o 

Fatigue of cement, 381 
Felt, waterproofing, 344 
Fences, 704 

Feret, R. Effect of Sea Water, 300 
Feret’s formula for normal consis¬ 
tency, 87 

Feret’s formulas for strength of 
mortar, 140 

Feret’s tests of strength of mortars, 
136 

Feret’s triangles, 144 
Ferroinclave system, 506 
Fiber stress vs. tensile stress, 121, 134 
Fineness of cement, advantages of, 82 
brief tests, 4 
below No. 200 sieve, 85 
effect on weight, 114 
specifications Natural cement, 31 
specifications Portland cement, 

3 ° 

standard test, 67 
strength affected by, 82 
Fire, Baltimore, 332 

Pacific Coast Borax Co., 331 
Fire protection, cinder vs. stone con¬ 
crete, 333 
concrete, 331 

concrete vs. terra-cotta, 333 
structural steel, 337 
theory, 334 

thickness concrete required, 333 
Fire resistance. References, 732 
Woolson’s tests, 335 
Fire-resisting qualities of concrete, 

3 2 7 

Flat slabs, 483 

foundation, 649 
tables of constants, 518 
Flexure and direct stress, diagram, 

5 6 9 - 57 2 > 573 

plain concrete, formulas, 561 
reinforced concrete, formulas, 564 






796 


INDEX 


Float, plasterer’s, 601 
Floors, construction, 608, 615 
design, 468, 609 
forms, 616 

illustration of reinforcement, 613 
Ingalls building, 611 
loads, 610 
materials for, 612 
proportions of concrete, 615 
reservoirs, 696 
slabs. See Slabs, 
weight of concrete in, 611 
Footings, design, 641 

combined, design of, 647 
I-beam, 643 
reinforced concrete, 644 
spread, 649 
square, design of, 644 
Forms. References. 732 

brief directions for constructing, 
J 9 

cautions, 2 a 
cellar wall, 620 
clamp for beam, 617 
conduit, 688 
floors, 616 
greasing, 296 
hollow walls, 623 
mass concrete, 293 
removing, 296 
specifications, 37 
time building, 9 
wall, 621 

Formulas. See article in question. 
Foundation bolts, 650 
Foundations, 639 
References, 733 
See also Footings 
beams and slabs, 649 
bearing power of soils and rock, 

6 39 

column, 643 
flat slabs, 649 
safe loads, 643 
spread, reinforced, 649 
under water, 656 
under water, laying, 303 
Freezing. References, 742 
effect of, 8, 319 
effect of calcium chloride, 326 
effect of salt, 324 
effect upon sidewalks, 602 
experiments, 321 
protection from, 323 
Freezing weather, construction in, 32 3 
specifications for laying in, 37 
French commission, method of pro¬ 
portioning, 192 


French commission, permeability 
test, 128 

porosity test, 126 
setting tests for cement, 89 
sieves for cement, 84 
standard sand,92 
yield tests, 129 

Friction, internal angle of, 662 
Frost. See Freezing 
Fuller’s beam tests, 376 
Fuller’s rule for quantities, 16 
Fuller, 'William B. Proportioning 
Concrete, 183 

Gabriel system, 506 
Gaging. See also Consistency 
water for sand, 179 
with sea water, 159b 
Gang for mixing concrete, 254 
Gates for sand and stone bins, 247 
German standard briquette, 92 
Gillmore vs. Vicat needles, 89 
Girders. See also Beams, reinforced, 
typical illustration of, 453, 613 
Glycerine, effect of. References, 741 
Grain elevators, 703 
Gram, English equivalents, 10 
Granite Branch Bridge, 590 
Granite, specific gravity, 163 
Granolithic, definition, 2c 
Granolithic finish for water-tight 
work, 341 

Granulometric composition of sand, 
142 

conversion to mechanical analy¬ 
sis, 151 

Grappiers cement, 50 

chemical analysis, 47 
definition, 2c 

Gravel, bearing power, 640 

characteristics. References, 736 
compacting of, 179 
cost of, 25 

cost of screening, 239 
screened vs. unscreened, 188 
selection of, 12 

size affecting strength of con¬ 
crete, 389 
specifications, 34 
specific gravity, 163 
tables of quantities for concrete, 
231 

voids vs. broken stone voids, 174 
weight of, 662 

Gravel concrete, vs. broken stone con¬ 
crete, 385 
weight, 3 

I Gravity mixers, 263 




INDEX 


797 


Greasing forms, 296 
Greenhouses, 704 
Griffin mill, 716 
Grinding cement, 712, 715 
See also Fineness 
Groined arches, 696, 698 
Groover for sidewalks, 601 
Grout for water-tight surfaces, 342 
Grouting, sand cement for, 42 
Growth in strength of cement mortar, 
99 

Growth in strength of concrete, 374 
Gutter, concrete, 603 
Gypsum, effect in sea water, 310 
effect on time of setting, 90 
Gyratory crushers, 244 

Habrich and Diising system, 506 
Handling concrete, 276 
data, 9 

Hand mixing of concrete, 251 
vs. machine, 251, 372 
Harvard Stadium. Frontispiece 
mixing machinery, 269 
pouring seat slabs, 628 
Haunch, design, 429 
length, 430, 472 
Heat. See also Temperature 
effect upon concrete, 335 
References, 742 

Heater for concrete materials, 324 
Heating concrete materials, 323 
Hennebique system, 506 
Herringbone frame, 506 
High carbon steel, specifications for, 

3 8 . 

vs. mild, 413 

Highway bridges, liveloads, 541 

Hinges for arches, 539 

Historical notes, 705 

Holzer system, 506 

Hooked bars, value in bond, 466 

Hooped columns, 492 

Hot tests, 106 

See also Soundness 
Houses, 704 
House chimneys, 704 
Hyatt system, 506 
Hydrated lime, 53 

added for water tightness, 342 
use with Portland cement, 43 
Hydraulic lime, 52 

chemical analysis, 47 
definition, 2c 
where used, 42 
Hydraulic modulus, 57 

Impermeable concrete. See Water¬ 
tight concrete 


Impermeability. See Water-tight- 
ness 

Impurities of sand, character, 154b 
effect upon strength of mortar, 
154a 

vegetable or organic, 154b 
washing tests for organic, 159a 
Inertia, moment of. See Moment of 
inertia 

Ingalls building, 607, 611, 621 
Internal friction, angle of, 662 
Inverts, durability of concrete, 681 

James River cement, definition, 2c 
Jaw crushers, 242 
Jerome park reservoir, 275 
Jersey t'ity Water Co. conduit, 683, 
689 

Johnson ring kiln, 721 
Johnson rods, 506 
Joints. See also Contraction joints 
construction of, 284 
in reinforced concrete, 284 
old and new concrete, 284 
specifications, 37 
Kahn bars, 506 
Kent mill, 717 

Kilns, rotary. See Rotary kilns 
Kilns, stationary, 721 
Kilograms per sq. cm., ratio to lb. per 
sq. in., 9, 93 

Kilograms, ratio to pounds, 10 
Kimball’s tests of concrete, 365 

Labor. See Time 

Laboratory, cement testing appara¬ 
tus, 80 

Laitance, chemical analysis, 302 
definition, 2c 
effect on strength, 384 
Laitier cement, definition, 2d 
Lath, metal, plastered walls, 627 
Laying concrete, elementary out¬ 
line, 11 
methods, 276 
specifications, 36 
time, 9 

Laying rubble concrete, 300 
Laying waterproofing felt, 345 
Leaks, closing, 691 
Length to embed bars, 464 
Lime and cement mortar, where used, 
42 

Lime, added for water-tightness, 342 
chemical analysis, 47 
effect of. References, 741 
effect upon strength of mortar, 
i54d 

hydrated. See Hydrated lime 






798 INDEX 


Lime, hydraulic. See Hydraulic lime 
in cement, limited in seawater, 

3 11 

in Portland cement, 62 
manufacture, 52 
mortar, where used, 42 
of Teil, 52 

of Teil, definition, 2d 
unslaked, 156 
weight and volume of, 156 
Limestone, chemical analyses, 710 
for cement manufacture, 709 
method of analyzing, 745 
specific gravity, 163 
Limestone concrete, weight, 3 
Line of pressure in arches, 555 
Liter, English equivalents, 10 
Literature, references to, 725 
Little Falls, N. J., feed tank, 700 
Live loads for highway bridges, 541 
railroad bridges, 543 
Loads, bridges, 541 
column, 623 

distribution from slab to beams, 
4 3 1 

floor, 610 

foundation, safe, 643 
roof, 618 

Loam, bearing power, 640 
effect upon mortar, 154a 
weight of, 662 
Lock-woven steel fabric, 506 
Louisville cement, chemical analysis, 
47 . . 

definition, 2d 
Lubricating forms, 296 
Lug bars, 506 

Lye and alum, waterproof wash, 342 

Machine mixing vs. hand, 251, 372 
Magnesia in cement for sea water, 31 o 
Magnesia in Portland cement, tests, 
5 . 6 . 

limiting percentage, 5, 30 
Magnesian lime, 53 

chemical analysis, 47 
Manufacture cement, 705 
Manufacture lime, 52 
Manufacture Natural cement, 722 
Manufacture Portland cement, 707 
processes, 7 1 o 
raw materials, 55, 708 
Manufacture Puzzolan cement, 723 
Manure, effect upon concrete, 393 
Marine construction. See also Sea 
water 

References, 734 

Marl for cement manufacture, 709 


Marl for cement manufacture, chem¬ 
ical analysis, 710 
Mass concrete, forms, 293 
McKibben, Arches, 533 
T-beam tests, 480 

Measurers for materials, automatic, 
264 

Measuring box, illustration, 18 
Measuring materials for concrete, 252 
Measuring water for concrete, 266 
Mechanical analysis, 193 
broken stone, 198 
conversion to granulometric com¬ 
position, 151 

curves, plotting of, 196, 775 
proportioning, 206 
sieves, 194 
typical sands, 194 
Melan system, 506 
Melan system of arches, 537 
Metal lath, walls plastered, 627 
Meter, English equivalents, 10 
Metric system, ratios for converting, 9 
Metric units of strength, converting 
to English units, 93 
Mica, effect on strength of mortar, 
1 54 c 

Microscopical examination of cement, 

JI 5 

Mild steel vs. high carbon, 413 
Mill, ball, 715 

Mill construction, cost, 608 
Mill, tube, 716 
Millimeter, ratio to inch, 10 
Minimum depth of T-beams 424, 525 
example, 470, 47 1 
Mixers for concrete, 256 
batch, 256 
continuous, 256 
duplex paddle, 258 
gravity, 263 
revolving pan, 258 
rotary, 258 
rotary cube, 258 
Mixing concrete, 251 
belt conveyors, 272 
Blackwell’s Is. bridge piers, 274 
Cambridge bridge piers, 271 
Cambridge Electric Light Sta¬ 
tion, 269 
cautions, 2a 
central plant, 268 
Chalmette docks at New Orleans, 
2*75 

Charlestown bridge pier, 269 
Chicopee River dam, 269 
detail directions, 20 
East Boston tunnel, 271 







INDEX 


799 


Mixing concrete, gang, 254 
hand, 251 

hand vs. machine, 251, 372 
Harvard Stadium, 269 
Jerome Park reservoir, 275 
machine, 255 
Painesville bridge, 275 
Parsippany dike, 273 
platform over mixer, 266 
specifications, 36 
stationary plant, 267 
time, 9 

Williamsburg bridge pier, 273 
Mixing machinery, portable, 264 
Modulus of elasticity of concrete, 403 
beams vs. columns, 406 
cinder concrete, 394 
determining of, 403 
effect of consistency, 407 
in compression, 403, 405 
in tension, 408 
• Kimball’s tests, 405 

ratio of moduli, 403, 408, 529 
tests with different proportions, 
404 

Modulus of elasticity of steel, 402 
Moist closet, illustration, 75 
Molded blocks, 307 
Mold, for adhesion test, 122 

for briquettes for tension, 72 
for concrete cubes, 397 
Molds for concrete. See Form 
Molds, pouring concrete, 628 
Moment, bending, concentrated load, 
441 

crown, arches, 551 
diagrams, 522, 524 
diagram, continuous beam, 435 
for beam design, 439 
formulas for, 434 
Moments of inertia, table 438 
effect of varying, 430 
Moments of resistance of beams, 753 
Money, foreign, U. S. equivalents, 10 
Monier system, 506 
arches, 537 

Mortar, affected by freezing, tests, 
3 21 

affected by sea water, 309 
composition of various, 136 
compressive tests of prisms, 406 
definition, 2d 
density, 138 

elasticity tests of prisms, 406 
effect of regaging, 157 
Feret’s tests of strength, 136, 146 
gaging with sea water, 159b 
porosity, 127 


Mortar, selection of sand, 149 

strength and composition of, 132 
table of quantities and volumes, 
229 

tests. See Cement testing 
tests with coarse vs. fine sand, 
149 

tests of sand for, 159 
weight, 3 
yield tests, 129 
Mushroom system, 506 
Mushy concrete, 280 
Mushy concrete, rammers,- 282 
Mystic River bridge, 590 

Natural cement. See also Cement 
Natural cement, affected by freezing. 
320 

chemical analyses, 47 
classification, 49 
definition, 2d, 31 
growth in strength, 100 
manufacture, 722 
specifications, 31 
vs. Portland cement mortar, 
cost, 43 
weight, 2d 
where used, 41 

Natural Portland cement, 48 
Neutral axis, location of, 416 
table, 521 

Talbot’s formula, 479 
Newbury, Spencer B. Chemistry of 
Cements, 54 

New York subway, 347, 693 
Notation, standard, 529 

Office building construction, cost, 607 
Office buildings. See Ingalls build¬ 
ing 

Ogden, Utah, dam, 678 
Oil, effect upon concrete, 393 
Oil for greasing forms, 296 
Organic impurities in sand, 159a 
Ornamental construction, 628 

Pacific Coast Borax Co., factory, 621 
fire, 331 

Paddle mixers, 258 

Paint, cement for protecting steel, 

33 ° 

Painesville bridge, 275 
Parabola, construction of, 775 

theory of stress, formulas, 762 
vs. straight line theory, 407 
Parker’s cement, definition, 2d 
Parmley ystem, 506 
Parsippany dike, mixing plant, 273 



8 oo 


INDEX 


Paste. See also Mortar 
definition, 2d 
weight and volume, 3 
Pavement, street, 606 
Peat, effect of. References, 741 
Penstock, Grenoble, France, 684 
Percentage of cement in concrete, 
298 

Percolation. See Permeability 
Permeability. See also Water-tight- 
ness 

Permeability. References, 734 

cement, effect of percentage of, 

35 1 

concrete, 338 

coarseness of sand, effect of, 353 
laws of, 349 
method of testing, 347 
mortar, 128, 338 
pressure, increase with, 351 
results of tests, 351 
shape of stone, effect of, 351 
size of stone, effect of, 352 
specimen for testing, 348, 349, 
35o 

tables, 352, 353 

tests of cement and mortar, 128 
Philadelphia subway, 347, 693 
Pick for facing concrete, 289 
Picked surface of concrete, 290 
Piers, Blackwell’s Is. bridge, laying, 
274 

bridge, 654 

Cambridge bridge, 271, 305 
Charlestown bridge, 269, 303 
design, 655 
reservoir, 696 

standard, N. Y. C. R. R., 657 
Williamsburg bridge, laying, 273 
Piles of concrete, 650 

Boston Woven Hose and Rubber 
Co., 654 
cast, 651 
cores for, 652 
reinforced, 651, 654 
sheet, 653, 655 
with enlarged footing, 653 
Piles of timber, 640 

concrete capping for, 641 
formula, 640 
safe loads, 640 
spacing, 641 
Pipes, circular, 694 
Placing concrete. See Depositing 
Plane section before and after bend¬ 
ing, 402 

Plants for making concrete, 266 
Plastering, 292 


Plastering, for water-tight work, 341 
Plaster of Paris. See also Gypsum, 
effect of. References, 742 
effect on time of setting, 90 
Plasters and coatings, 318 
Plastic concrete, 308 
Poles, telegraph, 702 
Poling boards of concrete, 653 
Porosity. References, 734 
concrete, 339 
different mortars, 127 
tests of mortar, 125 
Portable mixing machinery, 264 
Portland cement. See also Cement 
affected by freezing, 319 
brief specifications, 29 
chemical analyses, 47, 710 
color, 113 
composition, 58 
definition, 2d, 29, 48 
full specifications, 29 
growth in strength, 99 
manufacture, 707 
materials for manufacture, 55, 
708 

method of analyzing, 745 
structures requiring, 41 
vs. Natural cement mortar, cost, 
43 

weight packed and loose, 2d 
Pounds per sq. in., ratio to kg. per 
sq. cm., 9, 93 

ratio to tons per square foot, 10 
Probst’s tests on corrosion of steel, 

33 6 

Pressure, earth. See Earth pressure 
Pressure, line of, in arches, 555 
Prisms, strength of, 369 
Production of cement, 706 
Proportioning concrete, 183 
arbitrary selection, 187 
cautions, 2 a 

determination of cement, 186 
elementary directions, 13 
French method, 192 
Fuller’s method, 202 
importance of proper, 183 
inaccurate methods, 190 
in practice, 213 
laws of, 204 

materials by weight, 265 
mechanical analysis, 193 
mechanical analysis diagrams, 
206 

methods of, 184 

practical, during progress of 
work, 211 
principles, 185 







INDEX 


801 


Proportioning concrete, Rafter’s , 
method, 192 

sea-water construction, 316 
trial mixtures, 210 
typical structures, 212 
units for, 217 
void determination, 189 
volumetric synthesis, 210 
Proportioning concrete, volumes, 218 
water-tight work, 339 
Proportions, expressing, 217 
for concrete floors, 615 
for concrete sidewalks, 594 
for various structures, 14 
rawmaterialfor Portland cement, 
55 - 7 ° 8 

sand and stoneaffectingstrength, 
174 

specifications for concrete, 35 
Protection of metal, 327 
References, 735 
Puddling concrete, 281 
Pug mill, 720 

Pulverized rock, effect upon water¬ 
tightness, 343 
Purity test for cement, 4 
Puzzolan cement, 50 

added for water-tightness, 342 
chemical analysis, 47, 724 
definition, 2d 

effect of addition. References, 742 
manufacture, 723 
mixed with Portland, in sea 
water, 313, 317 

water-tightness, effect upon, 342 
where used, 42 

Quaking concrete, 280 
Quantities materials. References, 

743 

for concrete, 14, 231 
for concrete sidewalks, 596 
for mortar, 229 
for rubble concrete, 298 
formulas, 16, 221 
Quartering, method, 398 
Quicklime. See Lime. 

Rabitz system, 506 
Rafter’s method of proportioning, T9 2 
Railroad bridges, live loads, 543 
Rammers, for dry concrete, 281 
for mushy concrete, 282 
Ramming concrete, 281 
labor, 9, 283 
Ransome system, 506 
Reaction at supports, formulas, 433 


Rectangular beams. See Beams, 
reinforced 

References to concrete literature, 
. 7 2 5 

Regaging mortar and concrete, 157 
effect upon adhesion, 159 
effect upon setting, 159 
retarded set. References, 742 
Reinforced beams. See Beams, rein¬ 
forced 

Reinforced columns, 489. 

See also Columns 
Reinforced concrete, 399 
brief laws, 7 

strength. References, 740 
working stresses, 527 
Reinforced concrete footings. See 
Footings 

Reinforced floors, 609 
Reinforced slabs. See Slabs 
Reinforcement. See also Steel 
arch, 535 
beam, types, 453 
caution, 2a 

diagonal tension, example, 472, 
473-474 

placing, specifications, 37 
stirrups, types, 455 
typical floor, beams, and col¬ 
umns, 613 

vertical and inclined, 448 
Removing forms, 296 
Repetitive loadings, tests of beams, 
481 

Reservoirs, 695 

References, 735 
Albany Filtration Plant, 696 
Astoria Water Works, 346 
circular, design, 701 
covered, 695 
floors, 696 
open, 695 
piers, 696 
roofs, 698 
storage, 701 
walls, 696 
Waltham, 701 
waterproofing, 346 
Reset concrete, 308 
Residences, 704 
Retarded set. See Regaging 
Retaining walls, 659 

angle of internal friction, 662 
backing, 662 
copings, 674 
earth pressure, 663 
foundations, 660 
gravity section, 661 







802 


INDEX 


Retaining walls, reinforced concrete, 
667 

table for gravity sections, 661 
T-type, design of, 668 
with counterforts, design of, 671 
Revolving pan mixer, 258 
Revolving screens, 240 
Rib shortening, effect in arches, 558 
Roadbeds, 703 
Rock, bearing power, 639 
Rockingham Power Company, 
washing plant, 250 
Rods. See Bars 
Roebling system, 506 
Roller, dot, for sidewalks, 602 
Rollers for conveyor belt, 272 
Roman cement, chemical analysis, 47 
definition, 2d 
Roofs, construction, 618 
loads, 618 
reservoirs, 698 

Rosendale cement, chemical analysis, 
47 . . 

definition, 2d 
Ross Drive bridge, 590 
Rotary kilns, for dry materials, 711 
for wet materials, 719 
vs. stationary, 722 
Rotary mixers, 258 
cube mixer, 258 
Roundhouse, 703 
Rubble concrete, 296 
Boonton dam, 300 
core walls, 678 
costs, 675 
definition, 2d 
labor, 300 
laying, 300 

proportion of rubble, 299 
quantities of materials, 298 
table of materials, 236 
table of volumes, 237 
Rusting of steel in concrete beams, 
tests, 336 

Rust prevention, 327 
Rusty steel, protection, 328 

Salt in mortar, 324 
References, 742 
percentage to use, 325 
Sampling cement, standard method, 
64 

Sampling iron, illustration, 64 
Sand, absolute volumes, 145 

American vs. European stand¬ 
ards, 90 

bearing power, 640 
cautions, 1 


Sand, characteristics. References, 
736 

chemical composition of, 159b 
coarseness, effect on permeabil¬ 
ity, 353 

compacting, 181 
comparative tests, 151 
cost, 25 

cost of screening, 239 
defining coarseness, 181 
effective size, 182 
effect of shape of grain, 174 
effect of size, 147 
essentials, 1 

Feret’s 3-screen analysis, 142 

for sea-water construction, 316 

granulometric composition, 142 

impurities, 154a 

microscopical examination, 159b 

moisture in, 176 

mortar tests with various, 136 

photographs, 175 

properties, 5 

selection, 12, 149 

shaken vs. loose, 145 

sharpness, 154a 

specific gravity, 163 

specifications, 33 

standard, 71 

table of quantities for mortar, 
2 29 

tables of quantities for concrete, 
231 

tests for mortar and concrete, 
J 59 

typical mechanical analyses, 200 
uniformity coefficient, 181 
vs. screenings, 153 
washing, 250 
water for gaging, 179 
weight of, 223, 662 
Sand cement, definition, 2d 
manufacture, 48 
use of, 42 

Sandstone concrete, weight, 3 
Sandstone, specific gravity, 163 
Sawdust, effect of. References, 742 
Scales for cement, illustration, 68 
Schoefer kiln, 721 
Schulter system, 506 
Scofield system, 506 
Screened vs. unscreened gravel or 
stone, 188 

Screening sand and gravel, 239 
Screenings, effect of moisture, 176 
properties of, 5 
specifications, 33 
vs. sand, 153 ..... . 


INDEX 


803 


Screens, inclined, 240 
rotating, 240, 246 
Sea water. References, 736 

action of sulphate waters, 310 
concrete in, 308 
effect of, 8, 309 

experiments with cement in, 312 
gaging with, 159b 
laying concrete under water, 301 
marine construction. Refer¬ 
ences, 734 

sign of injury from, 310 
Set, Hash of cement, 2a 
Setting of cement, arbitrary periods, 
88 

brief tests, 4 
chemical process, 57 
European tests, 89 
flash set in concrete, 2a 
rate, 90 

regaged mortar, 159 
rise in temperature, 130 
specifications, Natural cement, 
3 1 . 

specifications, Portland cement, 
3 ° 

standard tests, 70 

Setting of cement, typical cements, 
90 

Sewers. See also Conduits 
References, 737 
Chicago Clearing Yard, 683 
N. Y. Transit Commission, 686 
Williamsport, Pa., 683 
Sharpness of sand, 154a 
Shear, chimney, 772 

computation in beams, 446 
crown, arches, 551 
diagonal tension, 443 
horizontal, in a reinforced beam, 
443 

strength of concrete, 382 
vertical, in a reinforced beam, 
442 

vertical, in flange of a T-beam, 
442 

working stress, 528 
Shears and bending moments, 433 
diagrams, 435 

Shearing forces in beams and slabs, 
441 

Shearing tests of concrete, 382 
Schuylerville, N. Y., dam, 677 
Sheet piling, concrete, 653, 655 
Shrinkage. See Contraction 
reinforcement, 499 
Sidewalks, 593 

affected by frost, 602 


Sidewalks, color, 595 

cost and time of construction, 
604 

foundation, 598 

materials, 593 

method of laying, 598 

proportions of concrete for, 594 

thickness, 598 

tools, 597 

vault light construction, 603 
wearing surface, 600 
Sieves, American vs. European, 84 
for mechanical analysis, 194 
for sand tests, 159a 
for standard cement tests, 67 
Silica cement. See Sand cement 
Silos, 704 

Slabs, reinforced, 421 

cross reinforcement, 422 
design, 421 

example of design, 469 
flat, 483 

ratio of steel, computing of, 422 
shearing forces, 441 
span of continuous, 431 
square and oblong, 422 
tables for cinder concrete slabs, 

5 1 5 

tables for flat slabs, 518 
tables of safe loads, 512-515 
weight of, 612 

Slab load, distribution to the sup¬ 
porting beams, 431 
Slag cement. See Puzzolan 
definition, 2d 

mixture with cements, 317 
Slag, chemical analyses, 724 

for Portland cement manufac¬ 
ture, 709 

for Puzzolan cement, 723 
Slate, specific gravity, 163 
Soap and alum waterproof mixture. 
344 

Soap for greasing forms, 296 
Soda, effect of. References, 742 
Soil, bearing power, 639 
Soundness of cement, 101 

apparatus for steaming, 78 
appearance of pats, 104, 108 
brief tests, 3 

elementary directions for test¬ 
ing, 79. 

specifications, Natural cement, 

3 2 

specifications, Portland cement. 

30 

standard test, 77 

Spacing of stirrups. See Stirrups 





8o4 


INDEX 


Spacing of tension bars in a beam, 
459 

Spandrels for arches, 5 38 
filled, 538 
open, 539 

Specific gravity, cements, 81 
cinders, 163 

device for dropping material, 81 
gravel, 163 

Le Chatelier’s apparatus, 66 
sand, 163 

specifications, Natural cement, 
3 \ 

specifications, Portland cement, 
3 ° 

standard cement test, 65 
stone, 162, 163 
test for sand and stone, 164 
Specifications. References, 737 

first-class or high-carbon steel, 38 
mild steel, 34 
Natural cement, 31 
Portland cement, 29 
Portland cement concrete, 32 
proportioning concrete, 217 
reinforced concrete, 32 
waterproofing, 344 
Specimens for testing concrete, 395 
Specimens for testing permeability, 
348 

Stadium, Harvard. See Harvard 
Stadium 

Standard notation, 529 
Stairs, design, 617 
Stand-pipe, Milford, Ohio, 700 
Stationary kilns, 721 
vs. rotary, 722 
Steaming. See Soundness 
Steaming apparatus, illustration, 78 
Steel, adhesion to concrete, 456 
adhesion. References, 728 
areas and weights of rods, 507 
area in T-beams, 426 
area in T-beams, diagram, 525 
area in T-beams, example, 470, 
471 

bars. See Bars 
bending tests, 415 
bond to concrete, 456 
chemical union with cement, 330 
high carbon vs. mild, 413 
modulus of elasticity, 402 
protection by concrete, 327, 337 
protection. References, 735 
quality for reinforcement, 413 
reinforcement of arches, 535 
rods. See Bars 

spacing of bars in beams, 459 


vSteel, specifications for first-class, 38 
specifications for mild, 34 
types of bars, 505 
working stress, 529 
yield point, 413 
Stirrups, 445 

beams, rectangular not requir¬ 
ing, 455 

diameter, 453, 472 
illustration of action of, 445 
in continuous beam, 450 
points, where not needed, 451 
spacing, 450, 472 
spacing, graphical method of, 

452 , 473 
types, 452 

Stone, broken. See Broken stone 
Stone, compressive strength, 392 
specific gravity, 162, 163 
washing of, 250 
Stone crushers, 242 
Stone crushing, 241 
cost, 246 

Storage of cement, 239 
Storage reservoir, 701 
Straight line theory of reinforced 
beams, 415 

Street pavements, 606 
Strength, compressive. See Compres¬ 
sive strength 

transverse. See Transverse 
strength 

shearing. See Shearing strength 

Strength o' cement, 99 

affected by fineness, 83 
Strength of cinder concrete, 394 
Strength of columns, 371 
Strength of concrete, 354 
References, 738 
consistency, effect of, 383 
cubes vs. cylinders vs. columns, 

37 ° 

density, relation to, 204 
eccentric loading, effect of, 372 
effect of fine material in filling 
voids, 154c 
growth, 374 
heat, effect of, 335 
laitance, effect of, 384 
laws, 6, 390 

machine vs. hand mixed, 372 
percentage of cement, effect of, 
39.2 

quality of stone, effect of, 390 
relative proportions of sand and 
stone, effect of, 173 
safe, 29, 373 




INDEX 


805 


Strength of concrete, size of stone or 
gravel, effect of, 389 
tables, 360, 376 
Strength of mortar, 99, 132 
affected by freezing, 323 
affected by impure sand, 154a 
affected by lime, i54d 
affected by mica, 154c 
affected by quantity of water, 
!52 

affected by size of sand, 147 
Feret’s formulas, 140 
Feret’s tests, 136, 146 
gaging with sea water, effect of, 
J 59h 

■aws, 6, 133 
relation to density, 134 
Strength of reinforced beams, tables, 
5 ° 9 , 5 X 9 

Strength of reinforced slabs, tables, 
5 12 > 5i5 

Stress-deformation curve, 403 
Stresses, working unit, in arches, 583 
in reinforced concrete, 527 
Stretch in concrete. See Elongation 
Structural steel, protected by con- 
crete, 337 

reinforcement of columns, 497 
Structures, miscellaneous, 702 
Subways, 692 
design, 692 
New York, 347, 693 
Philadelphia, 347, 693 
Sugar, effect of. References, 742 
Sulphate of lime in cement material, 
56 

Sulphate waters, effect on concrete, 
3 }° 

Sulphuric acid, effect on concrete, 

3 ro . 

limit in Portland cement, 5, 30 
Sulphuric anhydride. See Sulphuric 
acid 

Surfacing walls, 288 
specifications, 37a 
Systems of reinforcement, 504 

Tables. See also matter in question, 
areas, weights and circumfer¬ 
ences of bars, 507 
beams with steel in top and 
bottom, 516 

chimney design, 635, 636 
constant C, for design of rein¬ 
forced beams, 519, 520 
depth of neutral axis, 521 
earth pressure, 665 
flat slabs, 518 


Tables, retaining walls, 661, 663 

safe loadings for rectangular 
beams, 509, 510, 511 
safe loadings for slabs (for design¬ 
ing), 512, 513 

safe loadings for slabs (cinder 
concrete), 514 

safe loadings for slabs (for 
review), 514 

Talbot’s reinforced beam tests, 410, 
477 

Tallow, effect of. References, 742 
Tanks, 698 

References, 735 
construction, 699 
Illinos Steel Co., 700 
for immersing briquettes, 76 
Little Falls, N. J., 700 
Tar for waterproofing, 344 
T-beams reinforced, breadth of 
flange, 424, 470 
design, 423 
details of design, 426 
diagram for design, 525 
economical depth, 425 
economical depth, example, 470 
example of design, 469, 471 
McKibben’s tests, 479 
minimum depth, 424 
minimum depth, example, 470 
shear, vertical, in flange, 442 
steel, area of, 426 
steel area, example, 470, 471 
web determined by shear, 424 
web determined by shear, exam- 
. pie, 470, 47 y 
Teil, lime of, definition, 2d 
Telegraph poles, 702 
Temperature, Boonton dam, 285 
effect on strength, 322 
rise in concrete while setting, 131 
rise in mortar while setting, 130 
Temperature stresses, 499 
arches, 555 
reinforcement, 499 
table of percentage of reinforce¬ 
ment, 502 

Tensile resistance in concrete, 412 
Tensile strength. References, 739 
cement and mortar, 99 
machines for testing, 93 
specifications, Natural cement, 31 
specifications, Portland cement, 
4 , 3 ° 

standard cement test, 75 
various mortars, 136 
vs. compressive, 119 
vs. fiber stress, 121, 134 






8 o6 


INDEX 


Tension, diagonal, 443 
chimney, 772 
computation, 446 
illustration, 445 

reinforcement for, example, 472, 
473 . 474 

working stress, 528 
Terracotta, substitute for sand, 156 
vs. concrete, 333 

Testing cement. See Cement testing 
Testing concrete, form for records, 
39.6 

specimens, 395 

Testing machines, compressive, 116, 
tensile, 93 

Testing permeability, 347 
Testing sand for concrete, 159 
sieves for, 159a 

washing tests for organic im¬ 
purities, 159a 

Testing steel, specifications, 39 
Tests. See material ir question 
See also Cement testing 
Thacher rods, 5oh 

Theory, of a concrete mixture, 186, 
220 

reinforced beams, 751 
Thermal conductivity of concrete, 

335 

Three-hinged arch, 546 
Thrust arches, effect of, 555 
Thrust at crown, arches, 551 
Ties, railroad, 703 
Tile, concrete, 629 
Time, building forms, 9 
facing concrete, 289 
filling barrows, 9 
mixing and laying concrete, 9 
ramming concrete, 283 
screening sand, 239 
sidewalk construction, 604 
Tonne, English equivalents, 10 
Tons, per sq. ft., ratio to lb. per sq. 
in, 10 

Tools for concrete work, 17 

for sidewalk construction, 597 
Transporting concrete, 276 
Transverse strength, concrete, 378 
concrete, table, 376 
various mortars, 136 
vs. compressive, 134, 381 
Transverse stress, formula, 379 
Transverse tests of cement, 120 
Trap concrete, weight, 3 
Trap, specific gravity, 163 
Triangle mesh, 506 
Triangles, Feret’s, 144 
Trowel, edging, 602 


Trowel, plasterer’s, 601 
Troweling surface for water-tightness, 
. 34 * 

Trussit system, 506 
T-shaped beams. See T-beams 
Tube mill, 716 

Tubes for depositing under water, 303 
Tunnels, 689 

References, 743 
closing leaks, 691 
conduits, 688 
construction, 690 
design, 689 
East Boston, 689 
Harlem River, 689 
Pennsylvania R. R., 689 
Pittsburgh, Carnegie & Western 
R. R., 689 

Turneaure’s reinforced beam 
tests, 408 

Two-hinged arch, 547 

Uniformity coefficient of sand, 181 
Unsoundness. See Soundness 

Vassy cement, 49 

chemical analysis, 47 
definition, 2d 

Vault light construction, 603 
Vegetable impurities, 154b 
Vicat needle, illustration of, 69 
vs. Gillmore needle, 89 
Vissintini system, 506 
Voids, definition, 2d 

in aggregates, laws, 160 
in concrete, 339 
in gravel vs. broken stone, 174 
in mixed aggregates, 168 
in mortar, 127 
in pile of spheres, 168 
in sand and stone, determining, 
i6 5 

in sand and stone, tables, 166 
in sand, effect of moisture, 176 
proportioning concrete by, 189 
Volume of concrete, formulas, 221 
tables, 234 

Volume of loose concrete, 277 
Volume of mortar, tables, 229 
Volumetric composition of mortar, 
T r 35 

Volumetric synthesis, 210 
Volumetric tests, concrete, 140 
mortar, 138b 

Walls, 619, 621 
cellar, 619 

cutter for facing, 289 



INDEX 


807 


Walls, facing, 288 
forms, 621 
hollow, 623 

illustration of reinforcement, 613 
mortar, plastered upon metal 
lath, 627 

photographs of surfaces, 290 
placing concrete, 623 
reservoir, 696 

retaining. See Retaining walls 
Walnut Lane bridge, 532, 592 
Waltham reservoir, 701 
Washed surface of concrete, 290 
Washing plant, Bellows Falls Canal 
Company, 250 

Rockingham Power Company, 
250 

Washing sand and stone, 250 
Washing test for organic impurities, 
159a . 

Water, approximate percentages for 
testing cement, 87 
depositing concrete under, 301 
effect of excess in concrete, 302 
effect upon strength of mortar, 

J 5 2 

for chemical combination, 85 
for mortar of normal consist¬ 
ency, 88 

for paste and mortar, 85 
in concrete. See Consistency 
in concrete. References, 743 
measuring for concrete, 266 
required for gaging sand, 179 
Waterproofing, alum and lye, 342 
asphalt, 344- 346 
materials and methods, 344 
felt, 344 

specifications, N. Y. Subway, 344 
Waterproofing, treatment of surface, 

34 1 . . 

granolithic finish, 341 
grout, 342 
plastering, 341 
troweling surface, 341 
Water-tight concrete, construction 
without waterproofing, 347 
laying, 338 
proportions for, 339 
thickness for, 340 
treatment of surface, 341 
AVater-tight joints, 286 
Water-tightness, 338 

alum and soap, effect of, 344 
brief laws, 8 


Water-tightness,conduits, 681 
effect of consistency, 338 
effect of lime and Puzzolan 
cement, 342 
experiments, 347 
pulverized rock, effect of, 343 
Wear, ability to withstand, 654, 
Wearing surface, concrete sidewalks, 
600 

Wearing tests of mortar, 125 
Weighing machine, automatic, 713 
Weight, bag of Natural cement, 31 
bag of Portland cement, 29 
barrel of Natural cement, 31 
barrel of Portland cement, 29 
broken stone, 249 
cement, affected by age, 115 
cement, affected by fineness, 114 
cement, loose and packed, 219 
cement, test, 114 
concrete, 3 

concrete of different propor¬ 
tions, 362 
concrete, loose, 277 
concrete in slabs and beams, 611 
concrete, table of tests, 376 
earth, 662 
gravel, 662 
hardpan, 662 
lime, 156 
loam, 662 
mortar, 3 
muck, 662 

proportioning concrete by, 265 
sand, 223, 662 
Welded wire fabric, 506 
Weston aqueduct, 682 
Wet concrete, 280 

depositing through trough, 278 
for protection of steel, 328 
Wheelbarrow, illustration, 18 
loads, 9 
time filling, 9 

Williamsburg bridge mixing plant, 

2 73 

Williamsport, Pa., sewer, 683 
Woolson tests, fire resistance, 335 
conductivity of concrete, 335 
Wunsch system of arches, 538 

Yale University dome, 626 
Yield tests of cement and mortar, 129 
Yield point, effect on reinforced 
beams, 413 

required in first-class steel, 39 






CARDS AND ADVERTISEMENTS 




Cement PAGE 

Alsen Portland Cement Works.'. xxxi 

Atlas Portland Cement Co. xxxv 

Chicago Portland Cement Co. xxxiii 

Dexter Portland Cement (Samuel H. French & Co.). xxxii 

Giant Portland Cement (American Cement Co.). xxxviii 

Lehigh Portland Cement Co. xxxiii 

Peerless Portland Cement Co. , xxxii 

Penn-Allen Portland Cement Co... . xxxii 

Pennsylvania Cement Co. xxxiv 

Sandusky Portland Cement Co. xxxvi 

Vulcanite Portland Cement Co. xxxii 

Cement Machinery 

Automatic Weighing Machine Company. xxx 

Lehigh Car, Wheel & Axle Works. xxix 

Chimneys 

Alphons Custodis Chimney Construction Co. xxv 

Construction Companies 

Alphons Custodis Chimney Construction Co. xxv 

Corrugated Bar Co. xxviii 

Eastern Expanded Metal Co. xxiv 

Ferro Concrete Construction Co. xxiii 

Gabriel Concrete Reinforcement Company. xxvii 

General Fireproofing Co. xxv 

Gilbreth, Frank B. xxvi 

Roebling Construction Co. xxv 

Trussed Concrete Steel Co. xxvii 

Engineers 

Andrews, D M. xxii 

Follett, W. V . xxii 

Fuller, Geor W. xxii 

Fuller, William B. xxiii 

Gowen, C. S. xxii 

Hains, Pete*-C. xxii 

Hering, Ru ph. xxii 

Humphn ichard L. xxii 

Kay, F' 7 xxii 

McKi 1 jikP . xxii 

Noyv xxii 


xix 


* 






































CARDS AND ADVERTISEMENTS 




Engineers— Continued page 

Russell, S. Bent. xx jj 

Swain, George .. XX1 1 

Thompson, Sanford E.• xx | 

Weston, Robert Spurr. xx i J 

Hydrated Lime 

Charles Warner Company. xxx 

Rockland-Rockport Lime Co. xxi 

Reinforcing Metal 

Corrugated Bar Co . xxvii 

Eastern Expanded Metal Co. xxiv 

Gabriel Concrete Reinforcement Co. xxvii 

General Fireproofing Co. xxv 

Roebling Construction Co. xxv 

Trussed Concrete Steel Co. xxvii 

Testing Apparatus 

Emil Greiner Co. xxiv 

Tinius Olsen & Co. xxiv 

Waterproofing 

Hydrated Lime (Rockland-Rockport Lime Co.). xxx 

Hydrex Felt & Engineering Co. xxiv 

Limoid (Charles Warner Company). xxxi 

Medusa Waterproof Compound (Sandusky Portland Cement Co.). xxxvi 

“Toxement” (Toch Brothers). xxxi 


xx 



























’i; ••• :.4 


Sanford E. T hompson 

M. AM. SOC. C. E. 

Consulting Engineer 

NEWTON HIGHLANDS, MASS. 

CONCRETE 

Review of designs, Advice in Design and Construction, Exam¬ 
inations, Tests, Investigations, Reports 

ESTIMATES 

Detail costs of all classes of construction. 
Organization of construction work. 


7 

i v 



) 


XXI 

















GEORGE F. SWAIN 

M. Am. Soc. C. E. 

Professor of Civil Engineering, Graduate 
School of Applied Science, Harvard Uni¬ 
versity; Consulting Engineer, Mass. Rail¬ 
road Commission. 

CONSULTING ENGINEER 
HARVARD UNIVERSITY, CAMBRIDGE 


FRANK P. McKIBBEN 

M. Am. Soc. C. E. 

Professor of Civil Engineering 

Lehigh University 

South Bethlehem, Pa. 



EDGAR B. KAY 

Consulting Engineer 

TUSCALOOSA, ALA. 

In charge State Testing Laboratory 
Hydraulic and Concrete Constructions 

Railroads, Water Supply, Sewerage 
Physical Tests of all kinds 


New York City 170 Broadway 

RUDOLPH HERING [Hydraulic 

Engineers 

AND and 

GEORGE W. FULLER, Sanitary 

Experts 

Specialties: Water Supply, Water Purification, 
Sewerage and Sewage Disposal. 



C. S. GOWEN 

M. Am. Soc. C. E. 

Civil and Hydraulic 
Engineer 

Water Works, Water Power and Sewerage 
OSSINING, N. Y. 


W. W. F O L L E T T 

M. Am. Soc. C. E. 

CONSULTING ENGINEER 

Trust Building 

irrigation and El Paso, Texas 

W A TER SUPPLY 



ELLIS B. NOYES 

M. Am. Soc. C. E. 

CONSULTING ENGINEER 

Norfolk, Va. 


S. BENT RUSSELL 
M. Am. Soc. C. E. 

Consulting Civil Engineer 
417 Pine Street, St. Louis 

Estimates, Plans and Specifications and Super¬ 
intendence of Engineering Construction 



Formerly of Corps of Engrs. U. S. Army 

PETER C. HAINS, M. Am. Soc. C. E. 
Consulting Engineer 

Concrete Work, Bridges, Harbor and River 
Works, Foundations, Docks, Wharves. 

UNION TRUST BUILDING , 

Washington, D. C. 


D. M. ANDREWS 

M. Am. Soc. C. E. 

Consulting Civil Engineer 

Specialties : Water Power Development in 
the South; Examinations, Surveys, Estimates; 
Reports for Investors or others; Power Plants 
designed and Construction Superintended. 

Montgomery, Alabama 



ROBERT SPURR WESTON, 
Assoc. M. Am. Soc. C. E. 

4 

14 Beacon St., Boston. 

Water Purification, Sewage 
Disposal, Analyses of all Kinds. 


RICHARD L. HUMPHREY, 

M. Am. Soc. C.E. 

CONSULTING ENGINEER 
Harrison Building, - - Philadelphia. 

Specialist in the manufacture, use and tests of 
Cement and Concrete. Inspection and tests of 
other materials. Reports made on cement and 
cement-making materials. Estimates, plans 
and specifications prepared, and construction 
superintended. 


• • 


XXI1 

























WILLIAM B. FULLER 

M. Am. Soc. C. E. 

Consulting Cl\ni engineer 

150 Nassau St., New York City 


Concrete Expert. Calculations, Design, and Supervision 
of Construction of Structures of Concrete and Reinforced 
Concrete. Mechanical analyses of materials. Sieves 
rated. Economical Proportioning of Concrete. Design 
of Contractor’s Plant for economical mixing and hand¬ 
ling of concrete. 



XXlll 

























The Emil Greiner Co. 


HYDREX 


NEW YORK CITY 



Manufacturers of 

SCIENTIFIC 

APPARATUS 


and Dealers in 

LABORATORY 

SUPPLIES 


Specialties for 

WATER, GAS, 
CEMENT, MILK 
AND SUGAR 
TESTING 


Apparatus according 
tc Jackson for Specific 
Gravity of Cement. 


THE WATERPROOFING FELT 

Experience has shown that the prime 
factor in all waterproofing work is not 
“How cheap”, but “How good” is the 
material and method. 

“Hydrex” Waterproof Felt was se¬ 
lected and specified for waterproofing 
the 50-foot high concrete retaining walls 
enclosing the vast excavation for the 
Pennsylvania R. R. Terminal, New 
York, and the tunnels in connection 
therewith, after excelling in official 
competitive tests every other water- 

proofing material on the market, in 
strength, elasticity and intrinsic qual¬ 
ity. Is not this fact of record of value 
to you in selecting a waterproofing 
material? 

HYDREX FELT & ENGINEERING CO. 

CHEMISTS AND MANUFACTURERS OF 
WATERPROOFING MATERIALS 

120 Liberty Street, New York 

CHICAGO WASHINGTON 



TESTING MACHINES 

— - - FOR -- 

Cement, Concrete, Stone, Road 
Materials, Brick, Macadam, 
Iron, Steel, etc. 

Complete Laboratory Apparatus 

TINIUS OLSEN & COMPANY 

500 North 12th Street, Philadelphia, Pa. 


EXPANDED METAL 

An approved form of steel reinforcement for all kinds of concrete construc¬ 
tion, such as sewers, culverts, bridges, dams, retaining walls, foundations, 
water tanks and reservoirs, penstocks, fireproof floors, walls, etc. 

Manufactured and sold by the 

EASTERN EXPANDED METAL C O. 

201 Devonshire St., Boston, Mass. 

Designs and information furnished upon request. See Fig. i55, p. 5o5. 

I—— 


XXIV 








































The Roebling System of Fireproof Construction 
The Roebling Standard Wire Lath 

The Roebling Expanded Metal Lath 

Catalogues and Quotations furnished upon request 

The Roebling Construction Company 

Fuller Building, New York 

BRANCHES 

Boston, Philadelphia, Buffalo, Chicago, San Francisco 






ALPHONS CUSTODIS CHIMNEY CONS. CO. 

BENNETT BLD’G, NEW YORK 

EXPERT BUILDERS AND DESIGNERS OF 

Brick Lined Reinforced Tapered 
Concrete Chimneys 

PATENTED METAL FORMS Write for Book and Prices 

Chicago— First National Bank Bldg. Boston—141 Milk St. 

Atlanta— Empire Bldg. Detroit—Moffat Bldg. 

Phila.—Penn Mutual Bldg. Montreal—12 University St. 




HERRINGBONE FRAME 

THE ONE FABRICATED REINFORCEMENT COMBINING CONVENIENCE, 

ECONOMY AND EFFICIENCY 



COLD TWISTED LUG BAR 



SQUARE LUG BAR 

LUG BARS—ALL ROLLED FROM VIRGIN BILLET STEEL, 
AFFORD HIGHEST MECHANICAL BOND 

The General Fireproofing* Company 

YOUNGSTOWN, O. 


XXV 























SYSTEM IN 
CONTRACTING 


We offer to put our organization at the disposal of owners con¬ 
templating any building operations. The owner availing himself of 
our services becomes for the time possessed of a highly trained and 
systematized organization, a construction department just as compact 
and smooth running as is any other department of his business. 
The expense of this department is incurred only when its services 
are required. Under this plan the owner and contractor stand in 
the position of employer and trusted department head. Moreover, 
every detail of the work, its cost, its quality, the manner in which 
speed is being made, are constantly under the owner’s supervision. 
He knows at all times how much of and for what his money has 
been spent. He knows how much remains to be spent. Every 
fortunate circumstance which may tend to reduce costs — and there 
are such chances on every job — benefits the owner and not the 
contractor., These are a few of the many benefits of the cost-plus-a- 
fixed-sum contract. 

We accept contracts only on the basis of 

COST-PLUS-A-FIXED-SUM, 

because we believe it to be the only form of contract equitable and 
advantageous to both owner and contractor. 


FRANK B. GILBRETH 

M. AM. SOC. M. E. 

General Contractor 

BOSTON NEW YORK 


XXVI 












flIAry on Column n continuous 
ondwcndj from 0 cHam #/ 
Cttomn to Cp „ * 


Monolithic Construction 

Odaptcc/ to meet at/ requirements 


/Hfernert/va Floor System* 


RBI 

JRRiHR 

SEB 

IBB& 

tzo! 


Lcfht Construction 




av;i 


•:- v - 

tv] 


IBS 

I 

□□ 

□□ 

I 

□□ 

□□ 


□□ 

□n 


□ □ 
□ □ 

1 

□ □ 
□ □ 


Concrete <W Cfc 
Heavy Construction 


A RECORD OF SUCESSFUL USE IN 
OVER 4500 IMPORTANT STRUCTURES 


KAHN TRUSSED BARS, FOR BEAMS, 

ARCHES ’ 

RIB METAL FOR 

SLABS, WALLS, 

SEWERS AND 
CONDUITS. 

BUILT-UP COL¬ 
UMN HOOPING 

CUP BARS, 

BENT AND 
STRAIGHT. 

UNITED STEEL 
SASH FOR FIRE¬ 
PROOF WINDOWS 


GIRDERS, FLOORS, AND 

HY-RIB FOR 

ROOFS, WALLS, 
SIDINGS, PARTI- 
T I O N S, AND 
CEILINGS. 
RIB LATH AND 
RIB STUDS, 
FOR PLASTER 
AND STUCCO. 
TRUS-CON PROD- 
UCTS, FOR 
WATERPROOF¬ 
ING AND FINISH¬ 
ING CONCRETE. 


CATALOGUES , ESTIMATES AND SUGGESTIONS SENT ON REQUEST. 

TRUSSED CONCRETE. STEEL CO. 

DETROIT, MICH 


GABRIEL CONCRETE REINFORCEflENT CO., 

1208 Penobscot Building, DETROIT, MICHIGAN. 


GABRIEL SYSTEM 

o r 

REINFORCED CONCRETE 

TYPICAL DETAILS 


Sectton cr> ln+ Art 


Section <f Column 
wine 3 3 


Heavy Construction 


XXVll 
































































































Corrugated Bars 


are rolled from billet stock, medium or higl 
carbon steel. Every shipment will be accom 
panied by test report when so requested. 


Corrbar Units 


the perfect reinforcement for beams and girders 
More economical than any loose bar method 
Our bulletins on “Designing Methods” ‘Fabri¬ 
cated Reinforcement” will be furnished on request 


CORRUGATED BAR CO 

1408 BANK OF COMMERCE BLDG. 

ST. LOUIS, MO. 


XXVlll 




























The 

Fuller-Lehigh 

Pulverizer 

Mill 


FULLER MILLS ADVERTISE THE FACT 
THAT THE CONSUMER GETS 38 


POUNDS MORE OF THE IMPALPABLE 


POWDER OR REAL CEMENT IN EVERY 
BARREL OF CEMENT PRODUCED BY 
THE FULLER MIL L THAN B Y ANY 
.OTHER ....... 


LEHIGH CAR. WHEEL & AXLE WORKS 

MAIN OFFICE: CATASAUQUA, PA. 

NEW YORK. N. Y. DENVER, COLORADO. 

HAMBURG, GERMANY 


Tests show that the tensile strength of a 1-5 mortar 
made with cement pulverized by the Fuller Mill is higher 
than the tensile strength of a 1-3 mortar made with cement 
pulverized to the fineness required by the Standard Specifi¬ 
cations. 


CEMENT COMPANIES EQUIPPED WITH 


Produces Commercially 

CEMENT HAVING A 
HIGHER PERCENT. 
AGE OF IMPALPABLE 
POWDER THAN CAN 
> BE OBTAINED BY ANY 
OTHER MILL. 


XXIX 



























Absolute Accuracy 

IS RECEIVED AND GIVEN BY OUR 

TANDEM AND TRIPLE-GANG 

MACHINES 

For Proportioning Raw Materials 

NO ELECTRICITY USED, PURELY MECHANICAL, 
POSITIVE CONTROL, MACHINES GUARANTEED 

Automatic Weighing Machine Company, 

134-140 Commerce Street, 

NEWARK, N. J. 

715 Tennessee Trust Bldg., P. O. Box 42, 

Memphis, Tenn. San Francisco, Cal. 

See page 713 for illustration of weighing machine. 


Effective proportions of 

HYDRATED LIME FOR 
WATERPROOFING CONCRETE 


For 

U 


are as follows: 

Cement Sand Stone 

12 4 add 8% Pine Cone Hydrated Lime 

1 2.V U “ 12% “ 

“ 13 5 16% “ 

These percentages are based on the weight of the dry hydrated lime to 

the dry Portland Cement. 

\ 

CEMENT-LIME MORTAR FOR 
MASONRY CONSTRUCTION 

3 bags ( 300 lbs.) Pine Cone Hydrated Lime 

2 bags ( 190 lbs.) Portland Cement 
5 bbls (1800 lbs.) Sand 

Note what is said on the above subjects in this book, pages 154d and 342 

ROCK LAND-ROCK PORT LIME CO. 


Rockland, Me. 


New York 
Fuller Building 


Boston 

24 Milk Street 


xxx 











“T OXE.ME.NT” 

(PATENTED) 

A patented material which is to be added to cement 
or concrete for the purpose of waterproofing against 
pressure. 

TWO PER CENT of “Toxement” added to any 
concrete waterproofs it in thirty days, up to fifty pounds 
pressure per square inch, irrespective of the thickness 
of the concrete. 

u Toxement” can be readily mixed with water. It 
does not float on water, nor does it repel water. It pro¬ 
duces a distinct chemical reaction between the cement 
and itself which physically fills up all the voids. 

Write for our descriptive pamphlets on “Toxement,” 
and our various dampproofing specialties. 

TOCH BROTHERS 

Established 1848 

320 Fifth Avenue, New York. 

MAKERS OF TECHNICAL PAINTS, ENAMELS, VARNISHES 
AND DAMPPROOFING COMPOUNDS 

Works: Long Island City, N. Y. 


WATER-TIGHT CONCRETE 

Competent Engineers agree that the only method of rendering 
concrete WATER-TIGHT is by filling the PORES of the WHOLE 
MASS. This can best be accomplished by using 

LIMOID (Hydrated Lime) 

CEMENT MORTARS are made MORE PLASTIC, trowel more 
easily, and CARRY MORE SAND when LIMOID is used. 

See pages 154d and 342. 


CHARLES WARNER COMPANY 

WILMINGTON, DEL. PHILADELPHIA NEW YORK BOSTON 



XXXI 



































































































































































































































































THE BRAND WITH 
A REPUTATION 


SLOW SETTING 



15 YEARS UNDER 
ONE MANAGEMENT 
19 JO 

QUICK HARDENING 


Capacity (actual) 2 million barrels per annum 

VULCANITE PORTLAND CEMENT CO. 

Main Sales Office Main Office 

Fifth Avenue Building, New York Land Title Building, Philadelphia 


A. W. Wright, Pres’t J. R. Patterson, Gen’l Mgr. 

S. O. Bush, V.-Pres’t Wm. M. Hatch, Sec’y & Treas. 

A. Lundteigen, Ass’t Mgr. & Chemist 


peerless ^ottlanh Cement Co. 

Manufacturers of 

HIGHEST GRADE PORTLAND 

CEMENT ONLY 


Union City 


Michigan 



One Brand—One Quality—The Best 

“PENN-ALLEN” 


Used in numerous reinforced 
concrete buildings, dams, etc. 

PENN-ALLEN PORTLAND 
CEMENT CO. 

Commonwealth Bldg. Allentown, Pa. 


Remember the Sign of the “Right Cement” 


“THE RIGHT HAND OF STRENGTH” 

SOLE AGENTS 

SAMUEL H, FRENCH & CO, 

Established 1844 PHILADELPHIA 




DEXTER 



PORTLAND CEMENT 


XXXll 


































—“CHICAGO AA”= 
PORTLAND CEMENT 



HIGHEST QUALITY 
THE BEST THAT CAN BE MADE 


Chicago Portland Cement Company 


108 LaSalle Street .Chicago, Illinois 

(■Booklets on request) 


“LEH I G H” 

IS THE LEADING BRAND OF 


PORTLAND CEMENT 


Guaranteed to meet the highest specifications. 

Write for catalogue which contains useful information. 


Lehigh Portland Cement Co. 

ALLENTOWN, PA. 

Capacity, 8,000,000 Barrels Yearly 


xxxm 

















PENNSYLVANIA PORTLAND 

HAS NO EQUAL 

HIGHEST QUALITY 


PENNSYLVANIA CEMENT CO. 

26 CORTLANDT ST. f NEW YORK 

(MAIN OFFICE) 

66 DEVONSHIRE ST. BUILDERS EXCHANGE BLDG. 

BOSTON, MASS. BALTIMORE, MD. 


GIANT 

PORTLAND CEMENT 


CROTON SYSTEM 
DAMS AND RESERVOIRS 
1,750,000 bbls. 

PENNSYLVANIA R. R. 
TUNNELS 

900,000 bbls. 



NEW YORK CITY 
SUBWAYS 
1,500,000 bbls. 

HUDSON CO. 

TUNNELS 

500,000 bbls. 


We cannot offer a better guarantee than the endorsement of the 
celebrated engineers who conducted these world-famous enterprises. 

(SEND FOR OUR BOOKLETS) 


AMERICAN CEMENT CO., Philadelphia 

LESLEY & TRINKLE CO. UNITED BUILDING MATERIAL CO, 

Penna. Bld’g, (Sales Agents) 30 Church St., New York 
Phila - 101 Milk St., Boston 


XXXIV 





















>0 -rf 

V A? VrttfV* 
x?v * ^XmIKto • v". 


*w* v .' 


V? - 

* '{a • 

4 ,<y xb ' «, 

o **, 
*p 

* r ^r 0 V °xj> 



C * 

» 
o 

^ #'VvmN^ *° v^ ^ 0 0 # 

V '*3V % *7?WJ> \ 

. ^ < V /,A^Vc ^ vV* ^ 



* #*% \ 

A^ .»♦ 

,v o » • . 


# 

£S -?<ur~ % * o ^ '>W-' a.K 

o. ><y ,jv., *> V v 

° 


* ^rv 

♦ A? ^ ' 

«« ,<T * ** „ 

<0 c> *7 

C°" yJsStLlv 

» 

<*, 





"oV 4 


*£ 0y v 1 

* w ' ^ 1 _R^X Vv * 

,*\A : -S 5 # /\ v 

j? ..... V’**** / .... v** 1 «-' 

4* ^ c° .v<W:' °o , 4 ? -* 

** * %t> a t 



. -;> V ^ 

° V*y : 

.VV* • 

^ <£■ °. 


• vsswl/ar - *-° ■’* 

+ 1* <> ' 

!*. »«, i • ^p 

^ v .;^l'. *> 



* *P t <f 

« ^CT 





•*• »VIVAS' ** V* 

& * • * <L^ O * <t T#^ r -' f 0 

^ * «° ^ *'•#•»* A 0 ' 

V »IV 9 * C\ *0 V »»v % *> 



<V '• 

^ * <J> 

; -^b V :£ms&b- V 


: v^ • 


c5 ^ : 

* A* * 




• Vr-^ •’ 

® o 


i ■« A^ 






w 



y v' o 

. ^ ••• v^.--.-% *" , *>°J 

’V .VV ♦ 

v*V % 


- v' f ..... V'V .••■ 'X 

*'^v. \ . 

l ”* 

1 ° . ^ '•• 

«■ ” ♦ o ^ 

% VVVvWn^ # 4 1 * JKTttl/SjP* *7 

'"oV :gm£*\ v„ 

,' >° ^ „ »" V ^ s 1 ■»* 

V y\‘&efc*. ^ ^ V s -• 



♦ ^ * 

V > <“. 'Ot'l* ,(fr » * <\ 

V" s'jltol* *■*■ «^L*» y ..<.. 

«» SK v,l//yy> * ^ a v ^vx\\v.~5x . v .m a MtsrrjrL. i 






W 


* -<L V riA - 




/> 

• °bV • 

O 

* V * 



% ,v .^i 
: W * 

*• : 

* .<? ^ * 


O "V 


* 




* V 


*1 *' .o 1 


‘"*. ^ c° sJfsLi'*°o ^ c o v .•!•.. -o 

^ .v^HV. . 0 / ^ o' 




*. '.w.* ,«r ♦+ v 

' *° . % '• 

K 

G * 


* * 0 4^ c in **** * x <F* * 

V G> <9 *> 

4, * A 9s,r$ ., • X> % 

♦° 4?\ 1* ^ 


w 



s^> V - 

' ^ V*OEy,* V V •FJPUr* <,V V, „ 

*'.*. »* A <s sy * 

«. °JL* * % 




^ «. » 

>£■ A v ♦ - 

VV 




V ^ > *. 

.<V <v '< 

j* sLjrfrZ - 

^ xp. 



,..' •*• ■■■ -'■■ '-* -*■ -"■ “-'••* *' <■> •<> 
*' AJ J- ♦ _ 

*. ^ 0 < o, 

A^ ^ \ 

*" ♦ ^.r Q_ * ^ 

*>. * • * « ° ,<2> * f * * • . . *> ♦ 0 „ 0 0 *,' 

' ' °‘ O^ aV »LVw * ^\ , » 

C? * T^miJk * V* A v * 

O 

*c 

* o 

; -35 *? * 

• .%* °* **.’*’ <o J 



* <t? 

♦ *S » * ,4. 

<. * ,0 V 

4 ' * * <£» (V . 9 " * „ ^ Q 

r/jT^z. * ^ a v ^ <^^v* 

* ^ o' ® 

4 O - 


^ V .A..'^'” of 
S*,jt7*L ' ^ C° • 

n,V* • 


>U\NSSS^ * V v ’ * ♦ rv ■-<-, ♦> 

"•»•* ^ °^. *•••>* A° .. %^‘ 

V % »’*«» ^ a0 »1.!^^ * > 



'^cr 



» m « 



y ^ 



o'. 

. v* v .* 

* ,j Co>. * 

^ .A V .11.. <J> 0 V .<,.•- 

■» G 


b. •- 

- *• 

♦ <y <& ° 



^ .. 


^ / 




*o K 


» # i * At ' $> * 

a0■ o’^'o 



^ 0 X 


** 0° \> % ‘*7r^* *P 



9 ^ 


^ ^ V* 



AW' V'O.V.O V' 

V' ♦*V°<» 'C. a 0 »L*rL'+ \f f, 1 



■*■ 4 

, /‘. 

- v*cr 

* ^ v*^-\/ V'- T v 


r cv jvuv" % * n o 
•■•' ... V **” _^ 

V ♦jA^^/k e> * *^4* A 

c,.r. . V^. W//R&K&S% vT. 



* 4/ ^ _ 

»;* ,.v ^ v 





. 1 » 
\\ i 

! ' \ ‘ , ' ' 1 , 


j l } 

S ■ 5 V; t •; 

: 1 ’ i 






















